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Name: Dan R.
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: Thursday, April 25, 2002


Question:
This question has raised some interesting discussions at my middle school. Please help!

Q: A person swings a baseball bat and hits the ball with 10 newtons of force.

A: How much force does the ball exert on the bat? The obvious answer is 10 newtons because of equal and opposite forces, etc. However, does it matter what the velocity of the ball is? Would a ball pitched by a 10 year old and struck with a force of 10 newtons exert the same amount of force as one pitched by a professional baseball pitcher and traveling at 93 mph?

With force being equal to velocity x the distance the object traveled, some of us think the velocity of the ball makes a difference. Others think does not make any difference at all. The bat will exert 10 newtons of force on the ball and the ball will exert 10 newtons of force on the bat no matter what.


Replies:
I think you may be more concerned about momentum than force. If the bat hits the ball with 10 N of force, then the ball pushes back with 10 N of force. Momentum is defined as mass times velocity (p=mv). The bat and ball having different masses and different velocities will have different momentums before contact. BUT, during contact a change in momentum is going to occur, most likely to the ball because of its mass compared to the mass of the bat. The definition of a change in momentum is impulse, which is also defined as a force acting over time; therefore Ft=m2v2-m1v1. So, the longer a force of object 1 stays in contact with object 2, the more it can change the momentum of object 2. Changing the momentum of object 2 means that it will change the velocity of the object because momentum must be conserved. So, physics (and a good batting coach) tells you to follow through on your swing because that means more contact time and thus a greater change in momentum of the ball.

Chris Murphy, PE
Mechanical Design Engineer


Dan,

First, force is not equal to the product of velocity and distance traveled. Force is determined by how hard the objects push on each other: how hard the bat pushes on the ball and how hard the ball pushes on the bat. The rate of change of the balls velocity, its acceleration, is determined by the force felt by the ball. It equals the ratio of force to mass, based on Newton's Second Law: F=ma. Note that in this equation force is the cause and acceleration is the effect.

The effect of the acceleration is a change of velocity. Acceleration is the rate at which the velocity changes: m/s per second. How much the velocity changes depends on how much time the ball is in contact with the bat. This is why a swing with a good "follow-through" produces a better hit: the force is exerted on the ball for a longer time. In a simplified mathematical model, change of velocity is the product of the acceleration and the time over which the acceleration acts. Ten Newtons of force applied to a slow pitch will quickly reverse the direction of the ball and send it flying. The same force applied to the 93mph pitch will be devoted to slowing the ball down. The ball will drop to the ground before there is enough time to reverse its velocity. In fact, it would be difficult to exert only ten Newtons of force on such a pitch. The batter may only intend to exert 10 N on the ball, but the ball may have other plans. It will press very hard on the bat, feeling the same force in return from the mass of the bat itself. If the swinger cannot exert enough force to keep the bat moving forward, the bat will be knocked out of his hands.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


Newton's Third Law is inviolate! To hit a ball travelling fast with the same force as the bat hits a slowly moving ball, the bat must be moving more slowly. In fact, if the ball is hanging on a string and the bat is swung rapidly enough to exert a 10 N force on the ball, the reaction force of the ball on the bat is exactly 10 N.

Conversely, if the bat is held stationary (as in a bunt) and the ball is thrown rapidly enough to exert a 10N force on the bat, the reaction force of the bat on the ball is exactly 10 N.

If Newton's 3rd law were not always valid, momentum would not be conserved with many weird consequences. For example, the bat would not slow down if there were no reaction force on it when it hit a ball. It could then hit an infinite number of balls without slowing down and thereby produce an infinite amount of energy without cost.

There is no free lunch!

Best, Dick Plano...


There would be a difference, but it is due to several complicating factors:

1. neither the ball nor the bat is rigid. Both are elastic, and deform when the ball is struck.

2. Both are rotating (especially the ball) so there is "spin" angular momentum. The difference between a "hot" grounder and a "slow" roller.

3. The impact plane is not horizontal. The difference between a "high fly" and a "line drive".

So the actual physics is pretty complicated. I believe there is a book on the physics of baseball, but I do not have a title. Similar complicated physics occurs in various aspects in tennis, golf, soccer, billiards, table tennis -- in fact in any "hit-the-ball" sport or game.

Vince Calder


Dan,

There are definitely some problems here. Unfortunately I am not the right person to figure them all out. However, I may be able to point you in the right direction to figure them out for yourselves.

First, just because two objects meet does not mean they are exerting equal and opposite forces on each other. When the forces are unequal there is an acceleration. For example, consider pushing on a car. If the brakes are released and it is in neutral it will start to roll (i.e., it will accelerate). While the velocity is increasing you are exerting more force on the car than it is on you. Once it is rolling at constant speed then the two forces are equal. You are exerting just enough force to match the forces due to rolling friction (deformation of the tires, bearing friction, etc.).

The baseball undergoes a tremendous acceleration, from 90 mph to more than 90 mph in the opposite direction in a fraction of a second, and hence must have a large force applied to it. The bat undergoes a more modest acceleration but is a larger mass than the ball. Force is mass times acceleration. To figure out the force of the ball on the bat you would need to determine how much it accelerates in the collision.

Secondly, force is mass times acceleration [1 Newton is 1 kg-m/(second squared)], not velocity times distance [(meters squared)/second].

Hope this helps!

Greg Bradburn


There really is not space here to thoroughly explain force, velocity, distance, momentum, and energy. However, there does seem to be some confusion about these terms behind the question. For starters, force is NOT equal to velocity x distance. In fact, that product does not correspond to any commonly-used quantity. Force is mass x acceleration. The more massive an object is, or the more sharply it is accelerated, the greater the force must be.

If you were actually to follow the interaction between the ball and bat in these cases, you would certainly see that the forces between them change over time. You cannot just say "10 Newtons", because as the ball compresses and then bounces away from the bat, the force will increase and then decrease. The relative velocities, positions, and composition of both the ball and bat will affect the magnitude, direction, and time progress of the force between them.

The simple answer to your question is that at any time that the bat exerts 10 Newtons of force upon the ball, the ball in turn exerts 10 Newtons on the bat in the opposite direction. However, that answer does not provide any insight into the actual questions that underlie the questions you have stated.

A ball pitched by a 10-year old will surely be going slower and have less kinetic energy than a ball pitched by a major-league pitcher. To reverse the balls' directions and send them flying back into the outfield, the ball thrown by the major leaguer will need to have a much greater kinetic energy change than the ball thrown by the 10-year old.

The kinetic energy change is equal to (the force applied) x (the distance over which it is applied). For the 10-year old's and the major leaguer's pitch to be hit with the same force, the distance of contact will have to be much greater for the major leaguer's pitch. This really does not make any sense. In reality, when hitting a major leaguer's pitch, there will be more force, more kinetic energy transfer, and more momentum transfer than when hitting a 10-year old's pitch.



Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois



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