Concept explainers
The reason for the given situation in the problem is not possible.
Answer to Problem 54P
The speed of the child is too large, so static friction does not have the strength to keep the child in place on the incline. Hence the situation is impossible.
Explanation of Solution
Assume that, the friction points up the incline, the net force is directed left towards the centre of the circular path in which the child travels, and a
Free body diagram of the child is shown in Figure.
Write the expression for net force in the horizontal direction, from the free body diagram.
Here,
Write the expression for net force in the horizontal direction, from the free body diagram.
Here,
Multiply equation (I) by
Multiply equation (II) by
Add equation (III) and (IV), and solve for
Multiply equation (I) by
Multiply equation (II) by
Add equation (VI) and (VII), and solve for
Equation (V) and (VIII) are consistent only when
Use equation (V) and (VIII) in
Here,
Use
Here,
If
Conclusion:
Substitute,
Since, the speed of the child is too large, so static friction does not have the strength to keep the child in place of the incline. Hence the situation is impossible.
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Chapter 5 Solutions
Principles of Physics: A Calculus-Based Text
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