Physics final (concepts)

In case 1, one end of a horizontal plank of mass M and length L is attached to a wall by a hinge and the other end is held up by a wire attached to the wall. In case 2 the plank is half the length but has the same mass as in case 1, and the wire makes the same angle with the plank. 1)In which case is the tension in the wire biggest?

Same Tension depends on weight and angle and those are the same

In case 1, one end of a horizontal massless rod of length L is attached to a vertical wall by a hinge, and the other end holds a ball of mass M. In case 2 the massless rod is twice as long and makes an angle of 30o with the wall as shown. 1)In which case is the total torque about an axis through the hinge biggest?

Same case 1:moment about hinge M1 = MgL case 2:length is doubled and inclined to wall at 30 degree angle moment about hinge M2 = Mgsin(30)2L = Mg2L/2 = MgL

Now the professor is spinning at a constant rate we call it w1 and they are holding the weights with arms extended. This time the student drops the weights and the professor lets the weights fall onto the floor. Will the professor's angular velocity increase, decrease, or stay the same?

As the weights fall, they continue to have angular momentum that they had while spinning so it will stay the same.

A ball of mass 3M at x=0 is connected to a ball of mass M at x=L by a massless rod. Consider the three rotation axes A, B and C as shown, all parallel to the y axis. For which rotation axis is the moment of inertia of the object smallest? (It may help you to figure out where the center of mass of the object is.) A B C

B because it is at the center of mass then the inertia is the smallest

A physics demo launches a ball horizontally while dropping a second ball vertically at exactly the same time.

Both hit at the same time because they both have the same vertical distance to the ground and are heading to the ground at the same time at the same initial vertical velocity and experiencing the same acceleration.

A destroyer simultaneously fires two shells with different initial speeds at two different enemy ships. The shells follow the parabolic trajectories shown. Which ship is hit first?

Both ships are hit at about the same time. If the speeds are correctly accounted for, it should make up for the angle at they are shot and it should strike both ships at the same time.

Suppose you hang one end of a beam from the ceiling by a rope and the bottom of the beam rests on a frictionless sheet of ice. The center of mass of the beam is marked with a black spot. Which of the above configurations best represents the equilibrium condition of this setup? A B C

C because the rope is completely straight

Consider the two collisions shown above. In both cases a solid disk of mass M, radius R, and initial angular velocity ω0 is dropped onto an initially stationary second disk having the same radius. In Case 2 the mass of the bottom disk is twice as big as in Case 1. If there are no external torques acting on either system, in which case is the final kinetic energy of the system the biggest?

Case 1 because KE=.5IW^2 so if w/2 or w/3 multiplied by w/2 gives w/4 or w/6 making w/4 bigger making case 1 bigger

In both cases shown below a hula hoop with mass M and radius R is spun with the same angular velocity about a vertical axis through its center. In Case 1 the plane of the hoop is parallel to the floor and in Case 2 it is perpendicular. In which case does the spinning hoop have the most kinetic energy?

Case 1 because the Inertia of a hoop is .5mr^2 and the radius is .5 in the other and KE= .5IW so the second case yields a smaller number

Identical balls are dropped from the same initial height and bounce back to half the initial height. In Case 1 the ball bounces off a cement floor and in case 2 the ball bounces off a piece of stretchy rubber. In which case is the average force acting on the ball during the collision the biggest?

Case 1 because the contact time with the floor is less thus the average force is more

In the two cases shown above identical ladders are leaning against frictionless walls and are not sliding. In which case is the force of friction between the ladder and the ground the biggest?

Case 1 because the farther out it moves the greater the force of friction is needed to keep it in place

In both cases, the beam has the same mass and length and is attached to the wall by a hinge. In which of the static cases shown is the tension in the supporting wire bigger?

Case 2 because holding onto something in the center vs at the edge requires more strength

A girl twirls a rock on the end of a string in a horizontal circle above her head.The diagram illustrates how this looks from above. 1)If the string breaks at the instant shown, which arrow best represents the path the rock will follow? A B C D

Choice C, It should continue in a tangent motion

A student sits at rest on a stool that can rotate freely. The student holds a bicycle wheel that is spinning counterclockwise. The student quickly flips the wheel over so that it's spinning clockwise when viewed from above, with the same angular speed it had initially. Will the student remain clockwise, counterclockwise or remain at rest at the end of the experiment?

Counterclockwise because the upward angular momentum is transferred from the wheel to the student.

Which plot best represents the acceleration curve associated with the displacement and velocity curves shown above?

It is the graph where the straight line goes through the (0,0) point at a steady slope

A destroyer simultaneously fires two shells with the same initial speed at two different enemy ships. The shells follow the parabolic trajectories shown. Which ship is hit first?

Ship 2 is hit first because the time should depend on velocity as well as angle. If they have the same velocity, the angle is the only thing that should affect the timing. Thus the smaller angle should be the one to reach the other boat first, and the other will spend more time in the air before hitting ship 1

Two objects are racing down a ramp. They're both cylinders but one has a larger mass and a larger radius. Which one wins the race?

Since speed is independent of mass and radius. They will tie.

A block sits at rest on a horizontal frictionless surface. Which of the follwoing sketches most closely resembles the correct free body diagram for all forces acting on the block. Each red arrow represents a force.

Sketch A because It has the weight force and the normal force

Two blocks of wood with masses 10kg and 30kg are initially glued together, and the pieces are held up by a string that goes through a pulley. Let's neglect the effects of friction in the pulley and the mass of the string for this problem. Then the glue comes apart, and the blocks separate, so that the 10kg block is hanging on one side connected to the string and the 30kg block is hanging on the other side connected to the string. When the blocks come apart, does the tension in the string increase, decrease or stay the same?

Tension decreases because the blocks can start moving since they are apart and the rope doesn't have to hold much, the mass will accelerate downward so less force is needed by the rope thus the decrease.

A student drops some weights in the professor's hands perfectly as they are spinning on a stool at a constant rate. When the professor catches the weights, will their angular velocity increase, decrease, or stay the same?

The professor's angular velocity will decrease because the professor will have to speed up the weights in order for the weights to go the same speed as the professor. This represents a force on the weights which is also a force back on the professor by Newton's third law.

In Case 1, a force F is pushing perpendicular on an object a distance L/2 from the rotation axis. In Case 2 the same force is pushing at an angle of 30 degrees a distance L from the axis. In which case is the torque due to the force about the rotation axis biggest?

They are the same by solving for torque using t=Frsinθ you get .25f for each

An object is made by hanging a ball of mass M from one end of a plank having the same mass and length L. The object is then pivoted at a point a distance L/4 from the end of the plank supporting the ball, as shown below. 1)Is the object balanced?

Yes T=Force x distance; finding it on each side you get MGL/4

A yummy glazed doughnut is shown above. 1)Where is the center of mass of this fantastic culinary delight? a) In the center of the hole. b) Somewhere inside the solid part of the doughnut. c) The center of mass is not defined in cases where mass is missing.

a) In the center of the hole because the symmetry lies between the hole.

A block slides on a table pulled by a string attached to a hanging weight. In case 1 the block slides without friction and in case 2 there is kinetic friction between the sliding block and the table. 1)In which case is the tension in the string the biggest? a) Case 1 b) Case 2 c) Same

b) Case 2 because tt not only has the pull, but it has a pull back from static friction making it resist movement and increasing tension

The net force on a box is in the positive x direction. Which of the following statements best describes the motion of the box? a) Its velocity is parallel to the x axis. b) Its acceleration is parallel to the x axis. c) Both its velocity and its acceleration are parallel to the x axis. d) Neither its velocity nor its acceleration need to be parallel to the x axis.

b) Its acceleration is parallel to the x-axis because force and acceleration are directly related

A box of mass m hangs by a string from the ceiling of an elevator that is accelerating upward. 1)Which of the following best describes the tension T in the string? a) T < mg b) T = mg c) T > mg

c) T > mg because it is accelerating upward thus it has not only mg acting on it but also the tension from pulling it up

A block of wood sits on a table, and we throw a clay ball at it to get it to move. Call the mass of the clay m, the mass of the block M, and the initial horizontal speed of the clay v. The coefficient of friction between the block and the table is Pk. Let's say the clay ball is much less massive than the block, m M. The ball hits the block and sticks, which gets the block moving. Assume the collision is very quick, so the block starts moving "instantly." What if the initial starting speed of the clay were doubled to 2v? Would the block + clay move twice as far? Four times? How much further would it move this time?

since deltaX is proportional to vi squared, if velocity doubles (2vi)^2, deltaX would quadruple

A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down the ramp and onto a floor where friction causes it to stop a distance D from the bottom of the ramp. The coefficient of kinetic friction between the box and the floor is μk. 1)What is the macroscopic work done on the block by friction during this process? a. mgh b. -mgh c. ukmgD d. 0 2)What is the macroscopic work done on the block by all forces during this process?

1) -mgh because only one force working opposite the block 2)0 because it starts and ends at rest

Two blocks on a horizontal frictionless track head toward each other as shown. One block has twice the mass and half the velocity of the other. 1)The velocity of the center of mass of this system before the collision is... a. toward the left. b. toward the right. c. zero. 2)Suppose the blocks collide elastically. Picking the positive direction to the right, what is the velocity of the bigger block after the collision takes place? a. +2V b. +V c. zero. d. -V. e. -2V.

1) c. zero because ptotal=mv-mv so 1(2)-(2)1 gives zero 2) b. +V because they are both conserved

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding as the truck accelerates to the left as shown. What direction best describes the static frictional force acting on the box? 1. Left 2. Right 3. No Direction

1. Left because static friction will move in the same direction as acceleration.

1) The net force acting on your car a) Points radially inward, toward the center of the track. b) Points radially outward, away from the center of the track. c) Points forward, in the same direction you are moving. d) Points backward, opposite to the direction you are moving. e) Is zero. 2) The momentum of your car a) Points radially inward, toward the center of the track. b) Points radially outward, away from the center of the track. c) Points forward, in the same direction you are moving. d) Points backward, opposite to the direction you are moving. e) Is zero.

1. a) Points radially inward, toward the center of the track. 2. c) Points forward, in the same direction you are moving. The net force is related to acceleration and acceleration points inward. Velocity goes tangent and momentum relates to velocity, thus the momentum moves tangent.

Push two identical masses A and B continuously from a starting line to a finish line, exerting the same constant force F on each. A is initially at rest and B is initially moving to the right. Which mass has the larger change in momentum, and which has a larger change in kinetic energy (KE)? (Circle the correct choices.) a. A has a larger change in momentum, and A has a larger change in KE b. B has a larger change in momentum, and B has a larger change in KE c. They have the same change in momentum and the same change in KE. d. A has a larger change in momentum, but they both have the same change in KE. e. B has a larger change in momentum, but they both have the same change in KE.

A has a larger change in momentum, but they both have the same change in KE. W= DeltaKE and w=FDeltaX so DeltaKE=FDeltaX, B starts first so A will have a larger change in momentum

A ball is rolling around in a bowl as shown. Let's say it rolls around at constant speed in the circle shown. Choose the arrow that represents the the direction of the net force.

Arrow C because that's the only direction there's a centripital acceleration there.

Driving along at a constant speed you come to a small dip on the road, Rank the magnitude of the force by the seat on you at points A, B, and C

For A: The force is O For B: Fn= mg-ma (<mg) For C: Fn= mg+ma (>mg)

How does the force by the seat on you (Force seat on You) compare with the force by you on the seat (Force you on seat) at each of the points? For each point, fill in the blank with a greater than, less than, or equal sign.

For points A, B, and C the forces are equal both ways by Newton's third law.

A block is given an initial velocity so that it starts going up a ramp. It goes up the ramp and then slides back down. The ramp and block do not have negligible friction between them. Which is true, about the motion of the block? a. Its acceleration on the way up is greater than its acceleration on the way down. b. Its acceleration on the way up is less than its acceleration on the way down. Its acceleration on the way up is the same as its acceleration on the way down. c. Its acceleration throughout is greater than it would be if there were no friction. d. Its acceleration throughout is less than it would be if there were no friction. e. None of these is correct.

Its acceleration on the way up is greater than its acceleration on the way down because weight and friction act down on the hill which slows the box down, whereas going down the hill, weight only acts downhill whereas friction acts uphill.

Consider two identical objects released from rest high above the surface of the earth (neglect air resistance for this question).In Case 1 we release an object from a height above the surface of the earth equal to 1 earth radius, and we measure its kinetic energy just before it hits the earth to be K1.In Case 2 we release an object from a height above the surface of the earth equal to 2 earth radii, and we measure its kinetic energy just before it hits the earth to be K2. Compare the kinetic energy of the two objects just before they hit the surface of the earth a. K2=2K1 b. K2=4K1 c. K2= (4/3)K1 d. K2= (3/2)K1

K2 = (4/3) K1

A block slides to the right with speed V on a frictionless floor and collides with a bigger block which is initially at rest. After the collision the speed of both blocks is V/3 in opposite directions. 1)Was the collision elastic?

No because they don't equal the original velocity

A "binary star" is a system of two stars. Sometimes one of the stars is "dead" - it no longer gives off light - so it can't be seen directly. In one such system, the two stars are believed to have equal mass, and we see the shining star moving in a circular orbit. What should we expect the dead star is doing? You must explain why your answer is correct (use the space below). a). The dead star moves in about the same circle ahead of the shining star. b). The dead star moves in about the same circle following the shining star. c). The dead star is motionless at the center of the bright star's orbit. d). The dead star moves in about the same circle opposite the shining star. e). None of these answers is necessarily correct.

The dead star moves in about the same circle opposite the shining star the correct answer is that the center of mass of the system is in the middle of the two.

The work done on the box by the static frictional force as the accelerating truck moves a distance D to the left is? a) Positive b) Zero c) Negative d) Depends on the speed of the truck.

a) Positive because it moves in the same direction as the truck and there is no angle. It should rely on friction and distance

Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck. Which box ends up moving faster? a. Box 1 b. Box 2

a. Box 1 because It doesn't have the added mass of the ball.

A cylinder and a hoop have the same mass and radius. They are released at the same time and roll down a ramp without slipping. Which one reaches the bottom first? a. Cylinder b. Hoop c. Both reach the bottom at the same time

a. Cylinder because It has a larger moment of inertia

A constant force acts for a time Δt 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 twice 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.

a. Four times as long △t=mv/F so if 2mv/(F/2) the two would flip up thus 4mv/F

A box sliding on a frictionless surface collides and sticks to a second identical box that is initially at rest. Compare the initial and final kinetic energies of the system of two boxes. a. Kinitial > Kfinal b. Kinitial = Kfinal c. Kinitial < Kfinal

a. Kinitial>Kfinal because of the conservation of momentum to solve to get velocity then do kinetic energy broken into two parts

Suppose you are on a cart, initially at rest, which rides on a frictionless horizontal track. If you throw a ball off the cart towards the left, will the cart be put into motion? a. Yes, and it moves to the right. b. Yes, and it moves to the left. c. No, it remains in place

a. Yes it moves to the right because momentum should be conserved thus something left means movement right

A car drives up a hill with constant speed. 1)Which statement best describes the total work done on the car by all forces as it moves up the hill with a constant speed? a) Positive b) Zero c) Negative

b). Zero because work is the force times displacement thus if the force is zero work is then zero

Two guys who weigh the same are holding onto a massless pole while standing on horizontal frictionless ice. If the guy on the left starts to pull on the pole, where do they meet? a. -3 m b. 0 m c. +3 m

b. At zero because there is no friction so he should be moving in too

A block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps. The block slides without friction and the ball rolls without slipping. 1)Which one makes it the furthest up the ramp? a. Block b. Ball c. Both reach the same height.

b. Ball because It has rotational energy as well

Two wheels can rotate freely about fixed axles through their centers. The wheels have the same mass, but one has twice the radius of the other. Forces F1 and F2 are applied as shown such that the angular acceleration of the two wheels is the same. Compare the magnitudes of the two forces. a. F2 = F1 b. F2 = 2 F1 c. F2 = 4 F1

b. F2= 2*F1 because it is double since it's FR and the radius is double thus 2F

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. Which of the following orderings is correct? a. Ia > Ib > Ic b. Ia > Ic > Ib c. Ib > Ia > Ic

b. Ia>Ic>Ib because a is far away from two of the masses and c is far away from one mass and b is in the middle so it goes a c then b

A green block of mass m slides to the right on a frictionless floor and collides elastically with a red block of mass M which is initially at rest. After the collision, the green block is at rest and the red block is moving to the right. How does M compare to m? a. m > M b. m = M c. m < M

b. M=m because momentum is conserved so if v1 was 5 and v2 was 0 then if v1 goes to zero v2 goes to 5

The angular momentum of a freely rotating disk around its center is Ldisk. You toss a heavy block horizontally onto the disk along the direction shown. Friction acts between the disk and the block so that eventually the block is at rest on the disk and rotates with it. We will choose the initial angular momentum of the disk to be positive. What is the Ltotal, the magnitude of the angular momentum of the disk-block system? a. Ltotal > Ldisk b. Ltotal = Ldisk c. Ltotal < Ldisk

b. ltotal=ldisk because pushing with or against will be equal

A box sliding on a horizontal frictionless surface runs into a fixed spring, compressing it a distance x1 from its relaxed position while momentarily coming to rest. If the initial speed of the box were doubled, how far x2 would the spring compress? a. x2= Root2x1 b. x2= 2x1 c. x2=4x1

b. x2=2*x1 because the compressed length and velocity should be proportional thus making the ratio double

The potential energy of an object U as a function of x looks like the plot shown above. 1)Where is the force the biggest in the negative x direction? a b c d

c because it has the greatest slope

A box of mass m is hung by a spring from the ceiling of an elevator. When the elevator is at rest, the length of the spring is L = 1m. 1)As the elevator accelerates upward, the length of the spring will be? a) L < 1 m b) L = 1 m c) L > 1 m

c) L > 1 m because the string stretches even more with acceleration upward forcing it to stretch out more

A wheel that is initially at rest starts to turn with a constant angular acceleration. After 4 seconds it has made 4 complete revolutions. How many revolutions has it made after 8 seconds? a. 8 b. 12 c. 16

c. 16 because w0 is 0 and we know theta is 4 and theta i is 0 so we can use the first constant angular acceleration equations to determine acceleration and then plug the new time back in to find the new # of revolutions

The angular momentum of a freely rotating disk around its center is Ldisk. You toss a heavy block horizontally onto the disk along the direction shown. Friction acts between the disk and the block so that eventually the block is at rest on the disk and rotates with it. We will choose the initial angular momentum of the disk to be positive. What is the magnitude of the final angular momentum of the disk-block system? a. Ltotal > Ldisk b. Ltotal = Ldisk c. Ltotal < Ldisk

c. Ltotal<Ldisk because it's at an angle so it slows versus the other entered perpendicular so it should remain the same as it doesn't push back in the opposite direction of rotation

A box sits on a horizontal table. A string with tension T pulls to the right, but static friction between the box and the table prevents the box from moving. 1)What is the magnitude of the static frictional force acting on the box? a) Mg b) μMg c) T d) 0

c. T because it is not moving therefore static friction needs to equal the force so the net force is zero

A small light cylinder and a large heavy cylinder are released at the same time and roll down a ramp without slipping. Which one reaches the bottom first? a. Small cylinder b. Large cylinder c. Both reach the bottom at the same time.

c. The same because It is independent of mass and radius

Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of of a string. 1)In which case does the object have the biggest total work done on it by all forces during its motion? a) Free Fall b) Incline c) String d) Same

d) Same because work doesn't depend on the path.

Two objects, one having twice the mass of the other, are initially at rest. Two forces, one twice as big as the other, act on the objects in opposite directions as shown above. Which of the following statements about the acceleration of the center of mass of the system is true? a. a = F/M to the right b. a = F/(3M) to the right c. a = 0 d. a = F/(3M) to the left e. a = F/M to the left

d. a= F/3M to the left because F=ma but you add 3M and the force is split in 3's

Three balls of equal mass are fired simultaneously at equal speeds from the same height h above the ground. Ball 1 is fired straight up, ball 2 is fired straight down, and ball 3 is fired horizontally. Rank in order from largest to smallest the speeds of the balls, v1, v2, and v3, just before each ball hits the ground.

v1=v2=v3 because they should all have the same initial energy potential since it depends on height velocity and mass which are all the same and because there is a conservation of energy they would end with the same energy and have the same velocity