Question:
A ball is dropped from a height of $20 m$ If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ___$m$
A ball is dropped from a height of $20 m$ If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ___$m$
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The rebound height after a collision is determined by the square of the coefficient of restitution.
Updated On: Mar 20, 2025
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Correct Answer: 5
Solution and Explanation
The height to which the ball rebounds is given by:
\[
h' = e^2 \times h
\]
where \( e \) is the coefficient of restitution and \( h \) is the initial height.
Substituting the values:
\[
h' = (0.5)^2 \times 20 = 0.25 \times 20 = 5 \, \text{m}
\]
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Concepts Used:
Work, Energy and Power
Work:
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- The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.
Energy:
- A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
- There are two types of mechanical energy such as; Kinetic and potential energy.
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Power:
- Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
- Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.