Physics 123 Units 1-24 HW Questions
Unit 12: A bumper car with mass m1 = 119 kg is moving to the right with a velocity of v1 = 4.5 m/s. A second bumper car with mass m2 = 84 kg is moving to the left with a velocity of v2 = -3.7 m/s. The two cars have an elastic collision. Assume the surface is frictionless. 1) What is the velocity of the center of mass of the system? 2) What is the initial velocity of car 1 in the center-of-mass reference frame? 3) What is the final velocity of car 1 in the center-of-mass reference frame? 4) What is the final velocity of car 1 in the center-of-mass reference frame? 5) What is the final velocity of car 2 in the ground (original) reference frame? 6) In a new (inelastic) collision, the same two bumper cars with the same initial velocities now latch together as they collide. What is the final speed of the two bumper cars after the collision? 7) Compare the loss in energy in the two collisions: |ΔKEelastic| = |ΔKEinelastic| |ΔKEelastic| > |ΔKEinelastic| |ΔKEelastic| < |ΔKEinelastic|
1) 1.107 m/s 2) 3.393 m/s 3) -3.393 m/s 4) -2.286 m/s 5) 5.9135 m/s 6) 1.107 m/s 7) |ΔKEelastic| < |ΔKEinelastic|
Unit 14: Rotational Kinematics And Moment Of Inertia. A disk with mass m = 11.9 kg and radius R = 0.32 m begins at rest and accelerates uniformly for t = 17.5 s, to a final angular speed of w = 32 rad/s. 1) What is the angular acceleration of the disk? 2) What is the angular displacement over the 17.5 s? 3) What is the moment of inertia of the disk? 4) What is the change in rotational energy of the disk? 5) What is the tangential component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? 6) What is the magnitude of the radial component of the acceleration of a point on the rim of the disk when the disk has accelerated to half its final angular speed? 7) What is the final speed of a point on the disk half-way between the center of the disk and the rim? 8) What is the total distance a point on the rim of the disk travels during the 17.5 seconds?
1) 1.829 rad/s^2 2) 280 rad 3) 0.60928 kg * m^2 4) 311.951 J 5) 0.58528 m/s^2 6) 81.92 m/s^2 7) 5.12 m/s 8) 89.6 m
Unit 17: A gymnast with mass m1 = 49 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 120 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam. 1) What is the force the left support exerts on the beam? 2) What is the force the right support exerts on the beam? 3) How much extra mass could the gymnast hold before the beam begins to tip? 4) Now the gymnast (not holding any additional mass) walks directly above the right support. What is the force the left support exerts on the beam? 5) What is the force the right support exerts on the beam? 6) At what location does the gymnast need to stand to maximize the force on the right support? at the center of the beam at the right support at the right edge of the beam
1) 1549.98 N 2) 107.91 N 3) 11 kg 4) 1069.29 N 5) 588.6 N 6) at the right edge of the beam.
Unit 2: Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 24 m/s at an angle 35 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground. 1) What is the horizontal component of the ball's velocity right before Sarah catches it? 2) What is the vertical component of the ball's velocity right before Sarah catches it? 3) What is the time the ball is in the air? 4) What is the distance between the two girls? 5) After catching the ball, Sarah throws it back to Julie. However, Sarah throws it too hard so it is over Julie's head when it reaches Julie's horizontal position. Assume the ball leaves Sarah's hand a distance 1.5 meters above the ground, reaches a maximum height of 13 m above the ground, and takes 2.399 s to get directly over Julie's head. What is the speed of the ball when it leaves Sarah's hand? 6) How high above the ground will the ball be when it gets to Julie?
1) 19.66 m/s 2) 13.77 m/s 3) 11.17 m 4) 55.44 m 5) 27.5 m/s 6)
Unit 2: A soccer ball is kicked with an initial horizontal velocity of 19 m/s and an initial vertical velocity of 15 m/s. 1) What is the initial speed of the ball? 2) What is the initial angle θθ of the ball with respect to the ground? 3) What is the maximum height the ball goes above the ground? 4) How far from where it was kicked will the ball land? 5) What is the speed of the ball 1.6 seconds after it was kicked? 6) How high above the ground is the ball 1.6 seconds after it is kicked?
1) 24.21 m/s 2) 38.29 degrees 3) 11.47 m 4) 58.12 m 5) 19.012 m/s 6) 11.44 m
Unit 16: A green hoop with mass mh = 2.8 kg and radius Rh = 0.13 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.1 kg and radius Rd = 0.1 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass ms = 3.2 kg and radius Rs = 0.19 m. The system is released from rest. 1) What is magnitude of the linear acceleration of the hoop? 2) What is magnitude of the linear acceleration of the sphere? 3) What is the magnitude of the angular acceleration of the disk pulley? 4) What is the magnitude of the angular acceleration of the sphere? 5) What is the tension in the string between the sphere and disk pulley? 6) What is the tension in the string between the hoop and disk pulley? 7) The green hoop falls a distance d = 1.62 m. (After being released from rest.) How much time does the hoop take to fall 1.62 m? 8) What is the magnitude of the velocity of the green hoop after it has dropped 1.62 m? 9) What is the magnitude of the final angular speed of the orange sphere (after the green hoop has fallen the 1.62 m)?
1) 3.297 m/s^2 2) 3.297 m/s^2 3) 32.975 rad/s^2 4) 17.353 rad/s^2 5) 14.771 N 6) 18.2364 N 7) 0.991 s 8) 3.268 m/s 9) 17.202 rad/s
Unit 3: Train Ride. You are on a train traveling east at speed of 29 m/s with respect to the ground. 1) If you walk east toward the front of the train, with a speed of 1.7 m/s with respect to the train, what is your velocity with respect to the ground? 2) If you walk west toward the back of the train, with a speed of 2.5 m/s with respect to the train, what is your velocity with respect to the ground? 3) Your friend is sitting on another train traveling west at 25 m/s. As you walk toward the back of your train at 2.5 m/s, what is your velocity with respect to your friend?
1) 30.7 m/s 2) 26.4 m/s east 3) 51.5 m/s east
Unit 1: Two Thrown Balls: A blue ball is thrown upward with an initial speed of 19.8 m/s, from a height of 0.6 meters above the ground. 2.4 seconds after the blue ball is thrown, a red ball is thrown down with an initial speed of 8.9 m/s from a height of 22.3 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s2. 1) What is the speed of the blue ball when it reaches its maximum height? 2) How long does it take the blue ball to reach its maximum height? 3) What is the maximum height the blue ball reaches? 4) What is the height of the red ball 3.12 seconds after the blue ball is thrown? 5) How long after the blue ball is thrown are the two balls in the air at the same height? 7) Which statement is true about the blue ball after it has reached its maximum height and is falling back down? A. The acceleration is positive and it is speeding up B. The acceleration is negative and it is speeding up C. The acceleration is positive and it is slowing down D. The acceleration is negative and it is slowing down
1. 0 m/s 2. 2.018 s 3. 20.582 m 4. 13.349 m 5. 2.9 s 7. The acceleration is negative and it is speeding up.
Unit 22: A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T =
1.53 seconds
Exam #1: If there was no friction, what would be the magnitude of the acceleration of the block down the ramp in the original configuration?
2.207 m/s^2
Exam #1: You are on a train traveling west at a speed of 38 m/s with respect to the ground. Your friend is sitting on another train on tracks right next to yours traveling east at 63 m/s. As you walk toward the back of your train at 3.0 m/s, what is your velocity with respect to your friend?
98 m/s
Exam #1: A tennis ball connected to a string is spun around in a vertical, circular path at a uniform speed. The ball has a mass m = 0.165 kg and moves at v = 4.89 m/s. The circular path has a radius of R = 0.78 m. A) What is the magnitude of the tension in the string when the ball is at the bottom of the circle? B) What is the magnitude of the tension in the string when the ball is at the top of the circle?
A) 6.677 N B) 3.44 N
Exam #1: A police car notices you speeding past him at 90 mph (40.23 m/s). They immediately respond and accelerate for 9 seconds at a rate of 7 m/s^2 in the same direction. A) What is the final speed of the police car? B) If the police car maintains a constant speed after 9 seconds into the chase, how long does it take them to catch up to your car?
a) 63 m/s b) 12.45 s
Unit 13: An object with total mass mtotal = 17.9 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.6 kg moves up and to the left at an angle of θ1 = 20° above the -x axis with a speed of v1 = 28.1 m/s. A second piece with mass m2 = 5.3 kg moves down and to the right an angle of θ2 = 25° to the right of the -y axis at a speed of v2 = 20.2 m/s. 1) What is the magnitude of the final momentum of the system (all three pieces)? 2) What is the mass of the third piece? 3) What is the x-component of the velocity of the third piece? 4) What is the y-component of the velocity of the third piece? 5) What is the magnitude of the velocity of the center of mass of the pieces after the collision? 6) Calculate the increase in kinetic energy of the pieces during the explosion.
1) 0 kg * m/s 2) 8 kg 3) 9.527 m/s 4) 6.542 m/s 5) 0 m/s 6) 3423.116 J
A transverse harmonic wave travels on a rope according to the following expression: y(x,t) = 0.17sin(2x + 17.5t) The mass density of the rope is μ = 0.112 kg/m. x and y are measured in meters and t in seconds. 1) What is the amplitude of the wave? 2) What is the frequency of oscillation of the wave? 3) What is the wavelength of the wave? 4) What is the speed of the wave? 5) What is the tension in the rope? 6) At x = 3.7 m and t = 0.43 s, what is the velocity of the rope? (watch your sign) 7) At x = 3.7 m and t = 0.43 s, what is the acceleration of the rope? (watch your sign) 8) What is the average speed of the rope during one complete oscillation of the rope? 9) In what direction is the wave traveling? +x direction -x direction +y direction -y direction +z direction -z direction 10) On the same rope, how would increasing the wavelength of the wave change the period of oscillation? the period would increase the period would decrease the period would not change
1) 0.17 m 2) 2.785 Hz 3) 3.142 m 4) 8.75 m/s 5) 8.575 N 6) -2.11 m/s 7) -36.724 m/s^2 8) 1.894 m/s 9) -x direction 10) the period would increase
Unit 14: A ceiling fan consists of a small cylindrical disk with 5 thin rods coming from the center. The disk has mass md = 3.4 kg and radius R = 0.23 m. The rods each have mass mr = 1.3 kg and length L = 0.85 m. 1) What is the moment of inertia of each rod about the axis of rotation? 2) What is the moment of inertia of the disk about the axis of rotation? 3) What is the moment of inertia of the whole ceiling fan? 4) When the fan is turned on, it takes t = 3 s and a total of 13 revolutions to accelerate up to its full speed. What is the magnitude of the angular acceleration? 5) What is the final angular speed of the fan? 6) What is the final rotational energy of the fan? 7) Now the fan is turned to a lower setting where it ends with half of its rotational energy as before. The time it takes to slow to this new speed is also t = 3 s. What is the final angular speed of the fan?
1) 0.313 kg * m^2 2) 0.08993 kg * m^2 3) 1.655 kg * m^2 4) 18.151 rad/s^2 5) 54.454 rad/s 6) 2453.61 J 7) 38.505 rad/s 8) 5.316 rad/s^2
Unit 8: A mass hangs on the end of a massless rope. The pendulum is held horizontal and released from rest. When the mass reaches the bottom of its path it is moving at a speed v = 2.9 m/s and the tension in the rope is T = 15.5 N. 1) How long is the rope? 2) What is the mass? 3) If the maximum mass that can be used before the rope breaks is mmax = 1.19 kg, what is the maximum tension the rope can withstand? (Assuming that the mass is still released from the horizontal.) 4) Now a peg is placed 4/5 of the way down the pendulum's path so that when the mass falls to its vertical position it hits and wraps around the peg. How fast is the mass moving when it is at the same vertical height as the peg (directly to the right of the peg)? 5) Return to the original mass. What is the tension in the string at the same vertical height as the peg (directly to the right of the peg)?
1) 0.429 m 2) 0.527 kg 3) 35.0217 N 4) 2.594 m/s 5) 41.364 N
Unit 10: Man On Boat. A man with mass m1 = 69 kg stands at the left end of a uniform boat with mass m2 = 165 kg and a length L = 3 m. Let the origin of our coordinate system be the man's original location as shown in the drawing. Assume there is no friction or drag between the boat and water. 1) What is the location of the center of mass of the system? 2) If the man now walks to the right edge of the boat, what is the location of the center of mass of the system? 3) After walking to the right edge of the boat, how far has the man moved from his original location? (What is his new location?) 4) After the man walks to the right edge of the boat, what is the new location the center of the boat? 5) Now the man walks to the very center of the boat. At what location does the man end up?
1) 1.058 m 2) 1.058 m 3) 2.115 m 4) 0.615 m 5) 1.058 m
Unit 18: A meterstick (L = 1 m) has a mass of m = 0.258 kg. Initially it hangs from two short strings: one at the 25 cm mark and one at the 75 cm mark. 1) What is the tension in the left string? 2) Now the right string is cut! What is the initial angular acceleration of the meterstick about its pivot point? (You may assume the rod pivots about the left string, and the string remains vertical) 3) What is the tension in the left string right after the right string is cut? 4) After the right string is cut, the meterstick swings down to where it is vertical for an instant before it swings back up in the other direction. What is the angular speed when the meterstick is vertical? 5) What is the acceleration of the center of mass of the meterstick when it is vertical? 6) What is the tension in the string when the meterstick is vertical? 7) Where is the angular acceleration of the meterstick a maximum? right after the string is cut and the meterstick is still horizontal when the meterstick is vertical - at the bottom of its path the angular acceleration is constant
1) 1.265 N 2) 16.817 rad/s^2 3) 1.446 N 4) 5.8 rad/s 5) 8.41 m/s^2 6) 3.073 N 7) right after the string is cut and the meterstick is horizontal.
Unit 10: Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below: mxyvxvy 1 7.7 kg-2.7 m-4.4 m2.9 m/s-4 m/s 2 8.2 kg-3.5 m3.5 m-5 m/s5.1 m/s 3 8.8 kg4.6 m-5.6 m-6.1 m/s2.2 m/s 4 9.3 kg5.7 m2.7 m4.2 m/s-2.9 m/s 1) What is the x position of the center of mass? 2) What is the y position of the center of mass? 3) What is the speed of the center of mass? 4) When a fifth mass is placed at the origin, what happens to the horizontal (x) location of the center of mass? It moves to the right. It moves to the left. It does not move. It can not be determined unless you know the mass. 5) When a fifth mass is placed at the center of mass, what happens to the vertical (y) location of the center of mass? It moves up. It moves down. It does not move. It can not be determined unless you know the mass.
1) 1.294 m 2) -0.863 m 3) 0.984 m/s 4) It moves to the left. 5) It does not move.
Unit 10: Playing Catch. A person with mass m1 = 51 kg stands at the left end of a uniform beam with mass m2 = 96 kg and a length L = 2.5 m. Another person with mass m3 = 61 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 14 kg (assume that the medicine ball is at the far right end of the beam as well). Let the origin of our coordinate system be the left end of the original position of the beam as shown in the drawing. Assume there is no friction between the beam and floor. 1) What is the location of the center of mass of the system? 2) The medicine ball is throw to the left end of the beam (and caught). What is the location of the center of mass now? 3) What is the new x-position of the person at the left end of the beam? (How far did the beam move when the ball was throw from person to person?) 4) To return the medicine ball to the other person, both people walk to the center of the beam. At what x-position do they end up?
1) 1.385 m 2) 1.385 m 3) 0.1585 m 4) 1.385 m
Unit 6: Accelerating Truck: A box rests on top of a flat bed truck. The box has a mass of m = 18 kg. The coefficient of static friction between the box and truck is μs = 0.84 and the coefficient of kinetic friction between the box and truck is μk = 0.65. 1) The truck accelerates from rest to vf = 19 m/s in t = 13 s (which is slow enough that the box will not slide). What is the acceleration of the box? 2) In the previous situation, what is the frictional force the truck exerts on the box? 3) What is the maximum acceleration the truck can have before the box begins to slide? 4) Now the acceleration of the truck remains at that value, and the box begins to slide. What is the acceleration of the box? 5) With the box still on the truck, the truck attains its maximum velocity. As the truck comes to a stop at the next stop light, what is the magnitude of the maximum deceleration the truck can have without the box sliding?
1) 1.462 m/s^2 2) 26.316 N 3) 8.2404 m/s^2 4) 6.3765 m/s^2 5) 8.2404 m/s^2
Unit 7: A mass m = 16 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4096 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.45. The mass leaves the spring at a speed v = 3.6 m/s. 1) How much work is done by the spring as it accelerates the mass? 2) How far was the spring stretched from its unstreched length? 3) The mass is measured to leave the rough spot with a final speed vf = 2.1 m/s. How much work is done by friction as the mass crosses the rough spot? 4) What is the length of the rough spot? 5) In a new scenario, the block only makes it (exactly) half-way through the rough spot. How far was the spring compressed from its unstretched length? 6) In this new scenario, what would the coefficient of friction of the rough patch need to be changed to in order for the block to just barely make it through the rough patch? 7) Return to a scenario where the blcok makes it throgh the entire rough patch. If the rough patch is lengthened to a distance of three times longer, as the block slides through the entire distance of the rough patch, the magnitude of the work done by the force of friction is: the same three times greater three times less nine times greater nine times less
1) 103.68 J 2) 0.225 m 3) -68.4 J 4) 0.968 m 5) 0.129 m 6) 0.224 7) three times greater
Unit 5: Loop-the-Loop: In a loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has a mass m = 299 kg and moves with speed v = 15.03 m/s. The loop-the-loop has a radius of R = 9 m. 1) What is the magnitude of the normal force on the care when it is at the bottom of the circle? (But as the car is accelerating upward.) 2) What is the magnitude of the normal force on the car when it is at the side of the circle (moving vertically upward)? 3) What is the magnitude of the normal force on the car when it is at the top of the circle? 4) Compare the magnitude of the cars acceleration at each of the above locations: abottom = aside = atop abottom < aside < atop abottom > aside > atop 5) What is the minimum speed of the car so that it stays in contact with the track at the top of the loop?
1) 10438.1199 N 2) 7504.9299 N 3) 4571.7399 N 4) abottom = aside = atop 5) 9.396 m/s
Unit 11: A blue car with mass mc = 499 kg is moving east with a speed of vc = 21 m/s and collides with a purple truck with mass mt = 1225 kg that is moving south with a speed of vt = 13 m/s . The two collide and lock together after the collision. 1) What is the magnitude of the initial momentum of the car? 2) What is the magnitude of the initial momentum of the truck? 3) What is the angle that the car-truck combination travel after the collision? (give your answer as an angle South of East) 4) What is the magnitude of the momentum of the car-truck combination immediately after the collision? 5) What is the speed of the car-truck combination immediately after the collision? 6) Compare the initial and final kinetic energy of the total system before and after the collision: KEi = KEf KEi > KEf KEi < KEf
1) 10479 kg * m/s 2) 15925 kg * m/s 3) 56.654 degrees 4) 19063.448 kg * m/s 5) 11.058 m/s 6) KEi > KEf
Unit 1: Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 5.9 m/s2 for 3.5 seconds. It then continues at a constant speed for 10.7 seconds, before applying the brakes such that the car's speed decreases uniformly coming to rest 303.71 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop. 1) How fast is the blue car going 2.1 seconds after it starts? 2) How fast is the blue car going 7.7 seconds after it starts? 3) How far does the blue car travel before its brakes are applied to slow down? 4) What is the acceleration of the blue car once the brakes are applied? 5) What is the total time the blue car is moving? 6) What is the acceleration of the yellow car?
1) 12.39 m/s 2) 20.65 m/s 3) 257.0925 4) -4.574 m/s^2 5) 18.715 s 6) 1.734 m/s^2
Unit 8: Loop the Loop: A mass m = 89 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 16.2 m and finally a flat straight section at the same height as the center of the loop (16.2 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) 1) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2) What height above the ground must the mass begin to make it around the loop-the-loop? 3) If the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4) If the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (16.2 m off the ground)? 5) Now a spring with spring constant k = 17100 N/m is used on the final flat surface to stop the mass. How far does the spring compress? 6) It turns out the engineers designing the loop-the-loop didn't really know physics - when they made the ride, the first drop was only as high as the top of the loop-the-loop. To account for the mistake, they decided to give the mass an initial velocity right at the beginning. How fast do they need to push the mass at the beginning (now at a height equal to the top of the loop-the-loop) to get the mass around the loop-the-loop without falling off the track? 7) The work done by the normal force on the mass (during the initial fall) is: zero
1) 12.606 m/s 2) 40.5 m 3) 28.189 m/s 4) 21.835 m/s 5) 1.575 m 6) 12.606 m/s 7) zero
A wave pulse travels down a slinky. The mass of the slinky is m = 0.94 kg and is initially stretched to a length L = 6.1 m. The wave pulse has an amplitude of A = 0.25 m and takes t = 0.424 s to travel down the stretched length of the slinky. The frequency of the wave pulse is f = 0.47 Hz. 1) What is the speed of the wave pulse? 2) What is the tension in the slinky? 3) What is the average speed of a piece of the slinky as a complete wave pulse passes? 4) What is the wavelength of the wave pulse? 5) Now the slinky is stretched to twice its length (but the total mass does not change). What is the new tension in the slinky? (assume the slinky acts as a spring that obeys Hooke's Law) 6) What is the new mass density of the slinky? 7) What is the new time it takes for a wave pulse to travel down the slinky? 8) If the new wave pulse has the same frequency, what is the new wavelength? 9) What does the energy of the wave pulse depend on? the frequency the amplitude both the frequency and the amplitude
1) 14.387 m/s 2) 31.895 N 3) 0.47 m/s 4) 30.61 m 5) 63.79 N 6) 0.077 kg/m 7) 0.424 s 8) 61.221 m 9) both the frequency and the amplitude
Unit 6: Carnival Ride. In a classic carnival ride, patrons stand against the wall in a cylindrically shaped room. Once the room gets spinning fast enough, the floor drops from the bottom of the room! Friction between the walls of the room and the people on the ride make them the "stick" to the wall so they do not slide down. In one ride, the radius of the cylindrical room is R = 6.5 m and the room spins with a frequency of 21.9 revolutions per minute. 1) What is the speed of a person "stuck" to the wall? 2) What is the normal force of the wall on a rider of m = 54 kg? 3) What is the minimum coefficient of friction needed between the wall and the person? 4) If a new person with mass 108 kg rides the ride, what minimum coefficient of friction between the wall and the person would be needed? 5) Which of the following changes would decrease the coefficient of friction needed for this ride? 6) To be safe, the engineers making the ride want to be sure the normal force does not exceed 2.2 times each persons weight - and therefore adjust the frequency of revolution accordingly. What is the minimum coefficient of friction now needed?
1) 14.907 m/s 2) 1846.124 N 3) 0.287 4) 0.287 5) increasing the radius of the ride, increasing the speed of the ride 6) 0.455
Unit 5: Hanging Masses 2: A single mass (m1 = 4.4 kg) hangs from a spring in a motionless elevator. The spring constant is k = 275 N/m. 1) What is the distance the spring is stretched from its unstretched length? 2) Now, three masses (m1 = 4.4 kg, m2 = 13.2 kg and m3 = 8.8) hang from three identical springs in a motionless elevator. The springs all have the same spring constant given above. What is the magnitude of the force the bottom spring exerts on the lower mass? 3) What is the distance the middle spring is stretched from its equilibrium length? 4) Now the elevator is moving downward with a velocity of v = -3 m/s but accelerating upward at an acceleration of a = 5.1 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.) What is the magnitude of the force the upper spring exerts on the upper mass? 5) What is the distance the lower spring is extended from its unstretched length? 6) Finally, the elevator is moving downward with a velocity of v = -2.1 m/s but accelerating downward at an acceleration of a = -2.1 m/s2. Compare the magnitude of the NET force on each mass: F1 = F2 = F3 F1 > F2 > F3 F2 > F3 > F1 7) What is the magnitude of the net force on the middle mass?
1) 15.696 cm 2) 86.328 N 3) 78.48 cm 4) 393.624 N 5) 47.712 cm 6) F2 > F3 > F1 7) 27.72 N
Unit 5: Two Masses Over Pulley: A mass m1 = 6.9 kg rests on a frictionless table. It is connected by a massless and frictionless pulley to a second mass m2 = 2.5 kg that hangs freely. 1) What is the magnitude of the acceleration of block 1? 2) What is the tension in the string? 3) Now the table is tilted at an angle of θ = 79° with respect to the vertical. Find the magnitude of the new acceleration of block 1. 4) At what "critical" angle will the blocks NOT accelerate at all? 5) Now the angle is decreased past the "critical" angle so the system accelerates in the opposite direction. If θ = 38° find the magnitude of the acceleration. 6) Compare the tension in the string in each of the above cases on the incline: Tθ at 79° = Tθcritical = Tθ at 38° Tθ at 79° > Tθcritical > Tθ at 38° Tθ at 79° < Tθcritical < Tθ at 38°
1) 2.609 m/s^2 2) 18.0021 N 3) 1.235 m/s^2 4) 68.757 degrees 5) 3.065 m/s^2 6) Tθ at 79° < Tθcritical < Tθ at 38°
Unit 15: An object is formed by attaching a uniform, thin rod with a mass of mr = 7.49 kg and length L = 5.04 m to a uniform sphere with mass ms = 37.45 kg and radius R = 1.26 m. Note ms = 5mr and L = 4R. 1) What is the moment of inertia of the object about an axis at the left end of the rod? 2) If the object is fixed at the left end of the rod, what is the angular acceleration if a force F = 452 N is exerted perpendicular to the rod at the center of the rod? 3) What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.) 4) If the object is fixed at the center of mass, what is the angular acceleration if a force F = 452 N is exerted parallel to the rod at the end of rod? 5) What is the moment of inertia of the object about an axis at the right edge of the sphere? 6) Compare the three moments of inertia calculated above: ICM < Ileft < Iright ICM < Iright < Ileft Iright < ICM < Ileft ICM < Ileft = Iright Iright = ICM < Ileft
1) 1573.592 kg * m^2 2) 0.724 rad/s^2 3) 128.821 kg * m^2 4) 0 rad/s^2 5) 289.351 kg * m^2 6) ICM < Ieft < Iright
Unit 3: You are on a cruise ship traveling north at a speed of 15 m/s with respect to land. 1) If you walk north toward the front of the ship, with a speed of 1.7 with respect to the ship, what is your velocity with respect to the land? 2) If you walk south toward the back of the ship, with a speed of 2.5 with respect to the ship, what is your velocity with respect to the land? 3) Your friend is sitting on another cruise ship traveling south at 14 m/s. As you walk toward the back of your ship at 2.5 m/s, what is your velocity with respect to your friend?
1) 16.7 m/s north 2) 12.5 m/s north 3) 26.5 m/s north
Unit 22: A torsion pendulum is made from a disk of mass m = 7.3 kg and radius R = 0.61 m. A force of F = 45.2 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? 3) What is the angular frequency of oscillation of this torsion pendulum? 4) Which of the following would change the period of oscillation of this torsion pendulum?
1) 17.553 N-m / rad 2) 110.288 N-m 3) 3.595 rad/s 4) increasing the mass, replacing the disk with a sphere of equal mass and radius
Unit 21: A solid cubical block with mass m = 7.6 kg is connected between two springs with spring constants kleft = 33 N/m and kright = 55 N/m. The cube is displaced a distance x = 0.2 m from its equilibrium position toward the left and released from rest. 1) Calculate the magnitude of the net force on the cube the moment it is released? 2) What is the effective spring constant of the two springs? 3) What is the period of oscillation of the block? 4) How long does it take the block to return to equilibrium for the first time? 5) What is the speed of the block as it passes through the equilibrium position? 6) What is the magnitude of the acceleration of the block as it passes through equilibrium? 7) Where is the block located, relative to equilibrium, at a time 1.07 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the block is right of equilibrium give the answer as a positive value) 8) What is the net force on the block at this time 1.07 s? (a negative force is to the left; a positive force is to the right) 9) What is the total energy stored in the system? 10) If the block had been given an initial push, how would the period of oscillation change? the period would increase the period would decrease the period would not change
1) 17.6 N 2) 88 N/m 3) 1.85 s 4) 0.46 s 5) 0.68 m/s 6) 0 m/s^2 7) 0.176 m 8) -15.511 N 9) 1.76 J 10) the period would not change
Unit 3: Plane Ride. You are traveling on an airplane. The velocity of the plane with respect to the air is 190 m/s due east. The velocity of the air with respect to the ground is 35 m/s at an angle of 30° west of due north. 1) What is the speed of the plane with respect to the ground? 2) What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due east). 3) How far east will the plane travel in 1 hour?
1) 175.14 m/s 2) 80.03 degrees East of due North 3) 621000 m
Unit 5: Satellite in Orbit. Scientists want to place a 4400 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem: mmars = 6.4191 x 1023 kgrmars = 3.397 x 106 mG = 6.67428 x 10-11 N-m2/kg2 1)What is the force of attraction between Mars and the satellite? 2) What speed should the satellite have to be in a perfectly circular orbit? 3) How much time does it take the satellite to complete one revolution? 4) Which of the following quantities would change the speed the satellite needs to orbit at? 5) What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?
1) 1815.088 N 2) 2050.305 m/s 3) 8.675 hrs 4) the mass of the planet, the radius of the orbit 5) 40764000 m
Unit 6: Two wooden crates rest on top of one another. The smaller top crate has a mass of m1 = 24 kg and the larger bottom crate has a mass of m2 = 87 kg. There is NO friction between the crate and the floor, but the coefficient of static friction between the two crates is μs = 0.83 and the coefficient of kinetic friction between the two crates is μk = 0.65. A massless rope is attached to the lower crate to pull it horizontally to the right (which should be considered the positive direction for this problem). 1) The rope is pulled with a tension T = 235 N (which is small enough that the top crate will not slide). What is the acceleration of the small crate? 2) In the previous situation, what is the frictional force the lower crate exerts on the upper crate? 3) What is the maximum tension that the lower crate can be pulled at before the upper crate begins to slide? 4) The tension is increased in the rope to 1229 N causing the boxes to accelerate faster and the top box to begin sliding. What is the acceleration of the upper crate? 5) As the upper crate slides, what is the acceleration of the lower crate?
1) 2.117 m/s^2 2) 50.808 N 3) 903.795 N 4) 6.3765 m/s^2 5) 12.367 m/s^2
Unit 12: A white billiard ball with mass mw = 1.64 kg is moving directly to the right with a speed of v = 3.16 m/s and collides elastically with a black billiard ball with the same mass mb = 1.64 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of θw = 22° and the black ball ends up moving at an angle below the horizontal of θb = 68°. 1) What is the final speed of the white ball? 2) What is the final speed of the black ball? 3) What is the magnitude of the final total momentum of the system? 4) What is the final total energy of the system?
1) 2.93 m/s 2) 1.184 m/s 3) 5.1824 kg * m/s 4) 8.188 J
Unit 22: A simple pendulum with mass m = 2.3 kg and length L = 2.23 m hangs from the ceiling. It is pulled back to an small angle of θ = 10.1° from the vertical and released at t = 0. 1) What is the period of oscillation? 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? 3) What is the maximum speed of the pendulum? 4) What is the angular displacement at t = 3.3 s? (give the answer as a negative angle if the angle is to the left of the vertical) 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward
1) 2.996 s 2) 3.957 N 3) 0.823 m/s 4) 8.12 degrees 5) 0 m/s^2 6) 0.304 m/s^2 7) increasing the length, hanging the pendulum in an elevator accelerating downward
Unit 18: Ladder: A ladder of length L = 2.2 m and mass m = 23 kg rests on a floor with coefficient of static friction μs = 0.53. Assume the wall is frictionless. 1) What is the normal force the floor exerts on the ladder? 2) What is the minimum angle the ladder must make with the floor to not slip? 3) A person with mass M = 67 kg now stands at the very top of the ladder. What is the normal force the floor exerts on the ladder? 4) What is the minimum angle to keep the ladder from sliding?
1) 225.63 N 2) 43.332 degrees 3) 882.9 N 4) 49.14 degrees
Unit 4: Newton's Laws: A jet with mass m = 1.4 × 105 kg jet accelerates down the runway for takeoff at 1.7 m/s2. 1) What is the net horizontal force on the airplane as it accelerates for takeoff? 2) What is the net vertical force on the airplane as it accelerates for takeoff? 3) Once off the ground, the plane climbs upward for 20 seconds. During this time, the vertical speed increases from zero to 26 m/s, while the horizontal speed increases from 80 m/s to 95 m/s. What is the net horizontal force on the airplane as it climbs upward? 4) What is the net vertical force on the airplane as it climbs upward? 5) After reaching cruising altitude, the plane levels off, keeping the horizontal speed constant, but smoothly reducing the vertical speed to zero, in 11 seconds. What is the net horizontal force on the airplane as it levels off? 6) What is the net vertical force on the airplane as it levels off?
1) 238000 N 2) 0 N 3) 105000 N 4) 182000 N 5) 0 N 6) -330909.0909
Unit 7: A mass m1 = 5.9 kg rests on a frictionless table and connected by a massless string over a massless pulley to another mass m2 = 3.7 kg which hangs freely from the string. When released, the hanging mass falls a distance d = 0.8 m. 1) How much work is done by gravity on the two block system? 2) How much work is done by the normal force on m1? 3) What is the final speed of the two blocks? 4) How much work is done by tension on m1? 5) What is the tension in the string as the block falls? 6) The work done by tension on only m2 is: positive zero negative 7) What is the NET work done on m2?
1) 29.0376 J 2) 0 J 3) 2.46 m/s 4) 17.852 J 5) 22.315 N 6) negative 7) 11.195 J
Unit 4: Newton's Laws: Three blocks, each of mass 14 kg are on a frictionless table. A hand pushes on the left most box (A) such that the three boxes accelerate in the positive horizontal direction as shown at a rate of a = 0.7 m/s2. 1) What is the magnitude of the force on block A from the hand? 2) What is the net horizontal force on block A ? 3) What is the horizontal force on block A due to block B? 4) What is the net horizontal force on block B? 5) What is the horizontal force on block B due to block C?
1) 29.4 N 2) 9.8 N 3) -19.6 N 4) 9.8 N 5) -9.8 N
Unit 13: A racquet ball with mass m = 0.259 kg is moving toward the wall at v = 13 m/s and at an angle of θ = 32° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t = 0.07 s. 1) What is the magnitude of the initial momentum of the racquet ball? 2) What is the magnitude of the change in momentum of the racquet ball? 3) What is the magnitude of the average force the wall exerts on the racquet ball? 4) Now the racquet ball is moving straight toward the wall at a velocity of vi = 13 m/s. The ball makes an inelastic collision with the solid wall and leaves the wall in the opposite direction at vf = -7.8 m/s. The ball exerts the same average force on the ball as before. What is the magnitude of the change in momentum of the racquet ball? 5)What is the time the ball is in contact with the wall? 6) What is the change in kinetic energy of the racquet ball?
1) 3.367 kg * m/s 2) 5.711 kg * m/s 3) 81.582 N 4) 5.387 kg * m/s 5) 0.066 s 6) -14.007 J
Unit 7: A mass m1 = 3.6 kg rests on a frictionless table and connected by a massless string to another mass m2 = 4.3 kg. A force of magnitude F = 42 N pulls m1 to the left a distance d = 0.81 m. 1) How much work is done by the force F on the two block system? 2) How much work is done by the normal force on m1 and m2? 3) What is the final speed of the two blocks? 4) How much work is done by the tension (in-between the blocks) on block m2? 5) What is the tension in the string? 6) The net work done by all the forces acting on m1 is: positive zero negative 7) What is the NET work done on m1?
1) 34.02 J 2) 0 J 3) 2.935 m/s 4) 18.521 J 5) 22.861 N 6) positive 7) 15.506 J
Unit 20: A merry-go-round with a a radius of R = 1.7 m and moment of inertia I = 219 kg-m2 is spinning with an initial angular speed of ω = 1.63 rad/s in the counter clockwise direection when viewed from above. A person with mass m = 65 kg and velocity v = 4.1 m/s runs on a path tangent to the merry-go-round. Once at the merry-go-round the person jumps on and holds on to the rim of the merry-go-round. 1) What is the magnitude of the initial angular momentum of the merry-go-round? 2) What is the magnitude of the angular momentum of the person 2 meters before she jumps on the merry-go-round? 3) What is the magnitude of the angular momentum of the person just before she jumps on to the merry-go-round? 4) What is the angular speed of the merry-go-round after the person jumps on? 5) Once the merry-go-round travels at this new angular speed, with what force does the person need to hold on? 6) Once the person gets half way around, they decide to simply let go of the merry-go-round to exit the ride. What is the magnitude of the linear velocity of the person right as they leave the merry-go-round? 7) What is the angular speed of the merry-go-round after the person lets go?
1) 356.97 kg * m^2 / s 2) 453.05 kg * m^2 / s 3) 453.05 kg * m^2/s 4) 1.991 rad/s 5) 438.03 N 6) 3.385 m/s 7) 1.991 rad/s
Unit 21: A solid cubical block with mass m =7.6 kg is hung from a vertical spring. When the block hangs in equilibrium, the spring stretches x = 0.2 m. When in this equilibrium position, the block is then given an initial push downward at v = 4.5 m/s. The cubical block oscillates on the spring without friction. 1) Determine the spring constant of the oscillating spring? 2) Determine the magnitude of the oscillation frequency? 3) Determine the cube's speed after t = 0.3 s has elapsed? 4) Determine the magnitude of the maximum acceleration of the block? 5) At t = 0.3 s what is the magnitude of the net force on the block? 6) Where is the potential energy of the system the greatest? At the highest point of oscillation At the new equilibrium position of the oscillation. At the lowest point of oscillation.
1) 372.78 N/m 2) 1.115 Hz 3) 2.278 m/s 4) 31.5 m/s^2 5) 206.442 N 6) At the highest point of oscillation. At the lowest point of oscillation.
Unit 6: Mass On Incline 2. A block with mass m1 = 9.4 kg is on an incline with an angle θ = 26° with respect to the horizontal. For the first question there is no friction between the incline and the block. 1) When there is no friction, what is the magnitude of the acceleration of the block? 2) Now with friction, the acceleration is measured to be only a = 3.05 m/s2. What is the coefficient of kinetic friction between the incline and the block? 3) To keep the mass from accelerating, a spring is attached with spring constant k = 141 N/m. What is the coefficient of static friction if the spring must extend at least x = 16 cm from its unstretched length to keep the block from moving down the plane? 4) The spring is replaced with a massless rope that pulls horizontally to prevent the block from moving. What is the tension in the rope? 5) Now a new block is attached to the first block. The new block is made of a different material and has a coefficient of static friction μ = 0.73. What minimum mass is needed to keep the system from accelerating?
1) 4.3 m/s^2 2) 0.142 3) 0.216 4) 22.56 N 5) 10.543 kg
Unit 6: Mass On Incline 1. A block with mass m1 = 9.4 kg is on an incline with an angle θ = 27° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.25 and μs = 0.275. 1) When there is no friction, what is the magnitude of the acceleration of the block? 2) Now with friction, what is the magnitude of the acceleration of the block after it begins to slide down the plane? 3) To keep the mass from accelerating, a spring is attached. What is the minimum spring constant of the spring to keep the block from sliding if it extends x = 0.16 m from its unstretched length. 4) Now a new block with mass m2 = 14.1 kg is attached to the first block. The new block is made of a different material and has a greater coefficient of static friction. What minimum value for the coefficient of static friction is needed between the new block and the plane to keep the system from accelerating?
1) 4.454 m/s^2 2) 2.268 m/s^2 3) 120.434 N/m 4) 1.525
Unit 3: Car on Curve. A car is traveling around a horizontal circular track with radius r = 180 m at a constant speed v = 29 m/s as shown. The angle θA = 28° above the x axis, and the angle θB = 63° below the x axis. 1) What is the magnitude of the car's acceleration? 2) What is the x component of the car's acceleration when it is at point A 3) What is the y component of the car's acceleration when it is at point A 4) What is the x component of the car's acceleration when it is at point B 5) What is the y component of the car's acceleration when it is at point B 6) As the car passes point B, the y component of its acceleration is A. increasing B. constant C. decreasing
1) 4.67 m/s^2 2) -4.12 m/s^2 3) -2.19 m/s^2 4) -2.12 m/s^2 5) 4.16 m/s^2 6) decreasing
Unit 17: A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.9 kg and the sign has a mass of ms = 15.7 kg. The length of the beam is L = 2.66 m. The sign is attached at the very end of the beam, but the horizontal wire holding up the beam is attached 2/3 of the way to the end of the beam. The angle the wire makes with the beam is θ = 33.9°. 1) What is the tension in the wire? 2) What is the net force the hinge exerts on the beam? 3) The maximum tension the wire can have without breaking is T = 780 N. What is the maximum mass sign that can be hung from the beam? 4) What else could be done in order to be able to hold a heavier sign? while still keeping it horizontal, attach the wire to the end of the beam keeping the wire attached at the same location on the beam, make the wire perpendicular to the beam attach the sign on the beam closer to the wall shorten the length of the wire attaching the box to the beam
1) 419.351 N 2) 474.351 N 3) 32.169 kg 4) while still keeping it horizontal, attach the wire to the end of the beam keeping the wire attached at the same location on the beam, make the wire perpendicular to the beam attach the sign on the beam closer to the wall
Unit 15: A uniform disk with mass m = 9.49 kg and radius R = 1.33 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 326 N at the edge of the disk on the +x-axis, 2) a force 326 N at the edge of the disk on the -y-axis, and 3) a force 326 N acts at the edge of the disk at an angle θ = 37° above the -x-axis.
1) 433.58 N-m 2) 0 N-m 3) 346.272 N-m 4) 0 N-m 5) 0 N-m 6) 87.308 N-m 7) 10.402 rad/s^2 8) 1021.642 J
Unit 11: A train car with mass m1 = 698 kg is moving to the right with a speed of v1 = 7.5 m/s and collides with a second train car. The two cars latch together during the collision and then move off to the right at vf = 4.6 m/s. 1) What is the initial momentum of the first train car? 2) What is the mass of the second train car? 3) What is the mass of the second train car? 4) Now the same two cars are involved in a second collision. The first car is again moving to the right with a speed of v1 = 7.5 m/s and collides with the second train car that is now moving to the left with a velocity v2 = -5.8 m/s before the collision. The two cars latch together at impact. What is the final velocity of the two-car system? (A positive velocity means the two train cars move to the right - a negative velocity means the two train cars move to the left.) 5) Compare the magnitude of the momentum of train car 1 before and after the collision: p1 initial = p1 final p1 initial > p1 final p1 initial < p1 final
1) 5235 kg * m/s 2) 440.043 kg 3) -7590.755 J 4) 2.357 m/s 5) p1 initial > p1 final
Unit 8: A mass m = 7.9 kg hangs on the end of a massless rope L = 1.9 m long. The pendulum is held horizontal and released from rest. 1) How fast is the mass moving at the bottom of its path? 2) What is the magnitude of the tension in the string at the bottom of the path? 3) If the maximum tension the string can take without breaking is Tmax = 663 N, what is the maximum mass that can be used? (Assuming that the mass is still released from the horizontal and swings down to its lowest point.) 4) Now a peg is placed 4/5 of the way down the pendulum's path so that when the mass falls to its vertical position it hits and wraps around the peg. As it wraps around the peg and attains its maximum height it ends a distance of 3/5 L below its starting point (or 2/5 L from its lowest point). How fast is the mass moving at the top of its new path (directly above the peg)? 5) Using the original mass of m = 7.9 kg, what is the magnitude of the tension in the string at the top of the new path (directly above the peg)?
1) 6.106 m/s 2) 232.497 N 3) 22.528 kg 4) 4.729 m/s 5) 387.495 N
Unit 5: A tennis ball connected to a string is spun around in a vertical, circular path at a uniform speed. The ball has a mass m = 0.179 kg and moves at v = 4.81 m/s. The circular path has a radius of R = 0.92 m 1) What is the magnitude of the tension in the string when the ball is at the bottom of the circle? 2) What is the magnitude of the tension in the string when the ball is at the side of the circle? 3) What is the magnitude of the tension in the string when the ball is at the top of the circle? 4) What is the minimum velocity so the string will not go slack as the ball moves around the circle?
1) 6.257 N 2) 4.501 N 3) 2.7468 N 4) 3.003 m/s
Unit 4: Newton's Laws: Three boxes, each of mass 17 kg are on a frictionless table, connected by massless strings. A force of tension T1 pulls on the right most box (A) such that the three boxes accelerate in the positive horizontal direction at a rate of a = 1.2 m/s2. 1) What is the magnitude of T1? 2) What is the net horizontal force on box A? 3) What is the net force that box B exerts on box A? 4) What is the net horizontal force on box B? 5) What is the net force box C exerts on box B?
1) 61.2 N 2) 20.4 N 3) -40.8 N 4) 20.4 N 5) -20.4 N
Unit 7: A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4386 N/m after being compressed a distance x1 = 0.541 m from the spring's unstretched length. The floor is frictionless except for a rough patch a distance d = 2.5 m long. For this rough path, the coefficient of friction is μk = 0.47. 1) How much work is done by the spring as it accelerates the block? 2) What is the speed of the block right after it leaves the spring? 3) How much work is done by friction as the block crosses the rough spot? 4) What is the speed of the block after it passes the rough spot? 5) Instead, the spring is only compressed a distance x2 = 0.123 m before being released. How far into the rough path does the block slide before coming to rest? 6) What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released? 7) If the spring was compressed three times farther and then the block is released, the work done on the block by the spring as it accelerates the block is: the same three times greater three times less nine times greater nine times less
1) 641.849 J 2) 8.69 m/s 3) -195.95 J 4) 7.243 m/s 5) 0.42 m 6) 0.299 m 7) nine times greater
Unit 19: A person with mass mp = 79 kg stands on a spinning platform disk with a radius of R = 1.95 m and mass md = 185 kg. The disk is initially spinning at ω = 1.9 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.65 m from the center). 1) What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk? 2) What is the total moment of inertia of the system about the center of the disk when the person stands at the final location 2/3 of the way toward the center of the disk? 3) What is the final angular velocity of the disk? 4) What is the change in the total kinetic energy of the person and disk? (A positive value means the energy increased.) 5) What is the centripetal acceleration of the person when she is at R/3? 6) If the person now walks back to the rim of the disk, what is the final angular speed of the disk?
1) 652.129 kg * m^2 2) 385.109 kg * m^2 3) 3.218 rad/s 4) 816.91 J 5) 6.731 m/s^2 6) 1.9 rad/s
Unit 20: A disk with mass m = 6.6 kg and radius R = 0.43 m hangs from a rope attached to the ceiling. The disk spins on its axis at a distance r = 1.51 m from the rope and at a frequency f = 18.1 rev/s (with a direction shown by the arrow). 1) What is the magnitude of the angular momentum of the spinning disk? 2) What is the torque due to gravity on the disk? 3) What is the period of precession for this gyroscope? 4) What is the direction of the angular momentum of the spinning disk at the instant shown in the picture? 5) What is the direction of the precession of the gyroscope?
1) 69.392 kg * m^2 / s 2) 97.766 N-m 3) 4.46 s 4) right 5) clockwise as seen from above (looking down the rope)
Unit 16: A spherical bowling ball with mass m = 4.3 kg and radius R = 0.105 m is thrown down the lane with an initial speed of v = 8.5 m/s. The coefficient of kinetic friction between the sliding ball and the ground is μ = 0.32. Once the ball begins to roll without slipping it moves with a constant velocity down the lane. 1) What is the magnitude of the angular acceleration of the bowling ball as it slides down the lane? 2) What is magnitude of the linear acceleration of the bowling ball as it slides down the lane? 3) How long does it take the bowling ball to begin rolling without slipping? 4) How far does the bowling ball slide before it begins to roll without slipping? 5) What is the magnitude of the final velocity? 6) After the bowling ball begins to roll without slipping, compare the rotational and translational kinetic energy of the bowling ball: KErot < KEtran KErot = KEtran KErot > KEtran
1) 74.743 rad/s^2 2) 3.1392 m/s^2 3) 0.774 s 4) 5.636 m 5) KErot < KEtran
Unit 5: Satellite in Orbit 2: Scientists want to place a 4400 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2323 m/s in a perfectly circular orbit. Here is some information that may help solve this problem: mmars = 6.4191 x 1023 kgrmars = 3.397 x 106 mG = 6.67428 x 10-11 N-m2/kg2 1) What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.) 2) What is the force of attraction between Mars and the satellite? 3) What is the acceleration of the satellite in orbit? 4) Which of the following quantities would change the radius the satellite needs to orbit at? 5) What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?
1) 7939262.181 m 2) 3021.390 N 3) 0.68 m/s^2 4) the mass of the planet, the speed of the satellite 5) 1161.5 m/s
Unit 19: A solid disk of mass m1 = 9.9 kg and radius R = 0.22 m is rotating with a constant angular velocity of ω = 37 rad/s. A thin rectangular rod with mass m2 = 3.2 kg and length L = 2R = 0.44 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? 2) What is the initial rotational energy of the rod and disk system? 3) What is the final angular velocity of the disk? 4) What is the final angular momentum of the rod and disk system? 5) What is the final rotational energy of the rod and disk system? 6) The rod took t = 5.1 s to accelerate to its final angular speed with the disk. What average torque was exerted on the rod by the disk?
1) 8.864 kg * m^2/s 2) 163.992 J 3) 30.44 rad/s 4) 8.864 kg * m^2 / s 5) 135.283 J 6) 0.31 N-m
Unit 9: Trip to the Moon. You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem: mearth = 5.9742 x 1024 kgrearth = 6.3781 x 106 mmmoon = 7.36 x 1022 kgrmoon = 1.7374 x 106 mdearth to moon = 3.844 x 108 m (center to center)G = 6.67428 x 10-11 N-m2/kg2 1) On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get? 2) Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as vmin = 11068 m/s. If you leave the surface of the earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully write out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the earth even when the ship is at the surface of the moon! 3) Which of the following would change the minimum velocity needed to make it to the moon? the mass of the earth the radius of the earth the mass of the spaceship
1) 8446983.986 m 2) 2287.458 m/s 3) the mass of the earth and the radius of the earth
Unit 3: Car on Curve 2. A car is traveling around a horizontal circular track with radius r = 200 m as shown. It takes the car t = 69 s to go around the track once. The angle θA = 27° above the x axis, and the angle θB = 63° below the x axis. 1) What is the magnitude of the car's acceleration? 2) What is the x component of the car's velocity when it is at point A 3) What is the y component of the car's velocity when it is at point A 4) What is the x component of the car's acceleration when it is at point B 5) What is the y component of the car's acceleration when it is at point B 6) As the car passes point B, the y component of its velocity is A. increasing B. constant C. decreasing
1. 1.66 m/s^2 2. -8.27 m/s 3. 16.23 m/s 4. -0.75 m/s^2 5. 1.48 m/s^2 6. increasing
Unit 2: Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 24 m/s at an angle 35 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground. 1) What is the horizontal component of the ball's velocity when it leaves Julie's hand? 2) What is the vertical component of the ball's velocity when it leaves Julie's hand? 3) What is the maximum height the ball goes above the ground? 4) What is the distance between the two girls? 5) After catching the ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance 1.5 meters above the ground, and is moving with a speed of 23 m/s when it reaches a maximum height of 13 m above the ground. What is the speed of the ball when it leaves Sarah's hand? 6) How high above the ground will the ball be when it gets to Julie? (note, the ball may go over Julie's head.)
1. 19.66 m/s 2. 13.77 m/s 3. 11.17 m 4. 55.44 m 5. 27.5 m/s 6) 9.325 m
Unit 1: A red ball is thrown down with an initial speed of 1.5 m/s from a height of 26 meters above the ground. Then, 0.5 seconds after the red ball is thrown, a blue ball is thrown upward with an initial speed of 23.3 m/s, from a height of 1 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s2. 1) What is the speed of the red ball right before it hits the ground? 2) How long does it take the red ball to reach the ground? 3) What is the maximum height the blue ball reaches? 4) What is the height of the blue ball 1.8 seconds after the red ball is thrown? 5) How long after the red ball is thrown are the two balls in the air at the same height? 6) Which statement is true regarding the blue ball? A. After it is released and before it hits the ground, the blue ball is always moving faster than the red ball at any given time. B. After it is released and before it hits the ground, the blue ball is sometimes moving faster than the red ball at any given time. C. After it is released and before it hits the ground, the blue ball is never moving faster than the red ball at any given time. 7) Which statement is true about the red ball? A. The acceleration is positive and it is speeding up. B. The acceleration is negative and it is speeding up. C. The acceleration is positive and it is slowing down. D. The acceleration is negative and it is slowing down.
1. 22.5 m/s 2. 2.14 s 3. 28.67 m 4. 23 m 5. 1.3 s 6. After it is released and before it hits the ground, the blue ball is sometimes moving faster than the red ball at any given time 7. The acceleration is negative and it is speeding up.
Unit 1: A tortoise and hare start from rest and have a race. As the race begins, both accelerate forward. The hare accelerates uniformly at a rate of 1.5 m/s2 for 4.2 seconds. It then continues at a constant speed for 12.5 seconds, before getting tired and slowing down with constant acceleration coming to rest 109 meters from where it started. The tortoise accelerates uniformly for the entire distance, finally catching the hare just as the hare comes to a stop. 1) How fast is the hare going 2.5 seconds after it starts? 2) How fast is the hare going 9.1 seconds after it starts? 3) How far does the hare travel before it begins to slow down? 4) What is the acceleration of the hare once it begins to slow down? 5) What is the total time the hare is moving? 6) What is the acceleration of the tortoise?
1. 3.75 m/s 2. 6.3 m/s 3. 91.98 m 4. -1.166 m/s^2 5. 22.103 s 6. 0.446 m/s^2
Unit 9: A mass m = 17 kg is pulled along a horizontal floor with NO friction for a distance d =6 m. Then the mass is pulled up an incline that makes an angle θ = 36° with the horizontal and has a coefficient of kinetic friction μk = 0.4. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 36° (thus on the incline it is parallel to the surface) and has a tension T =62 N. 1) What is the work done by tension before the block goes up the incline? (On the horizontal surface.) 2) What is the speed of the block right before it begins to travel up the incline? 3) What is the work done by friction after the block has traveled a distance x = 1.5 m up the incline? (Where x is measured along the incline.) 4) What is the work done by gravity after the block has traveled a distance x = 1.5 m up the incline? (Where x is measured along the incline.) 5) How far up the incline does the block travel before coming to rest? (Measured along the incline.) 6) On the incline the net work done on the block is: positive negative zero
1. 300.94 J 2. 5.95 m/s 3. -80.952 J 4. -147.037 J 5. 3.344 m 6. negative
Unit 5: Hanging Masses: A single mass m1 = 4.8 kg hangs from a spring in a motionless elevator. The spring is extended x = 11 cm from its unstretched length. 1) What is the spring constant of the spring? 2) Now, three masses m1 = 4.8 kg, m2 = 14.4 kg and m3 = 9.6 kg hang from three identical springs in a motionless elevator. The springs all have the same spring constant that you just calculated above. What is the force the top spring exerts on the top mass? 3) What is the distance the lower spring is stretched from its equilibrium length? 4) Now the elevator is moving downward with a velocity of v = -3 m/s but accelerating upward with an acceleration of a = 5.1 m/s2. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.) What is the force the bottom spring exerts on the bottom mass? 5) What is the distance the upper spring is extended from its unstretched length? 6) Finally, the elevator is moving downward with a velocity of v = -2.1 m/s and also accelerating downward at an acceleration of a = -2.1 m/s2. The elevator is: speeding up slowing down moving at a constant speed 7) Rank the distances the springs are extended from their unstretched lengths: x1 = x2 = x3 x1 > x2 > x3 x1 < x2 < x3 8) What is the distance the MIDDLE spring is extended from its unstretched length?
1. 428.073 N/m 2. 282.528 N 3. 21.978 cm 4) 143.36 N 5) 100.35 cm 6) speeding up. 7) x1 > x2 > x3 8. 43.226 cm
Unit 2: Cannonball. A cannonball is shot (from ground level) with an initial horizontal velocity of 41 m/s and an initial vertical velocity of 23 m/s. 1) What is the initial speed of the cannonball? 2) What is the initial angle theta of the cannonball with respect to the ground? 3) What is the maximum height the cannonball goes above the ground? 4) How far from where it was shot will the cannonball land? 5) What is the speed of the cannonball 2.4 seconds after it was shot? 6) How high above the ground is the cannonball 2.4 seconds after it is shot?
1. 47.01 m/s 2. 29.29 degrees 3. 26.99 m 4. 192.25 m 5. 41 m/s 6. 27 m
Exam #1: Three boxes, each of mass 14 kg are on a frictionless table, connected by massless strings. A force of tension T1 pulls on the right most box (A) such that the three boxes accelerate in the positive horizontal direction at a rate of a = 6.0 m/s^2. A) What is the magnitude of T1? B) What is the net force that box B exerts on box A? C) What is the net horizontal force on box B?
A) 252 N B) -168 Ni C) 84 Ni
Exam #1: A cannonball is shot (from ground level) with an initial horizontal velocity of 41 m/s and an initial velocity of 33 m/s. A) What is the initial speed of the cannonball? B) How far does the cannonball travel before it hits the ground? C) How long does it take for the ball to reach the ground again?
A) 52.631 m/s B) 274.7 m C) 6.7 s
Exam #1: A block with mass M1 = 8.3 kg sits at rest on a narrow incline with an angle theta = 13 degrees with respect to the horizontal. A) What is the equation for the friction force keeping the block from sliding down the incline that would also work if the angle were reduced by 20%?
B. -M1gsin(theta)
Exam #1: The net force on a box is in the positive y direction. Which of the following statements best describes the motion of the box? The box may have been in motion before the net force acts on the box.
B. Its acceleration is parallel to the y axis.
Exam #1: A box of mass m hangs by a spring from the ceiling of an elevator that is accelerating downward. Which of the following best describes the condition of the spring relative to its equilibrium position?
B. it is compressed.
Exam #!: In both cases shown a box is sliding across a floor with the same kinetic coefficient of friction and the same initial velocity. The only difference between the two cases is the mass of the box. In which case will the box slide the furthest before coming to rest?
C. Same for either Case
Exam #1: An apple is initially sitting on the bottom shelf of a pantry. A student picks up the apple and puts the apple on a shelf somewhere above its original location. During this process, the work done on the apple by the student is:
positive.