Concept explainers
A 50.0-g toy car is released from rest on a frictionless track with a vertical loop of radius R. The initial height of the car is h = 4.00R.
a. What is the speed of the car at the top of the vertical loop?
b. What is the magnitude of the normal force acting on the car at the top of the vertical loop?
(a)
The speed of the car at the top of the vertical loop.
Answer to Problem 65PQ
The speed of the car at the top of the vertical loop is
Explanation of Solution
The diagram of the motion of the car is shown in figure 1.
Write the expression for the conservation of energy as the car moves from the initial position to the top of the vertical loop.
Here,
Write the equation for the initial potential energy.
Here,
The car is initially at rest so that its initial kinetic energy must be zero.
Write the expression for
`
Write the equation for the potential energy of the car at the top of the vertical loop.
Here,
Write the equation for
Here,
Put equations (II) to (V) in equation (I) and rewrite it for
Conclusion:
Given that the initial height is
Substitute
Therefore, the speed of the car at the top of the vertical loop is
(b)
The magnitude of the normal force acting on the car at the top of the vertical loop.
Answer to Problem 65PQ
The magnitude of the normal force acting on the car at the top of the vertical loop is
Explanation of Solution
The forces acting on the car are the normal force and the gravitational force. Both these force act in the downward direction and the vertical sum of these forces provides the centripetal acceleration required for the car to move in the circular track.
Write the expression for the Newton’s second law.
Here,
Write the expression for
Here,
The acceleration of the car is centripetal acceleration.
Write the expression for
Put the above two equations in equation (VII) and rewrite it for
Substitute
Conclusion:
Given that the mass of the car is
Substitute
Therefore, the magnitude of the normal force acting on the car at the top of the vertical loop is
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Chapter 8 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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