Bowling Ball Pendulum

Bowling Ball Pendulum:
Key Concept: Conservation of Energy

Energy cannot be created or destroyed. It can only change form. There are two observable forms of energy, kinetic energy (or “energy in motion”) and potential energy (or “stored energy”). The total energy of a system is equal to the sum of its potential energy and its kinetic energy: TE=KE+PE
How It Works:
In the picture shown to the left, the ball is at rest. Since it is at rest, it has zero kinetic energy. The ball does, however, have potential energy due to the force of gravity. Its potential energy is given by:

PE = mgh

where m=mass of the ball, g=gravity, and h=height of the ball.

So, as the height increases, the potential energy increases.

The kinetic energy is given by:

KE=1/2 mv2

where m=mass of the ball and v=velocity of the ball.

So, as the velocity increases, the kinetic energy increases.

Now, if the ball is pulled to position A shown in the picture to the left, its potential energy increases since its height increases. However, since the ball is at rest, it still has zero kinetic energy. The total energy of the system has increased, though, since the potential energy has increased.

If the ball is released, it begins to move, so its kinetic energy increases. Since the total energy is conserved, as the kinetic energy increases, the potential energy decreases (and vice versa). At position B in the picture, the potential energy is at its minimum and the kinetic energy is at its maximum. At position A and C (the turning points), the potential energy of the system is maximum, and the kinetic energy of the system is zero. If forces on this system other than gravity and the tension of the string were neglected, the ball would continue to oscillate forever.

When the ball moves from point A to point C and back to point A, we say that it has completed one revolution. The time it takes to complete a revolution is called the period.

The period is given by:

T= (l/g)1/2

where l=length of the string and g=gravity.

Question: What will happen to the period if the mass of the ball is increased? Will the period increase, decrease, or stay the same?

Question: What will happen to the period if the string is lengthened?

Question: Why doesn’t the ball swing to a height higher than its starting height?