A rope is attached to a crate at an angle to the horizontal, as shown on the left. The rope pulls the crate to the right across a rough horizontal surface at a constant speed. The free-body diagram on the right shows the forces exerted on the crate at the instant shown on the left. As the crate moves across the surface, the coefficient of kinetic friction between the crate and the surface increases but the speed of the crate remains constant. Which of the following free-body diagrams could show the forces exerted on the crate a short time later, after the coefficient of friction has increased?

The figures show the forces exerted on an object moving on a horizontal surface at two different moments in time. Which of the following correctly compares the change in direction, if any, of the velocity of the object in the two figures?

A person stands on a scale in an elevator. Consider the following four forces:

Fp–s : The force of the person on the scale

Fs–p : The force of the scale on the person

Fp–E : The force of the person on Earth

FE–p : The force of Earth on the person.

Which of the following correctly ranks the magnitudes of these forces while the elevator is moving upward with increasing speed?

A 10 kg block is connected to both ends of a rope. The rope passes over a pulley with negligible friction and mass, and the entire assembly is placed in an elevator. The elevator has a constant upward acceleration of $$2 m/s^2$$ . What is the magnitude of the tension force in the rope as the elevator accelerates?

Planets A and B, with masses 2m and m, respectively, orbit a distant star of mass M. Planet A is a distance 2R from the center of the star, and Planet B is a distance R from the center of the star. Which of the following is a correct expression for the magnitude of the net force exerted on Planet B?

A block of mass m is held at rest against a vertical wall by an applied force F_A. The wall exerts a normal force F_N on the block. The coefficient of static friction between the block and the wall is μ_s. If the magnitude of F_A is larger than the minimum required magnitude to keep the block in place, which of the following equations correctly describes the force of static friction, F_f, exerted on the block?

A block of mass m is attached to a spring on an inclined plane that makes an angle θ with the horizontal. Initially, the block is held in place with the spring at its unstretched length. The block is then slowly lowered until it comes to rest at equilibrium at a displacement x₀ from its original position. Which of the following expressions is equal to the spring constant of the spring?

A ball of mass m is attached to a vertical pole by a rope and travels in a horizontal circle. The rope is attached to the top of the pole, has length L, and makes an angle θ with the pole. The ball travels with constant speed v. Which of the following is a correct expression for the tension force in the rope?

An applied force is exerted on a textbook, pushing it against a rough wall, as indicated by the arrow in the figure. The applied force keeps the textbook at rest. Which of the following free-body diagrams could represent the forces exerted on the textbook?

A rod with uniform density is centered on x = 0, as shown in the figure. Spheres 1 and 2 with masses M₁ and M₂, respectively, are connected to the ends of the rod. The center of mass of the rod-spheres system is located at x_cm. If the mass of each of the two spheres is doubled, but the mass of the rod does not change, where will the new center of mass of the spheres-rod system be located?

The diagram shows a bucket that is holding a rock and being lifted by a rope. The rope, bucket, and rock are all moving upward together. Which of following claims must be true?

Which of the following is an example of an object in translational equilibrium?

In the three scenarios shown in the figure, forces are exerted on one or both of the boxes on a horizontal surface. The arrows indicate the direction of the forces, all of which have the same magnitude. There is negligible friction between the blocks and the surface. Which of the following correctly ranks the magnitudes, a_A, a_B, and a_C of the acceleration of the two-block system in the three scenarios?

A hypothetical planet has twice the radius of Earth and twice the mass of Earth. If an object has weight W_E on the surface of Earth, what would the object's weight be on the surface of the hypothetical planet?

Two carts are attached by a spring with spring constant 1000 N/m. The cart on the right has a mass of 2.0 kg, and the cart on the left has mass M. A rope attached to the cart on the right exerts a force of 100 N on the cart. Both carts have the same constant acceleration and the spring is 0.06 m longer than its relaxed length. Assuming the mass and internal friction of the wheels are negligible, what is the value of M?

In a classroom demonstration, an instructor swings a 0.10 kg object on a rope in a vertical circle of radius 0.40 m. What is the minimum speed the object can have at the highest point in its circular path and still stay in circular motion?

A toolbox is set on a rigid board that has negligible mass compared to the box. The frontmost part of the toolbox is Point A and the backmost part of the toolbox is Point B. The board is set on a pivot that is located midway between points A and B and is held in place, as shown in the left figure. When the board is released, Point A lowers and Point B rises, as shown in the right figure. Which of the following must be true about the toolbox?

A child pulls a strap on a 5.0 kg bag at an angle of 30° to the horizontal with a force of 26 N as it rests on a rough wooden floor, as shown. The child is unable to get the bag to slide. The magnitude of the force of friction between the bag and floor is most nearly:

A spring with a relaxed length of L₀ is hung vertically from a ceiling. When an object of mass m is attached to the end of the spring and slowly lowered until it reaches equilibrium, the length of the spring is L₀ + Δx. Which of the following indicates the length of the spring if the object of mass m is removed and an object of mass 4m is attached to the end of the spring and slowly lowered until it reaches equilibrium?

A coin rolls with constant speed v₀ in a circular path along the inside surface of a cone, as shown. The radius of curvature of the coin’s path is r₀ and the surface of the cone is at an angle θ₀ to the horizontal. The coin is then moved to another cone whose surface is at an angle θ₁ such that tan θ₁ = 9 tan θ₀ and the coin travels in a circle with a radius of curvature r₁ = r₀/4 at a constant speed of v₁. Which of the following correctly relates v₁ to v₀?

Box A rests on Box B, which rests on a flat, rough floor. A string pulls on Box A and the boxes move together to the right with constant speed. The friction force between Box A and Box B has magnitude f_{A-B} and the friction force between Box B and the floor has magnitude f_{B-F}. Another block is placed on top of Box A, and the string again pulls the boxes so that they move together with a constant speed. How do f_{A-B} and f_{B-F} change between Figure 1 and Figure 2?

A block on a surface with negligible friction is held against a compressed, horizontal spring. The block is then released. Which of the following statements correctly describes the force exerted on the block and the motion of the block immediately after the block is released?

Two cubes, A and B, are pushed at a constant velocity along a rough surface. The coefficient of kinetic friction between each cube and the surface is the same. Cube B has three times the surface area and twice the mass of Cube A. What is the ratio of the force F_fA of kinetic friction exerted on Cube A to the force F_fB of kinetic friction exerted on Cube B?

A truck is moving down a ramp, as shown in the left figure. The driver is applying the brakes and the truck is slowing down. In the back of the truck, a box is at rest relative to the truck and it remains stationary relative to the truck without slipping. A student draws a free-body diagram to represent the forces acting on the box, as shown in the right figure. Another student looks at the diagram and claims that it is not correct. Which of the following correctly indicates an error in the diagram?

The diagram shows the directions and magnitudes of the forces exerted on a puck on a horizontal surface. What is the magnitude of the vector sum of the forces exerted on the puck?

A box is pulled to the right with constant speed across a rough horizontal surface. The box is subject to the four forces shown in the diagram: a tension force $$F_T$$ , a friction force $$F_f$$ , a normal force $$F_N$$ , and a gravitational force $$F_g$$ . Which of the following pair of these forces, if any, represents an interacting force pair described by Newton’s third law?