A conservative net force $$F_x$$ is exerted on an object within a system. The force varies as a function of the position $$x$$ of the object, as shown in the graph. There are no net external forces exerted on the system. Which of the following correctly describes the potential energy $$U_{sys}$$ of the system as the object moves from 0 m to 0.10 m? 

A constant force is exerted on a block, causing the block to move across a horizontal surface in the positive $$x$$-direction. There is nonnegligible friction between the block and the horizontal surface. The diagram shows the position of the block at 0.5 s time intervals. Which of the following provides a velocity-time graph that could correspond to the diagram and provides correct reasoning? 

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Two disks, A and B, rotate for 4 seconds. Each of their angular velocities, $$\omega$$, are measured over time and graphed in the figure. Which of the following correctly compares the angular displacements $$\Delta\theta_A$$ and $$\Delta\theta_B$$ of disks A and B, respectively, during the period shown, and provides a correct reasoning?

Block X of mass 3.0 kg and Block Y of mass 5.0 kg are connected by a string and are on a level horizontal surface. There is negligible friction between the blocks and the surface. A force $$F = 12$$ N is exerted on Block Y, as shown. What is the tension in the string connecting the two blocks?

Student 1 is standing on a cart holding a small stone, while Student 2 is standing at rest on the ground, as shown. The cart is moving at a constant speed $$v$$ in the +$$x$$-direction, as indicated by the coordinate system. Student 1 drops the stone just as they pass Student 2. Which of the following best represents the path of the falling stone observed by Student 1 and the path of the falling stone observed by Student 2?

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A physical pendulum is constructed of a small block of mass $$2m$$ attached to the end of a uniform rod of length $$ℓ$$ and mass $$m$$. The rotational inertia of the rod about its end is $$13mℓ^{2}$$. The rod is pulled back a small angle $$θ$$ and released at time $$t=0$$, as shown. The rod is vertical at time $$t_{v}$$.

Which of the following is a correct expression for $$t_{v}$$ ?

A small sphere of mass $$m$$ is attached at the right end of a rigid rod of length $$\ell$$. The mass of the rod is negligible compared to $$m$$. The rod is free to rotate about a pivot at its left end, as shown. The rod-sphere system has rotational inertia $$I$$ about the pivot. By what factor should the length of the rod be increased to increase the rotational inertia of the rod-sphere system to $$2I$$ ?

Spheres X, Y, and Z have the masses and locations indicated in the figure. What is the magnitude of the net gravitational force on Sphere X due to the other two spheres? 

Two stones are thrown from the same height and with the same initial speed. Stone A is thrown vertically downward, and Stone B is thrown horizontally, as shown. If the stones are thrown at the same time and air resistance is negligible, which of the following is true?

Four satellites A, B, C, and D have circular orbits about Planets X and Y, as shown. Planet Y has twice the mass of Planet X. Satellite A has mass $$m$$ and orbits a distance $$R$$ from the center of Planet X. Satellites B and C have masses $$m$$ and $$2m$$, respectively, and orbit a distance $$2R$$ from the center of Planet X. Satellite D has mass $$m$$ and orbits Planet Y in a distance $$2R$$ from the center of the Planet X.  Which of the following correctly ranks the orbital periods $$T_{A}$$, $$T_{B}$$, $$T_{C}$$, and $$T_{D}$$ of satellites A, B, C, and D, respectively, from least to greatest?

Cart A of mass $$2m$$ is moving with constant speed $$v$$ to the right on a horizontal track. Cart B of mass $$m$$ is initially at rest, as shown. The carts collide elastically. Which of the following best describes the motion of the carts immediately after the collision? 

A block of mass $$m$$ is attached to one end of a spring with the other end of the spring attached to a wall. The block slides with negligible friction on a horizontal surface, as shown. When the block is at position $$x = x_{0}$$, the block has speed $$v = v_{0}$$ and the total energy of the block-spring system is $$E_{0}$$. When the block reaches position $$x = 2x_{0}$$, the block momentarily comes to rest. Which of the following correctly represents the total energy of the block-spring system when the block reaches position $$x=2x_{0}$$?

A narrow hole is drilled from the surface of a spherical asteroid to its center. The asteroid has a mass $$M$$ and radius $$R$$. A small object is dropped into the hole. What is the acceleration of the object when it reaches a distance $$\frac{R}{3}$$ from the center of the asteroid?

A sphere is held at rest at the top of a ramp, as shown. The sphere is released and rolls without slipping down the ramp. The gravitational potential energy of the sphere-Earth system is zero at the bottom of the ramp. Which of the following is true of the sphere when it reaches the bottom of the ramp?