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Why does a ball go farther when hit with an aluminum bat?

Asif Shakur, Chair of Physics and Engineering at Salisbury State University, gives the following explanation:

Aluminum is a hard material. It doesn't have a lot of "give." In other words, aluminum is highly elastic. Therefore, very little of the ball's initial kinetic energy (the energy associated with motion) is used up in permanently deforming the aluminum. Indeed, the aluminum springs back quickly and the ball retains much of its initial energy. In contrast, wood is less elastic: it is deformed permanently and to a greater extent than aluminum. As a result, a ball colliding with a wooden bat, such as the replica of Babe Ruth's Louisville Slugger (below), loses more of its initial kinetic energy. At the extreme, a ball colliding with silly putty--a plastic that is completely inelastic--could lose almost all its kinetic energy.

Babe Ruth's Baseball Bat
Babe Ruth's Baseball Bat

During an elastic collision, a ball experiences an incredibly large force for an incredibly short time, causing it to reverse direction at a speed that can be greater than its initial speed. For example, a bullet gains speed when it ricochets off an approaching artillery shell, but looses almost all of its kinetic energy when shot into a wooden block. One must be very careful to distinguish between the expressions "losing kinetic energy" and "losing energy." The total energy is not lost; the kinetic energy is transformed into other forms of energy such as heat. Although heat is a wonderful thing on a cold morning, it does not make our ball move any faster.

The law of conservation of momentum--a profound physical law--governs the motion of colliding objects. An object's momentum equals the product of its mass and its velocity, or mv. And conservation means that the total momentum of objects entering into a collision equals their total momentum after the collision. This law holds whether the collision is elastic or inelastic. On the other hand, the objects' kinetic energy--equal to 1/2mv2--before the collision is not necessarily equal to the kinetic energy after the collision. Indeed, elastic collisions are characterized by the conservation of kinetic energy, whereas inelastic collisions are characterized by the "loss" of kinetic energy into heat, sound and so forth.

Unfortunately, the only way to make this discussion more cogent is to resort to equations. Consider a bullet of mass m and speed v colliding with a stationary block of wood of mass M. After the collision, the bullet is lodged in the wood and the "system" of both the bullet and the block move with a common speed V. Conservation of momentum then says that mv + 0 = (m+M)V.

It would be incorrect to write a "conservation of kinetic energy" equation for this case, along the lines of 1/2mv2 +0 = 1/2(M+m)V2. That equation is patently incorrect. In fact, the first equation implies that the second cannot be true! Try yourself by plugging in some numbers. To further elucidate this point, let us calculate the ratio of the kinetic energy of the bullet and block system and the initial kinetic energy of the bullet: what is 1/2(M+m)V2 divided by 1/2mv2?

From the first equation, we know that V = m/(M+m). Substituting this value into our ratio, we find that the kinetic energy of the bullet and block divided by the kinetic energy of bullet alone equals m/(M+m). If m is 10 grams and M is 990 grams, the bullet loses more than 99 percent of its initial kinetic energy.

The moral of the story is that if you want the ball to have a high speed (lots of kinetic energy), make sure that the collision is as close to being elastic as possible. Of course, this begs the question: Why not use a big, bad steel bat? But that's another story for another day!

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