Exam 8: Potential Energy and Conservation of Energy

FIGURE 8-12 A 2-kg mass is moving along the x axis. The potential energy curve as a function of position is shown in Figure 8-12. The system is conservative. There is no friction. -Refer to Figure 8-12 If the object is at rest at the origin, what will be its kinetic energy at 10 m along the +x-axis?

A ball falls from the top of a building, through the air (air friction is present), to the ground below. How does the kinetic energy (K) just before striking the ground compare to the potential energy (U) at the top of the building?

Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?

FIGURE 8-10 An object of mass m is at rest on a rough inclined plane with height h, length 8 m, and which makes an angle of 30° with the horizontal. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4 m from the bottom of the inclined plane, as shown in Figure 8-10. The coefficient of kinetic friction on the inclined plane is 0.4 and g = 10 m/s². -Refer to Figure 8-10. What is the coefficient of kinetic friction for the horizontal surface?

FIGURE 8-3 A mass is attached to one end of a string. The other end of the string is attached to a rigid support. The mass is released at A and swings in a vertical arc to points B, C, and D, as shown in Figure 8-3. Neglect air resistance and use g = 10 m/ . -Refer to Figure 8-3. At what point does the mass have its highest speed?

An object of mass 4.00 kg is sitting at the top of an inclined plane of height h and angle θ with the horizontal. The object slides down the inclined plane and right before it reaches the bottom of the plane, it has speed of 16.0 m/s. Neglect friction and use g = 10.0 m/s². (a) What is the height of the inclined plane? (b) If the height of the inclined plane is raised to 15.0 m, what is the speed of the object right before it reaches the bottom of the inclined plane?

The force acting on an object is said to be conservative if the work done by this force on the object is independent of the path chosen.

4.00 J of work is needed to push an object of mass 2.00 kg from point A to point B of the inclined plane as shown in Figure 8-9. The angle of inclination is 30.0° with the horizontal. The height of the plane is h and the coefficient of friction between the object and the plane is 0.400. What is the length of the inclined plane? Use g = 10.0 m/s².

FIGURE 8-9 An object with a mass of 10.0 kg is at rest at the top of a frictionless inclined plane of height 8.00 m and an angle of inclination 30.0° with the horizontal. The object is released from this position and it stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown in Figure 8-9. The coefficient of kinetic friction for the horizontal surface is 0.400 and g = 10.0 m/s². -Refer to Figure 8-9. At what horizontal distance from the bottom of the inclined plane will this object stop?

An object of mass m moving with a certain speed has a kinetic energy of 0.0124 J. The object collides with a horizontal spring and compresses it by 0.800 m before it is brought to rest. What is the spring constant of this spring?

FIGURE 8-5 A 2.0-g bead slides along a wire, as shown in Figure 8-5. At point A, the bead is at rest. Neglect friction and use g = 10 m/s². -Refer to Figure 8-5. What is the kinetic energy of the bead at point A?

Two blocks of masses m₁ and m₂ are released from the top of two frictionless inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. Which of the blocks is going faster when it reaches the bottom of its respective incline?

FIGURE 8-7 Two masses M₁ = 2.0 kg and M₂ = 4.0 kg are attached by a string as shown in Figure 8-7. M₁ falls vertically down and M₂ moves on a frictionless surface. Initially the system is at rest. Use g = 10 m/s². -Refer to Figure 8-7. What is the potential energy of the mass M₁ just before it touches the ground?

A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope. When the skier reaches the bottom of the hill, her speed is 30.0 m/s. (a) How much work is done by friction as the skier comes down the hill? (b) What is the magnitude of the friction force if the skier travels directly down the hill?

The total mechanical energy of a system

FIGURE 8-4 An object of mass 2 kg is held at the top of a triangular wedge as shown in Figure 8-4, and then released. The reference level for potential energy is at the base of the triangle. Neglect friction and use g = 10 m/s². -Refer to Figure 8-4. What is the speed of the object just before it reaches the bottom of the wedge?

You and your friend want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy (U) of you and your friend, after you both reach the top.

On a certain planet an object of mass m is moving with an initial speed of 4 m/s. It comes to rest after traveling a horizontal distance of 10 m. If the coefficient of kinetic friction between the object and the surface is 0.2, what is the value of g on that planet?