When a batter strikes a ball with a bat some of the kinetic energy of the bat is transferred to the ball. The amount of energy transferred depends on the distance y between the pivot point (where the bat is held) to the point of impact with the ball. The position corresponding to the maximum energy transfer, y_maxE, is often called the "sweet spot" of the bat. Assuming the bat strikes the ball when it is at rest and that the collision is elastic then from conservation of kinetic energy and momentum it can be shown that

where I is the moment of inertia of the bat (which depends on its mass M and its length L) and m is the mass of the ball.

In fact the term "sweet spot" can also refer to another point on the bat. When a ball is struck there is an impulse on the bat and depending on where on the bat the ball is struck this impulse will be transferred as a shock or jarring on the hands at the pivot point. However, at a particular point on the bat the impulse on the hands is zero and this point is called the centre of percussion, y_cop. The location of the centre of percussion can be found by relating the net force on the bat to the net torque on the bat and it can be shown that

where M is the mass of the bat and y_cm is the position of the centre of mass of the bat.

Ideally the bat should be designed so that the position of the centre of percussion coincides with the position of maximum energy transfer. In this experiment you will try to identify the location of each of these "sweet spots" on a "bat" made from a long piece of wood and to see what factors you can adjust so that the sweet spots coincide.

Place the "bat" on a smooth horizontal surface and mark the position of the pivot point and the position of the centre of mass on the surface. Strike the bat firmly (but without unwarranted aggression) with a "cue" (you can use a metre stick) at a location of your choosing on the bat. Observe the deflection (either positive or negative) of both the pivot point and the centre of mass. Strike the "bat" at various locations along the bat and record your observations (describe the motion of the centre of mass and the direction of rotation). The centre of percussion will be the point of impact for which the deflection of the pivot point is zero. Record the position of the centre of percussion with uncertainty in your lab notebook. Check that it satisfies the formula for y_cop. You may worry that the location of the centre of percussion point will depend on the force with which you strike the "bat". Try to strike the "bat" with various degrees of force at the percussion point and record your observations in your notebook.

For this part of the experiment a low friction cart will play the roll of the "ball" that is being struck. The energy it gains will be measured by determining how high up a ramp it travels after being struck. Attach the pivot point of the "bat" to the ring stand so that the "bat" can swing freely. Position the cart at the end of the ramp in such a way that the plunger hangs over the end of the table. Pull back the "bat" to a fixed angle (be kind to the cart!) and release it. Record the position of the point of impact on the "bat" and the height that the car travels up the ramp. Adjust the height of the pivot point (but keep the actual pivot point the same) so that the point of impact changes. Repeat the above procedure, releasing the "bat" from the same fixed angle each time, until you have located the point of maximum energy transfer. Record this value, with uncertainty, in your lab notebook and check that is satisfies the formula for y_maxE.

At the point of maximum energy transfer what fraction of the initial potential energy of the "bat" is transferred to final potential energy of the cart?

Change the mass of the cart and find and record the new position of the point of maximum energy transfer.

Add masses to the end of the "bat" and observe how the position of the centre of percussion and the point of maximum energy transfer change. Try to get these to values to coincide.