Concept explainers
a. The speed of the ball at the lowest point of its path.
b. The speed of the ball at the top of the given circular path about the peg.
Answer to Problem 90GP
Solution:
a. The speed of the ball at the lowest point is
b. The speed of the ball at the top of the given circular path is
Explanation of Solution
Given:
The length of the horizontal cord is
The peg is at a distance of
This height is
Formula used:
The speed of the ball at the bottom of its path is calculated from the energy conservation equation. The kinetic energy of the ball is equal to its potential energy at the given lowest point.
Thus,
Once the value of v is known, at the top of the given circular path, the speed of the ball can be calculated.
Calculations:
Part a
If the speed at the lowest point of the path is
Part b
The radius of the circular path about the peg is:
Therefore, its diameter is:
Consider the energy conservation about this diameter of the circular path.
If the speed is
at the top path:
Conclusion:
a. The speed of the ball at the lowest point is
b. The speed of the ball at the top of the given circular path is
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