
Concept explainers
(a)
The speed at which the car reach the top of the loop.
(a)

Answer to Problem 92P
The speed at which the car reach the top of the loop is
Explanation of Solution
The mass of the roller coaster car is
Write the formula for the conservation of energy for the car.
Here,
Consider the initial state to be at the top at rest and final stage to be at the top of the loop. The initial kinetic energy is thus zero.
Re-write equation (I).
Here,
Re-write the above equation to get an expression for
Conclusion:
Substitute
The speed at which the car reach the top of the loop is
(b)
The force exerted by the track on the car at the top of the loop.
(b)

Answer to Problem 92P
The force exerted by the track on the car at the top of the loop is
Explanation of Solution
The mass of the roller coaster car is
At the top of the loop, the normal force and the weight of the car points downward and provide the
Write the equation for forces at the top of the loop in vertical direction.
Here,
Re-write the above equation to get an expression for
Conclusion:
Substitute
The force exerted by the track on the car at the top of the loop is
(c)
The minimum height for the release of the car so that the car does not lose contact with the track.
(c)

Answer to Problem 92P
The force exerted by the track on the car at the top of the loop is
Explanation of Solution
The mass of the roller coaster car is
At the top of the loop, the normal force and the weight of the car points downward and provide the centripetal force.
Write the equation for forces at the top of the loop in vertical direction.
Here,
At the minimum height for the release of the car so that the car does not lose contact with the track, the normal force is zero.
Re-write the above equation.
From section (a) write the formula for the velocity at the top of the loop.
Here,
Substitute equation (II) in equation (I).
Re-write the above equation to get an expression for
Conclusion:
Substitute,
The minimum height for the release of the car so that the car does not lose contact with the track is
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Chapter 6 Solutions
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