S3.4 Kinetic energy
[A] The work - energy theorem
- The work - energy theorem defines kinetic energy.
Key Point 3.7
Work-energy theorem. When a mass m is accelerated by a force along some path, the total work done on the mass by the force is
where the initial and final kinetic energies are Ki and Kf respectively.
Analysis
RevealHideAnalysis
It is straightforward to derive the work-energy theorem from results you have met already.
Consider the situation where a constant magnitude of force acts on an object increasing its velocity from v1 to v2 while moving it over a distance s. Then from Key Point 1.4
Rearranging gives
and thus
So that
Identifying
, we obtain Key Point 3.7
Example
Q: A golf ball is rolled in a straight line, say along the x-axis. Does its kinetic energy increase, decrease or stay the same if:
- [(a)] Its velocity changes from -4ms-1 to -1ms-1 ?
- [(b)] Its velocity changes from -4ms-1 to 4ms-1 ?
In each case is the work done positive negative or zero?
Solution
[(a)] From Key Point 3.7 and Key Point 3.8
Since
, the kinetic energy of the golf ball decreases and the work done is negative.
[(b)] Here
, so no change in kinetic energy and from Key Point 3.7, no work is done.
Q. Why no work?
A. In changing the ball’s velocity from -4ms-1 to rest, negative work is done, while changing the velocity from rest to 4ms-1, the same amount of positive work is done.
Learning Resources
![]() | HRW 7.5 |
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