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WAEC Physics 2018 Paper

Question : 5

Total: 50

During a training session, two footballers pass a ball repeatedly between each other. The 'to and fro' motion of the ball is not simple harmonic because the

I and III only
I and II only
II and III only
I, II and III

Validate

Solution:

Concept:

A motion is simple harmonic only if its acceleration is directly proportional to its displacement and is always directed toward a fixed mean position.

Explanation:

For simple harmonic motion (SHM), the acceleration obeys

a \propto -x

This means the acceleration increases as displacement increases, but it always points back toward the equilibrium position.

When the football is passed back and forth between two players, there is no fixed equilibrium point about which the ball oscillates.

The acceleration of the football is not proportional to its displacement from a fixed mean position.

Also, the acceleration is not always directed toward a fixed mean point.

Furthermore, the ball constantly loses energy to air resistance and friction with the ground at every kick.

Because of this, the motion cannot repeat itself in an ideal, undamped way.

Thus, every one of the stated reasons (I, II and III) correctly explains why this to-and-fro motion is not simple harmonic.

Answer:

D. I, II and III

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