Newton's Third Law
Name: Dan R.
Date: Thursday, April 25, 2002
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.
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
Chris Murphy, PE
Mechanical Design Engineer
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
Dr. Ken Mellendorf
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
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.
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
Hope this helps!
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
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.
PG Research Foundation, Darien, Illinois
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