Exam 8: Potential Energy and Conservation of Energy

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As an object of mass 60 kg approaches the bottom of a ramp, point A, its speed is 20 m/s. It goes up the frictionless plane and turns around at point B. What is the potential energy of this object at point B? Use g = 10 m/s2.

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D

An object approaches the bottom of a ramp, point A. It goes up the ramp and turns around at point B, which is 40.0 m above A. The ramp makes an angle of 30.0° with the horizontal. What is the speed of the object at point A? Neglect friction and use g = 10.0 m/s2.

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B

FIGURE 8-9 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/s<sup>2</sup>. -Refer to Figure 8-9. What is the speed of the object at the bottom of the inclined plane? 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. What is the speed of the object at the bottom of the inclined plane?

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B

Describe a conservative force.

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What distinguishes a conservative force from a non-conservative force?

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A block of mass m slides without friction on a table with speed v. It hits and compresses a spring of force constant k by a distance l. The spring then expands again ejecting the block in the opposite direction as it was originally traveling. Neglecting the mass of the spring, what is the speed of the object after it is ejected by the spring?

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Neglecting air resistance, when you toss a stone straight up in the air from Earth's surface, which of the following statements is true for the upward motion of the stone.

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FIGURE 8-4 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/s<sup>2</sup>. -Refer to Figure 8-4. What is the amount of work done by the gravitational force as the object comes to the bottom of the wedge? 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 amount of work done by the gravitational force as the object comes to the bottom of the wedge?

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The frictional force is a conservative force.

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King Kong falls from the top of the Empire State Building, through the air (air friction is present), to the ground below. How does his kinetic energy (K) just before striking the ground compare to his potential energy (U) at the top of the building?

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A ball is tied to the end of an 80.0-cm string and swings in a vertical circle about a fixed center under the influence of gravity. The speed of the mass at the bottom of the swing is 6.00 m/s. Which of the following statements is true?

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An 8 kg object moving with an initial velocity of 4 m/s comes to rest due to friction after it travels a horizontal distance of 10 m. If the initial speed of the object is doubled, what distance will it travel before coming to rest? Use g = 10 m/s2.

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An object is released from rest a height h above the ground. A second object with four times the mass of the first is released from the same height. The potential energy of the second object compared to the first is

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FIGURE 8-2 FIGURE 8-2   -Swimmers at a water park have a choice of two frictionless water slides (see Figure 8-2). Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v<sub>1</sub> of a swimmer reaching the end of slide 1 compares with v<sub>2</sub>, the speed of a swimmer reaching the end of slide 2? -Swimmers at a water park have a choice of two frictionless water slides (see Figure 8-2). Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2?

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FIGURE 8-5 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/s<sup>2</sup>. -Refer to Figure 8-5. What is the kinetic energy of the bead at point B? 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 B?

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FIGURE 8-12 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 kinetic energy of the object at the origin is 12 J, what will be the kinetic energy at 2.0 m along the +x-axis? 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 kinetic energy of the object at the origin is 12 J, what will be the kinetic energy at 2.0 m along the +x-axis?

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An object of mass 4.0 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s2. How high did the object go?

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Non-conservative forces convert mechanical energy into other forms of energy, or convert other forms of energy into mechanical energy.

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FIGURE 8-8 FIGURE 8-8   -6 J of work is needed to push an object of mass 2 kg from point A to point B of the inclined plane as shown in Figure 8-8. If the angle of inclination is 30°, the height of the plane is h, what is the length of the inclined plane? Use g = 10 m/s<sup>2</sup>. -6 J of work is needed to push an object of mass 2 kg from point A to point B of the inclined plane as shown in Figure 8-8. If the angle of inclination is 30°, the height of the plane is h, what is the length of the inclined plane? Use g = 10 m/s2.

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An object of mass 4 kg is thrown vertically upwards from ground level with an initial speed of 20 m/s. Ignore friction and use g = 10 m/s2. What is the kinetic energy of the object as it reaches its maximum height?

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