Explanation Given data: The mass of the cable car is 5200 kg. The distance travelled by the cable car is 360 m. The inclination of the hill is 12 ° . Formula used: The expression for gravitational potential energy is: U = m g h Here, U is the gravitational potential energy, m is the mass of the cable car, g is the acceleration due to gravity and h is the vertical distance between flat ground and the point on the hill to which the car travels. The expression for kinetic energy is: K . E . = 1 2 m v 2 Here, m is the mass of the cable car and v is the speed of the cable car. Explanation: Draw a schematic diagram of the motion of the cable car on a hill. Assume that there is no friction. So, the work done to move the cable car on the hill is equal to the increase in the gravitational potential energy. The sum of the kinetic energy and the potential energy at the starting position is the total energy of the system at the starting point. At the starting position, the cable is at rest; so there will be no kinetic energy (the initial velocity of the car is zero), which is also the case on the ground, and so, the potential energy will also be zero (height is zero). So, the total energy of the system at the starting position is zero. The sum of the kinetic energy and the potential energy at the final position is the total energy of the system at the final point. At the final position as well, the cable car is not moving (the final velocity of the car is zero); so, there will be no kinetic energy at the final position. At the final position, only potential energy is there (because it is at a certain height), which is calculated below. Calculate the height of the car at the final position as: h = ( 360 m ) sin12 ° = 74

2nd Edition

ISBN: 9780134601823

Author: ETKINA, Eugenia, Planinšič, G. (gorazd), Van Heuvelen, Alan

Publisher: Pearson,

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Chapter 7, Problem 15P

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The change in the total energy of the system while travelling in a cable car from the bottom to the top during a vacation in San Francisco, if the 5200 kg cable car covers a distance of 360 m on a hill inclined 12° above the horizontal. The car and the earth are a system. Also, mention all assumptions.

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Chapter 7, Problem 14P

Chapter 7, Problem 16P

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