AP Physics Sem 1 Final - Part 2

A 100 kg cart goes around the inside of a vertical loop of a roller coaster. The radius of the loop is 3 m and the cart moves at a speed of 6 m/s at the top. The force exerted by the track on the cart at the top of the loop is

200 N

A car with speed v and an identical car with speed 2v both travel the same circular section of an unbanked road. If the frictional force required to keep the faster car on the road without skidding is F, then the frictional force required to keep the slower car on the road without skidding is

F/4

Each of the figures above shows a tractor attached to an object. The tractor exerts the same constant force F on each object in every case. Which of the following is a true statement about an object and the relative magnitude of the force exerted by the object on the tractor?

The magnitude of the force exerted by each object on the tractor is equal, because the tractor exerts an equal force on each object.

A stone disk is sliding on frictionless ice to the west with speed v, as shown in the figure above. As the disk slides by, a child uses a rubber mallet to hit the disk at point X, exerting a force directly toward the center of the disk. The child hits point X every half second for about 10 s, changing the trajectory of the disk but not causing it to rotate. Which of the following most closely approximates the path of the disk while the child is hitting it?

a parabolic path (curve)

A rock attached to a string swings in a vertical circle, as shown above, with negligible air resistance. Which of the following diagrams could correctly show all the forces on the rock when the string is in the position above?

diagram of a downward "L" opening to the left

A projectile launched from a cliff at time t=0 follows the path indicated by the dashed line in the above figure. The axes indicate the positive horizontal and vertical directions. Which of the following graphs could represent the projectile's motion?

vertical velocity graph downwards diagonal

Box A of mass m sits on the floor of an elevator, with box B of mass 2m on top of it, as shown in the figure above. The elevator is moving upward and slowing down. FA is the magnitude of the force exerted on box A by box B, FB is the magnitude of the force exerted on box B by box A, and Fg is the magnitude of the gravitational force exerted on box B. Which of the following ranks the forces in order of increasing magnitude?

(FB = FA) < Fg

The horizontal wire shown on the right in the figure above will break when the tension in it exceeds the value Tmax. What is the maximum mass M that the hanging object can have without the horizontal wire breaking? (Assume the wire on the left does not break prior to the horizontal wire breaking.)

(Tmax tan(theta))/g

One end of a string is attached to the ceiling and the other end is attached to a small sphere traveling in a circular path, as shown above, with a constant speed of 1m/s. The string makes an angle of 30° to the vertical. If the tension in the string is 6N and the circumference of the circle is 1m, how much work is done on the sphere by the string as the sphere travels through one revolution?

0 J

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 board is hung from two springs, as shown in the figure above, with the board in equilibrium. Each spring has a spring constant of 10,000 N/m. How far will each spring stretch when a person of mass 50 kg sits on the board and the board again comes to equilibrium?

1/40 m

A student rolls a ball along the floor so that the ball has a speed of 16m/s. What is the speed of the ball relative to a second student who is running at 6m/s in the same direction that the ball is rolling?

10 m/s

To analyze the characteristics and performance of the brakes on a 1500 kg car, researchers collected the data shown in the table above. It shows the car's speed when the brakes are first applied and the corresponding braking distance required to stop the car. The magnitude of the average braking force on the car is most nearly

12,000 N

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

13 N/kg

A planet with half Earth's mass and half Earth's radius is discovered. What would an astronaut who weighs 800 N on Earth weigh on the planet?

1600 N

The graph above shows the speed of a truck as it moves along a straight, level road. How far does the truck travel in the 10s time interval shown?

180 m

Planet X has twice Earth's mass and three times Earth's radius. The magnitude of the gravitational field near Planet X's surface is most nearly

2 N/kg

The inclined plane in the figure above has two sections of equal length and different roughness. The dashed line shows where section 1 ends and section 2 begins. A block of mass M is placed at different locations on the incline. The coefficients of kinetic and static friction between the block and each section are shown in the table below. If the block is sliding up section 2, what is the magnitude of the force of friction that is exerted on the block by the incline?

2 μk Mg cos θ

A uniform spool is suspended from a vertical wall by a string attached to the spool's thin axle. The axle is horizontal, as shown above. The wall is smooth, so it exerts no frictional force on the spool. The tension in the string is 2.6 N. What is the weight of the spool?

2.4 N

Two blocks are connected by a string with negligible mass that passes over a pulley with nonzero rotational inertia I, as shown above. The axle of the pulley has negligible friction. The string does not slip on the pulley. Block 1 has mass 4kg and block 2 has mass 6kg. An additional force with magnitude F is initially exerted on block 1 so that the blocks do not move and is then removed. Which of the following is most nearly the value of F?

20 N

A student throws a rock horizontally from the edge of a cliff that is 20 m high. The rock has an initial speed of 10 m/s. If air resistance is negligible, the distance from the base of the cliff to where the rock hits the level ground below the cliff is most nearly

20 m

The graph above shows the acceleration a of a car as a function of time t. Assuming the car starts from rest, the total displacement of the car from time t=0s to time t=6s is most nearly

45 m

A car goes from rest to 30 m/s in 12 s with constant acceleration. How long does it take the car to go from rest to 15 m/s with the same acceleration?

6 s

A person exerts a continually increasing force on an object in a constant direction. A graph of the acceleration of the object as a function of the applied force is shown above. Which of the following best explains why a best-fit line would not pass through the origin?

An additional force is exerted on the object in the direction opposite the applied force.

The figure above represents the orbits of two planets of equal mass that orbit their star in the counterclockwise direction as a double-planet system. From the point of view of an observer on either planet, the planets appear to orbit each other while also orbiting the star. The dots on the orbits represent the position of the planets at time t0, and X is the position of their center of mass at that time. Which of the following arrows best represents the acceleration of the center of mass of the double-planet system when it is at point X ?

Arrow pointing downwards to the left

An object begins at position x = 0 and moves one-dimensionally along the x-axis with a velocity v expressed as a function of time t according to the graph above. At what time does the object pass through x = 0 again?

Between 20 s and 30 s

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?

Block B

A box of mass m is on a rough inclined plane that is at an angle θ with the horizontal. A force of magnitude F at an angle Φ with the plane is exerted on the block, as shown above. As the block moves up the plane, there is a frictional force between the box and the plane of magnitude f. What is the magnitude of the net force acting on the box?

F cosΦ - mg sin θ - f

Block A and block B move toward each other on a level frictionless track. Block A has mass m and velocity +v . Block B has mass 2m and velocity -v . The blocks collide, and during the collision the magnitude of the net force exerted on block A is F. What is the magnitude of the net force exerted on block B, and why does it have that value?

F, because the net force is equal to the mutual contact force between the blocks.

The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. Which of the following expressions correctly relates the magnitudes Ff and FT?

FT < Ff < 2FT

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(a+g)

Two blocks of masses m and M are suspended as shown above by strings of negligible mass. If a person holding the upper string lowers the blocks so that they have a constant downward acceleration a, the tension in the string at point P is

M(g-a)

The inclined plane in the figure above has two sections of equal length and different roughness. The dashed line shows where section 1 ends and section 2 begins. A block of mass M is placed at different locations on the incline. The coefficients of kinetic and static friction between the block and each section are shown in the table below. If the block is at rest on section 1 of the incline, what is the magnitude of the force of static friction exerted on the block by the incline?

Mg sin θ

Objects 1 and 2 have masses M1 and M2, respectively, where M1<M2. The objects are in outer space far away from any other objects, as shown above. Point P is located halfway between their centers. At what location, if any, is the gravitational field due to the two objects equal to zero?

Somewhere between object 1 and point

Planet 1 orbits Star 1 and Planet 2 orbits Star 2 in circular orbits of the same radius. However, the orbital period of Planet 1 is longer than the orbital period of Planet 2. What could explain this?

Star 1 has less mass than Star 2.

A kitten sits in a lightweight basket near the edge of a table. A person accidentally knocks the basket off the table. As the kitten and basket fall, the kitten rolls, turns, kicks, and catches the basket in its claws. The basket lands on the floor with the kitten safely inside. If air resistance is negligible, what is the acceleration of the kitten-basket system while the kitten and basket are in midair?

The acceleration is directed downward with magnitude equal to g because the system is a projectile.

A person is running on a track. Which of the following forces propels the runner forward?

The force of friction exerted by the ground on the person

A person stands in an elevator. The elevator starts from rest and travels from the first floor to the fifth floor of the building. Which of the following forces has a magnitude equal to the person's weight during the entire elevator ride?

The gravitational force exerted by the person on Earth

When a box is at rest on a level floor, forces are exerted between the atoms in the bottom surface of the box and atoms in the top surface of the floor. Why does the floor not exert a frictional force on the box?

The horizontal components of the forces exerted between atoms in the floor and atoms in the box are not negligible but sum to zero.

A crate is on a horizontal frictionless surface. A force of magnitude F is exerted on the crate at an angle θto 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. As the crate slides a distance d, it gains an amount of kinetic energy ∆K. While F is kept constant, the angle θ is now doubled but is still less than 90o. Assume the crate remains in contact with the surface. How does the new normal force exerted on the crate compare to FN ?

The new normal force is less than FN.

A ladder at rest is leaning against a wall at an angle. Which of the following forces must have the same magnitude as the frictional force exerted on the ladder by the floor?

The normal force exerted on the ladder by the wall

An object's velocity v as a function of time t is given in the graph above. Which of the following statements is true about the motion of the object?

The object's initial and final positions are the same.

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

When a rocket-propelled ship launches from the ground, it expels exhaust gas from the bottom of the ship, as shown above. Which of the following explains why the ship is able to leave the ground?

The ship exerts a downward force on the gas, and the gas exerts an upward force on the ship.

An object starts from rest and slides with negligible friction down an air track tipped at an angle θ from the horizontal. A student records values of the object's position along the track at various times. The value of θ can best be determined from which of the following?

The slope of a graph of position as a function of the square of time

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?

The two magnitudes are always equal in each of the stacks.

A spaceship is traveling from Earth to the Moon. Which of the following is true of the gravitational force on the ship due to the two objects when the ship is equidistant from Earth and the Moon?

There is a net force because the force exerted by Earth is greater than that exerted by the Moon.

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?

Train - Zero Person - vt east

When two charged, massive objects are placed a distance r apart, the gravitational force between them has magnitude F. When the distance between the objects is increased to 2r, the magnitude of the gravitational force between them becomes F/4. Did the electrostatic force between the objects also decrease to one fourth its initial magnitude as a result of the change in position, and why?

Yes, because both forces have the same 1/ r2 dependence.

A block moving to the right on a level surface with friction is pulled by an increasing horizontal force also directed to the right. As the applied force increases, which of the following is true of the normal force and the frictional force on the block?

both normal and frictional force remain constant

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 one arrow pointing outwards to left

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?

diagram of fg and force of box downwards and force of floor upwards

The table above shows equations describing the forces and acceleration a of three blocks that are connected by light strings, some of which run over pulleys. The pulleys are all massless and frictionless, and the coefficient of kinetic friction between each block and surface is μ. In the diagrams below, the mass of each block and the tension in each of the two strings are labeled. Which of the following arrangements could be described by the equations in the table above?

diagram of mx hanging diagonally down to the left, connected to my on flat, connected to mz hanging directly down to the right

Object A is released from rest at height h. At the same instant, object B is thrown downward from the same location. Which of the following graphs of speed of v as a function of time t is correct for the two objects?

graph of lines a and b, parallel with line a starting at origin and b starting above

A box of mass m hangs from massless strings, as shown in the figure above. The angle between strings 1 and 2 is 90o, and the angles that the strings make with the ceiling are Ѳ1 and Ѳ2, respectively. If T1 is the tension in string 1, which of the following are the magnitudes of the horizontal and vertical components of the tension in string 2 ?

horizontal component - T1cos(theta)1 vertical component - mg-T1sin(theta)1

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 graph - straight line below 0 then diagonal up to straight line above 0 gazelle graph - straight line at 0 then diagonal up to straight line farther away from 0

A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taut, with tensions T1 and T2, respectively. The strings and rod form the right triangle shown in the figure above. The ball rotates in a horizontal circle of radius r with speed v. What is the tension T1 in the upper string?

mg/cos θ

An object of mass m is attached to a spring on a frictionless inclined plane that makes an angle θ with the horizontal, as shown above. The object is released from rest with the spring in its unstretched position. As the object moves on the plane, its displacement from the unstretched position is x. The object subsequently oscillates about an equilibrium position at a displacement x0 from the unstretched position of the spring. What is the spring constant of the spring?

mgsin(theta)/xo

A person of mass 60kg is initially standing at one end of a small raft that has a mass of 40kg. The raft is in the middle of a lake, and the drag force between the raft and the water is negligible. The person begins to walk to the right, as shown above, at a speed v relative to the water. As a result, the raft will

move to the left at a speed greater than v

A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taut, with tensions T1 and T2, respectively. The strings and rod form the right triangle shown in the figure above. The ball rotates in a horizontal circle of radius r with speed v. What is the magnitude of the net force on the ball?

mv2 / r

A student wants to determine the coefficient of static friction μ between a block of wood and an adjustable inclined plane. Of the following, the minimum additional equipment the student needs to determine a value for μ is

protractor only

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.

raft - pushed 1 whole mark left person - at the other end of the raft

A box of mass m slides a distance d down a rough incline from an initial height h, as shown in the figure above. The surface of the incline has a coefficient of kinetic friction μ and makes an angle θ with the horizontal. How much mechanical energy is dissipated as the box slides to the bottom of the incline?

μdmg cos (theta)

The graph above shows velocity v as a function of time t for a 0.50 kg object traveling along a straight line. The graph has three segments labeled 1, 2, and 3. A rope exerts a constant force of magnitude FT on the object along its direction of motion the whole time. During segment 2 only, a frictional force of magnitude Ff is also exerted on the object. Which of the following correctly ranks the displacement ∆x for the three segments of the object's motion?

∆x3 > ∆x2 > ∆x1 > 0