Concept explainers
A roller-coaster car with a mass of 900 kg starts at rest from a point 22 m above the ground. At point B, it is 8 m above the ground. [Express your answers in kilojoules (kJ).]
- a. What is the initial potential energy of the car?
- b. What is the potential energy at point B?
- c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 30,000 J (30 kJ), what is the kinetic energy of the car at point B?
(a)
The initial potential energy of the car in kilojoules.
Answer to Problem 16E
The initial potential energy of the car is
Explanation of Solution
Given info: The mass of the car is
Write the expression for the gravitational potential energy at a given height.
Here,
Substitute
Conclusion:
Therefore, the initial potential energy of the car is
(b)
The potential energy of the car at point B.
Answer to Problem 16E
The potential energy of the car at point B is
Explanation of Solution
Given info: The mass of the car is
Write the expression for the gravitational potential energy at a given height.
Substitute
Conclusion:
Therefore, the potential energy of the car at point B is
(c)
The kinetic energy of the car at point B.
Answer to Problem 16E
The kinetic energy of the car at point B is
Explanation of Solution
Given info: The initial potential energy of the car is
During the motion of the car, the loss in potential energy is converted to the gain in kinetic energy. As well as the work done against the friction causes the dissipation of the kinetic energy.
The gain in kinetic energy during the motion from the initial point A to the final point B, is obtained as,
Here,
Substitute
The some of the kinetic energy gained is dissipated for the work done against the friction. Thus, the kinetic energy at the point B is given by,
Here,
Substitute
Conclusion:
Therefore, the kinetic energy of the car at point B is
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Chapter 6 Solutions
Physics of Everyday Phenomena
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