Concept explainers
(a)
The speed of the car when it reaches the bottom of the hill.
(a)
Answer to Problem 47PQ
The speed of the car when it reaches the bottom of the hill is
Explanation of Solution
It is given that the rolling friction is negligible. This implies the principle of conservation of energy can be applied on the system. The gravitational potential energy of the car is converted to its kinetic energy as it falls to the bottom of the hill.
Write the expression for the conservation of energy.
Here,
The initial kinetic energy of the car is zero.
Write the equation for
Assume that initially the car is at a height
Write the expression for
Here,
Assume the height of the car at the bottom of the hill is zero.
Write the expression for
Write the expression for
Here,
Put equations (II) to (V) in equation (I) and rewrite the equation for
Conclusion:
Given that the initial height of the car is
Substitute
Therefore, the speed of the car when it reaches the bottom of the hill is
(b)
The amount of thermal energy of the system that changes during the stopping motion of the car.
(b)
Answer to Problem 47PQ
The amount of thermal energy of the system that changes during the stopping motion of the car is
Explanation of Solution
Write the expression for the work-energy theorem.
Here,
Define the system as the plastic track and the roller coaster’s wheels. During the last stretch on the track, the coaster will be at the same height as that of its initial height. This implies there is no change in potential energy of the system.
There are no external forces doing work on the system.
Write the expression for
The roller coaster is stopped at the final configuration so that its final kinetic energy will be zero.
Write the expression for
Put the above three equations in equation (VII) .
Write the expression for
Here,
Conclusion:
In part (a), it is found that the value of
Substitute
Substitute
Therefore, the amount of thermal energy of the system that changes during the stopping motion of the car is
(c)
The coefficient of kinetic friction between the wheels and the plastic stopping track.
(c)
Answer to Problem 47PQ
The coefficient of kinetic friction between the wheels and the plastic stopping track is
Explanation of Solution
The change in thermal energy of the system occurs due to the work done by the
Write the expression for
Here,
Write the expression for
Here,
Write the expression for
Here,
Write the expression for
Put the above equation in equation (XII).
Put the above equation in equation (XI).
Put the above equation in equation (X) and rewrite it for
Conclusion:
It is given that the car stops at
Substitute
Therefore, the coefficient of kinetic friction between the wheels and the plastic stopping track is
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Chapter 9 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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