Concept explainers
Two inclines have the same height but make different angles with the horizontal. The same steel ball rolls without slipping down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.
The incline for which the speed of the ball at the bottom will be greater.
Answer to Problem 12Q
Solution:
The speed of the ball in both cases will be the same.
Explanation of Solution
Given:
The height is the same for both the inclines.
Formula used Total kinetic energy:
Where, m is the mass, v is the speed, I is the moment of inertia and
Moment of inertia of a sphere is:
Angular speed:
Calculation:
If h is the height of the two inclines, the total energy of the ball at the top of both is
At the bottom, all of this energy is converted into kinetic energy, which is given by,
I for the spherical ball is
Total kinetic energy does not depend on the angle of the incline.
Thus, the speed of the ball in both cases will be the same.
Conclusion
Thus, the speed of the ball in both cases will be the same.
Chapter 8 Solutions
Physics: Principles with Applications
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