7.97. Set Up: At the top of the loop, the net force needed to produce the centripetal acceleration, must be equal to or greater than the gravitational force for the car to remain on the track. Thus, a force balance results in or Next calculate the height, h , necessary to produce this speed by applying conservation of energy, Solve: The height must be at least Reflect: If the car is moving too slowly at B to stay on the track. In that case, gravity provides more downward force than is needed to maintain the circular path, and the car falls out of the circle. If then at B more downward force than gravity alone is needed and this additional downward force is sup-plied by the normal force that the track exerts on the car. 7.98. Set Up: First apply conservation of energy to find the kinetic energy of the wood as it enters the rough section: or Then determine the distance traveled using the work-energy relation, where and For part (b), use the same relation and the calculated distance to find the frictional work. Solve: (a)
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