Tag: uniform acceleration

Bouncing Ball

Q: Does a bouncing ball experience constant acceleration?

Answer:

The answer is NO during the bounces, but YES in between bounces.

In between bounces, the ball is always having a downward acceleration of g=9.81 m s^-2. As such, the displacement at equal time intervals display a square number sequence 0, 1, 4, 9, 16, 25… This makes sense since the s-t relationship is quadratic.

If we calculate the difference between each pair of square numbers (4-1, 9-4, 16-9, 25-16,…), we obtain the arithmetic progression 1, 3, 5, 7, 9… This shows that the distance travelled between equal time intervals increases at a constant rate. This makes sense since the v-t relationship is linear.

One Hand Juggler

Q: The ball slows down on the way up, but speeds up on the way down. So which is larger? The acceleration on the way up or the deceleration on the way down?

A: Same same. Whether the ball is rising or falling, the only force acting on it is mg. With a constant net force img (downward), the acceleration is also constant (g=9.81 m s^-2 downward)

Galileo’s Inclined Plane

Galileo may not be as famous as Newton or Einstein. But he is widely acknowledged as the father of modern science. This is because he was the first to subject his theories to experimental observations. Basically he pioneered the scientific method.

For example, instead of arguing philosophically over whether objects of different masses should fall at the same rate, he conducted experiments to observe whether they actually fall at the same rate.

But it was not easy to conduct such experiments. Falling objects accelerate too quickly. And Galileo did not have stopwatches nor slow-motion videos to work with. But he had a brilliant idea. Why not measure the rate at which balls roll down inclines instead? The incline will “dilute” gravity, and make the motion slower and more easily measurable!

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As you watch this video, ask yourself

Q: How can we tell that the golf ball is moving at constant acceleration?

A: The markings show that the distances it travels (between equal time intervals) increases at a constant rate. This means that its velocity increases at a constant rate, implying constant acceleration.