Practice Exam #2

A large skinny guy with mass 5M and a smaller guy with mass M are holding onto a massless pole while standing on frictionless ice, as shown below. If the little guy pulls himself toward the big guy, where would they meet?

-2 M

Unit 12 Question 2: A bumper car with mass m1 = 103 kg is moving to the right with a velocity of v1 = 4m/s. A second bumper car with mass m2 = 92kg is moving to the left with a velocity of v2 = −3.4m/s. The two cars have an elastic collision. Assume the surface is frictionless. See Figure 2.1. What is the velocity of the center of mass of the system?

. Center of mass velocity isvcm = m1v1 + m2v2 m1 + m2vcm = 0.509 m/s

Unit 11 Question 1: A bullet with mass 20 grams and velocity 100 m/s collides with a wooden block of mass 2.0 kg. The wooden block is initially at rest, and is connected to a spring with k = 800 N/m. The other end of the spring is attached to an immovable wall. What is the maximum compression of the spring?Note: You may assume that the spring is massless and that the collision between the bullet and the wooden block is completely inelastic.

0.0498m

HW 18 Hanging Beam Wording: A purple beam is hinged to a wall to hold up a blue sign. The beam has a mass of mb = 6.1 kg and the sign has a mass of ms = 16.8 kg. The length of the beam is L = 2.44 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 = 32.6 ◦ . See Figure 4. 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 = 977 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?

Hanging Beam: 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°.

A triangular shape is made from identical balls and identical rigid, massless rods as shown. The moment of inertia about the a, b, and c axes is Ia, Ib, and Ic respectively. Rank the three different axes in order of lowest to highest moment of inertia.

Ib, Ic, Ia

A block and a ball have the same mass and start at rest at the top of identical ramps. The block slides down the ramp without friction and the ball rolls down the ramp without slipping. Which one has the most kinetic energy at the bottom of the ramp? a. the block b. the ball c. they have the same kinetic energy

c. they have the same kinetic energy.

A constant force acts for a time change in t on a block that is initially at rest on a frictionless surface, resulting in a final velocity V. Suppose the experiment is repeated on a block with half the mass using a force that's half as big. For how long would the force have to act to result in the same final velocity? A. Four times as long. B. Twice as long. C. The same length. D. Half as long. E. One quarter as long.

C. The same length.

A block and a ball have the same mass and start at rest at the top of identical ramps. The block slides down the ramp without friction and the ball rolls down the ramp without slipping. Which one has the greatest translational (linear) speed at the bottom of the ramp?

the block

HW 18 Gymnast Wording: A gymnast with mass m1 = 41 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 108 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 masses) walks directly above the right support. What is the force the left support exerts on the beam? See Figure 3. 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?

1) 1334.16 N 2) 127.53 N 3) 13 kg 4) 931.95 N 5) 529.74 N 6) At the right edge of the beam

HW 16: A green hoop with mass mh = 2.8 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 1.9 kg and radius Rd = 0.09 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 = 3.8 kg and radius Rs = 0.22 m. The system is released from rest. 1) What is magnitude of the linear acceleration of the hoop? m/s2 2) What is magnitude of the linear acceleration of the sphere? m/s2 3) What is the magnitude of the angular acceleration of the disk pulley? rad/s2 4) What is the magnitude of the angular acceleration of the sphere? rad/s2 5) What is the tension in the string between the sphere and disk pulley? N 6) What is the tension in the string between the hoop and disk pulley? N 7) The green hoop falls a distance d = 1.68 m. (After being released from rest.) How much time does the hoop take to fall 1.68 m?

1) F=maa=(mh*g)/(7/5ms+1/2md+mh) 2) same answer as 1 because it is a system 3)a=alpha*Ralpha=a/Rd (use a from 1) 4) similar to 3alpha=a/Rs 5)F=maT=ms*aT=7/5ms*a (a from 1) 6)T=mh(g-a) 7)d=1/2at^2 (position formula - starting position and velocity are zero)t=sqrt(2d/a) (use a from 1) 8)vf^2=vi^2 +2ad (initial velocity =0)vf=sqrt(2ad) 9)omega=v/Rs

Unit 18: Ladder - Wording: A ladder of length L = 2.6 m and mass m = 15 kg rests on a floor with coefficient of static friction µs = 0.48. Assume the wall is frictionless. See Figure 8. 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 = 65 kg now stands at the very top of the ladder. What is the normal force the floor exerts on the ladder? See Figure 9. 4. What is the minimum angle to keep the ladder from sliding?

1) N1 = 147.15 N 2) θmin = 46.17◦ 3) N ′ 1 = 784.8 N 4) θ ′ min = 62.09◦

Unit 11 Question 3: A blue car with mass mc = 430 kg is moving east with a speed of vc = 20 m/s and collides with a purple truck with mass mt = 1288 kg that is moving south with a speed of vt = 10 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:a. KEi = KEfb. KEi > KEfc. KEi < KEf

1. 8600 kg m/s 2. 12880 kg.m/s 3. 56.3 degrees 4. 15487 kg m/s 5. 9.01 m/s 6. b

HW 18 Meterstick - Wording: A meterstick (L = 1 m) has a mass of m = 0.145 kg. Initially it hangs from two short strings: one at the 25 cm mark and one at the 75 cm mark. See Figure 5. 1. What is the tension in the left string? 2. Now the right string is cut! What is the magnitude of the initial angular acceleration of the meters 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? See Figure 6. 5. What is the magnitude of 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?

1. TL = 0.711 N 2. 16.817 rad/s^2 3. 0.813 N 4. 5.8 rad/s 5. 8.409 m/s^2 6. T = 2.642 N 7. Right after the string is cut and the meterstick is horizontal

Unit 10 Question 2: A person with mass m1 = 62 kg stands at the left end of a uniform beam with mass m2 = 94 kg and a length L = 3.5 m. Another person with mass m3 = 65 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 10 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. X(cm) = 1.85m2. Hint : no friction between beam and the ground so center of mass does not move.Ans. 1.85 m.3. X(cm) = 0.152 m4. Hint : This puts everyone at the center of mass.Ans. 1.85m.

Suppose you are on a cart which is initially at rest that rides on a frictionless track. You throw a ball at a vertical surface that is firmly attached to the cart. If the ball hits the wall and falls straight down, will the cart be put into motion after the ball falls to the bottom of the cart? A)Yes, and it moves to the right and keeps on going B)Yes, and it moves to the right and then stops C)No, it remains in place D)Yes, and it moves to the left and then stops E)Yes, and it moves to the left and keeps on going

C, Since the initial momentum is zero, the final momentum must be zero. Therefore it must come to a stop after its initial motion to the left. After it is all over, the cart will have moved slightly to the left to keep the CM at the same location

Suppose you are on a cart which is initially at rest that rides on a frictionless track. You throw a ball at a vertical surface that is firmly attached to the cart. If the ball bounces straight back as shown in the picture, will the cart be put into motion after the ball bounces back from the surface? A. Yes, and it moves to the right and keeps on going B. Yes, and it moves to the right and then stops C. No, it remains in place D. Yes, and it moves to the left and then stops E. Yes, and it moves to the left and keeps on going

E. Since the ball ends up moving to the right, the platform and dude must move left in order for the total momentum to remain at zero.

A bomb which is initially at rest in outer space explodes into 3 identical pieces. Which of the following configurations of final velocities is possible? A. A B. B C. C D. A & C E. All three are possible

Only in C do all the momentum vectors add up to 0, the original momentum of the stationary bomb.

HW 18 IE Sign Wording: A sign has a mass of 1050 kg, a height h = 1 m, and a width W = 4 m. It is held by a light rod of length 5 m that is perpendicular to a rough wall. A guy wire at 23◦ to the horizontal holds the sign to the wall. Note that the distance from the left edge of the sign to the wall is 1 m. See Figure 7. Suppose we rely upon friction between the wall and the rod to hold up the sign (there is no hinge attaching the rod to the wall). What is the smallest value of the coefficient of friction µ such that the sign will remain in place? u = 0.2829832

u = 0.2829832