Finals Szn

A newly discovered planet is found to have density 2/3 ρe and radius 2Re, where ρe and RE are the density and radius of Earth, respectively. The surface gravitational field of the planet is most nearly;

13 N/kg (D)

At the instant shown, three asteroids are in a line, and the distance between A and B is the same as the distance between B and C. Asteroids B and C have the same mass, while asteroid A has twice the mass. Rank the magnitude of the net force on each asteroid due to the other two asteroids.

Big, far, middle (ACB)

In Case A, a metal bullet penetrates a wooden block. In Case B, a rubber bullet with the same initial speed and mass bounces off of an identical wooden block. Will the speed of the wooden block after the collision be (a) greater in case A, (b) greater in case B, or (c) the same in both cases?

Greater in case B (b is for bullet!)

A block is placed on a rotating disc and moves in a circular path. The discs have the same rotation rate in each case, but the masses of the blocks and their distance from the center varies. Rank the magnitude of the frictional force on blocks by the discs.

Mass times radius (A=B, D, C)

A spacecraft is placed in a circular orbit around a planet with mass 6.4 x 10²³ kg . The spacecraft orbits at a height of 4.5 x 10⁷ m above the planet's surface. What additional information is needed to calculate the speed of the spacecraft in the orbit?

The planet's radius only (B)

A train is traveling east with constant speed vt. Two identical spheres are rolling on the floor of one train car. In the frame of reference of the train, the spheres are moving directly toward each other at one instant with the same speed vp parallel to the train's motion, as shown in the figure above. What is the velocity of the center of mass of the spheres in the frame of reference of the train and in the frame of reference of a person standing at rest alongside the train?

Zero; vt east (B)

A spacecraft of mass 4000 kg is traveling in a straight line in the positive direction. Engines can be fired so that the force exerted on the spacecraft is in the positive or negative direction. The graph above shows data for the force during one interval. Which of the following is the best estimate of the net change in the speed of the spacecraft from time t = 0 to time t = 4s?

+0.1 m/s (B)

A 50.0 N box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.50, and the coefficient of kinetic friction is 0.30. A horizontal 20.0 N force is then exerted on the box. The magnitude of the acceleration of the box is most nearly;

0 m/s² (A)

Cart A moves horizontally on a frictionless track. It collides and sticks to identical cart B, which is at rest. The speed of cart A before the collision is measured to be 3.0 m/s, with an uncertainty of ±0.2 m/s. Students are asked to predict the speed of the carts after the collision. Given the uncertainty of the measurement for the speed of cart A, which of the following is the best prediction?

1.4 to 1.6 m/s (D)

Cannonballs of two different masses are shot from cannons at various angles above the horizontal. The velocity of each cannonball as it leaves the cannon is given, along with the vertical component of that velocity, which is the same in all cases. Rank these cases on the time the cannonballs are in the air.

All the same

A spaceship and four cargo pods are connected together by rods, and they are all moving at a constant velocity of 5000 m/s. All masses are given in the diagram in terms of M, the mass of an empty pod. Rank the magnitude of the tension at the labeled points in the rods.

All zero

Carts that have a motor and brakes are traveling either up or down inclines at constant speeds. The carts are identical but they carry either a 2 kg or 4 kg load and are on one of two inclines. Incline angles, cart masses, and speeds are given in each figure. Rank these cases on the magnitude of the net force acting on the cart.

All zero

Two carts traveling in opposite directions are about to collide. The carts are all identical in size and shape, but they carry different loads and are traveling at different speeds. The carts stick together after the collision. There is no friction between the carts and the ground. Rank the speed of the two-cart systems after the collision.

All zero

Two wooden blocks with different masses are at rest, stacked on a table. The top block is labeled 1, and the bottom block is labeled 2. Rank the magnitude of the force the table exerts on the top block (1).

All zero

A student pushes two blocks across a desk. At the instant shown, the blocks are slowing down. The force exerted on block A by the student is directed horizontally to the left. The mass of block A is greater than the mass of block B.

Alphabetical order, like forces are equal (A=B, C=D)

The stacks of boxes shown in the figure above are inside an elevator that is moving upward. The masses of the boxes are given in terms of the mass M of the lightest box. How does the magnitude of the force exerted by the top box on the bottom box compare with the magnitude of the force exerted by the bottom box on the top box for each of the stacks?

Always equal (A)

Some students have determined the gravitational mass of an object and want to compare it to the object's inertial mass. Procedures that would allow them to accomplish this include which of the following? Select two answers.

Attaching the object to a spring of known spring constant, allowing it to oscillate horizontally on a nearly frictionless surface, and measuring the period; Attaching the object to a force sensor, using the sensor to pull the object across a nearly frictionless horizontal surface, and measuring the acceleration (C, D)

Three identical blocks each take a different path from a height h to the ground. Block A is released from rest and falls vertically. Block B is released from rest and slides down a frictionless incline. Block C is projected horizontally with an initial speed v. Which block takes the longest time to reach the ground?

B (B)

A bus is initially traveling north at a constant speed, as shown in the figure above. As the bus starts to make a left turn without changing speed, a passenger notices that a box on the floor starts sliding toward the right side of the bus. Which of the following top views of the box, when correctly labeled, would best represent all of the horizontal forces exerted on the box as it starts sliding?

Box with arrow moving to the left (B)

Identical treasure chests (shown from above) each have two forces acting on them. All chests start at rest. Rank these cases on the speed of the treasure chest after 2 seconds.

Calculate net forces (D, C=A, B)

A 100 N box is initially at rest on a rough horizontal surface. The coefficient of static friction is 0.6 and the coefficient of kinetic friction is 0.4. A constant 35 N horizontal force to the right is applied to the box. Four students are discussing the frictional force exerted on the box by the rough surface 1 second after the force is first applied. With which, if any, of these students do you agree?

Carlos

An object is moving to the right with speed vi when a force of magnitude F is exerted on it. In which of the following situations is the object's direction of motion changing and kinetic energy decreasing at the instant shown?

F arrow angled from left (D)

A block is held at rest against a wall by a force of magnitude F exerted at an angle θ from the horizontal, as shown in the figure above. Let Fg be the gravitational force exerted by Earth on the block, FN be the normal force exerted by the wall on the block, and Ff be the frictional force exerted by the wall on the block. Which of the following statements about the magnitudes of the forces on the block must be true? Select two answers.

Fcosθ = FN; Fsinθ = Fg ± Ff (B, C)

The stacks of boxes shown in the figure above are inside an elevator that is moving upward. The masses of the boxes are given in terms of the mass M of the lightest box. Assume the elevator is moving at constant speed, and consider the bottom box in the stack that has two boxes of mass 2M. Let Ffloor be the force exerted by the floor on the box, Fg be the force exerted by gravity on the box, and Fbox be the force exerted by the top box on the bottom box. Which of the following best represents the forces exerted on the bottom box?

Fg and Fbox pointing down (C)

Boxes are pulled by ropes along frictionless surfaces, accelerating toward the left. All of the boxes are identical, and the accelerations of all three systems are the same. Rank the tensions in the ropes.

First, middles, lasts (D, B=E, A=C=F)

Boxes are held at rest against rough vertical walls by forces pushing horizontally on the boxes as shown. Rank the magnitude of the normal force exerted on the walls by these boxes.

Force magnitude (A=B, D=E, C)

A block is tethered to a frictionless ramp by a horizontal string as shown. The block is at rest. Is the normal force exerted on the block by the ramp greater than, less than, or equal to the weight of the block?

Greater than

At the instant shown, three asteroids are in a line, and the distance between B and C is 4 times as large as the distance between A and B. Asteroids A and B have the same mass. There is no net force on asteroid B due to the other two asteroids. A student makes the following comment about the mass of asteroid C: "Since C is four times as far from B as A is, it is only going to have one-quarter the effect on B. To get the forces on B to balance, you'd need the mass of C to be four times as large." What, if anything, is wrong with the statement made by the student. If nothing is wrong, state that explicitly, and then explain why you think the statement is correct. If the statement is incorrect, state what is wrong and how you would correct it. In either case, explain your reasoning.

Incorrect; sixteen times as large

Cannonballs of two different masses are shot from cannons at various angles above the horizontal. The velocity of each cannonball as it leaves the cannon is given, along with the horizontal component of that velocity, which is the same in all cases. Rank these cases on the horizontal distance traveled by the cannonballs.

Largest angles (D, B=C, A)

A crate is on a horizontal frictionless surface. A force of magnitude F is exerted on the crate at an angle θ to the horizontal, as shown in the figure above, causing the crate to slide to the right. The surface exerts a normal force of magnitude Fn on the crate. While F is kept constant, the angle θ is now doubled but is still less than 90°. Assume the crate remains in contact with the surface. How does the new normal force exerted on the crate compare to Fn?

Less (B)

A skateboarder is skating over a circular bump. At the instant shown, she is at the top of the bump and is moving with a speed of 5 m/s. Is the normal force exerted on the skateboarder by the bump greater than, less than, or equal to the weight of the skateboarder?

Less than

Two identical rocks are thrown horizontally from a cliff with different velocities. The rocks are thrown at the same time, and are shown after a few seconds while they are still in the air.

Less; equal; equal; equal

A lion is running at constant speed toward a gazelle that is standing still, as shown in the top figure above. After several seconds, the gazelle notices the lion and accelerates directly toward him, hoping to pass the lion and force him to reverse direction. As the gazelle accelerates toward and past the lion, the lion changes direction and accelerates in pursuit of the gazelle. The lion and the gazelle eventually each reach constant but different speeds. Which of the following sets of graphs shows a reasonable representation of the velocities of the lion and the gazelle as functions of time?

Lion starts below, ends above; Gazelle starts past 0 (A)

Carts with spring plungers run into fixed barriers. The carts are identical, but are carrying different loads and so have different masses. The velocity of each cart just before and just after impact is given. Rank the magnitude of the change in momentum of the carts.

Mass times velocity (A, B=D, C)

Carts A and B are shown just before they collide. Four students discussing this situation make the following contentions. With which, if any, of these students do you agree?

None of them

Two identical blocks, 1 and 2, are connected by a massless string. In Case A, a student pulls on a string attached to block 2 so that the blocks travel to the right across a desk at a constant speed of 10 cm/s. In Case B, the student pulls on a string attached to block 1 so that the same blocks travel across the same desk to the left at a constant speed of 20 cm/s. Will the tension in the diagonal string connecting the two blocks be greater in Case A, greater in Case B, or the same in both cases?

Normal force is greater in A (greater in Case A)

A 50 N box has an applied force on it of 40 N that makes an angle of 30o with the horizontal. The box is moving to the right at a constant speed in both cases. Will the frictional force exerted on the box by the rough surface be greater in case A, greater in case B, or the same in both cases?

Normal force is greater in B (greater in Case B)

Two wooden blocks with different masses are at rest, stacked on a table. The top block is labeled 1, and the bottom block is labeled 2. Rank the magnitude of the force the table exerts on the bottom block (B).

Pairs (C=D, A=B)

A student stands at one end of a raft floating in a pool with equally spaced marks along the bottom, as shown above. The student and the raft have the same mass. The student walks to the opposite end of the raft. Which of the following best shows the final locations of the raft and student relative to the marks at the bottom of the pool? Assume that there is no drag force between the raft and the water.

Second from furthest back (C)

Two identical carts are free to move along a straight frictionless track. At time t₁, cart X is moving at 2.0 m/s when it collides with and sticks to cart Y, which is initially at rest. Which of the following graphs best shows the velocity of cart X before and after the collision?

Starts at 2, ends at 1 (C)

Two carts, of mass 2m and m, approach each other head-on with the same speed v, as shown in the figure above. When the carts collide, they hook together. Assuming positive momentum is to the right, which of the following best represents the momentum of the cart of mass m as a function of time before and after the collision?

Starts below, ends barely above (C)

These graphs are of net force vs. acceleration for different objects. All graphs have the same scale for each respective axis. Rank the mass of the object.

Steepness (CABD)

A box is held at rest against a rough vertical surface by a force pushing horizontally as shown. Values for the applied force and the weight of the boxes are given. The boxes are all made of the same material and the walls are identical. Rank the magnitude of the frictional force exerted on the wall by these boxes.

Weight of boxes (D, A=C, B)

The stacks of boxes shown in the figure above are inside an elevator that is moving upward. The masses of the boxes are given in terms of the mass M of the lightest box. Assume the elevator has upward acceleration a, and consider the stack that has two boxes of mass M. What is the magnitude of the force exerted on the top box by the bottom box?

m times a+g (D)

A spaceship and its shuttle pod are traveling to the right in a straight line with speed v, as shown in the top figure above. The mass of the pod is m, and the mass of the spaceship is 6m. The pod is launched, and afterward the pod is moving to the right with speed vp and the spaceship is moving to the right with speed vf, where vf > v , as shown in the bottom figure. Which of the following is true of the speed vc of the center of mass of the system after the pod is launched?

vc=v (D)