Download Note 13 Newton`s Third Law

Note 13 Newton’s Third Law
Newton’s second law is about the forces and the acceleration of an object. Newton’s third law
connects the forces between objects.
Experimenting with Newton’s Third Law
Let’s say I have two identical, frictionless carts of the same mass on a track. One moves toward
the other at some speed.
31.4 cm
36.7 cm
The two carts collide and each cart applies a force to the other.
force of right cart
on left cart
force of left cart
on right cart
Here is the result. The first cart stops and the second cart moves.
47.9 cm
53.2 cm
The before-collision speed of the left cart is 5.3 cm per 5/30 second or 31.8 cm/s to the right. The
after-collision speed of the right cart is also 5.3 cm per 5/30 second or 31.8 cm/s to the right.
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Formulating Newton’s Third Law
Let’s look the the right cart first. Here is its free-body diagram.
right cart
Fpush left on right
Let me set this to be the positive x direction. Newton’s second law says this.
!
!
ΣFx = max
!
!
Fpush from left cart on right cart = max
We measured that, during the collision, the speed of the right cart went from 0 m/s to +31.8 cm/s.
The time of the collision itself is about 3/30 second. The average acceleration of the right cart is
!
Δvx
!
31.8 cm/s − 0 cm/s
ax =
=
= 318 cm/s 2
Δt
3/ 30 s
The force applied to the right cart then is, assuming a constant, average force,
!
Fpush
from left cart on right cart
= (250 g)(318 cm/s 2 ) = (0.25 kg)(3.18 m/s 2 ) = 0.0795 N
Let’s look the the left cart. Here is its free-body diagram.
left cart
Fpush right on left
Newton’s second law says this.
!
!
ΣFx = max
!
!
Fpush from right cart on left cart = max
We measured that, during the collision, the speed of the left cart went from 31.8 cm/s to 0 cm/s.
The collision time is about 3/30 second. The average acceleration of the left cart is
!
Δvx
!
0 cm/s − 31.8 cm/s
ax =
=
= −318 cm/s 2
Δt
3/ 30 s
The force applied to the left cart then is this. The collision time is the same as for the right cart.
!
Fpush from right cart on left cart = (250 g)(−318 cm/s 2 ) = (0.25 kg)(−3.18 m/s 2 ) = −0.0795 N
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Newton’s Third Law of Motion
You can do the above experiment on any two objects acting on each other and you will always find
that the two forces each applies to the other have the same magnitude and in opposite directions.
Newton’s third law of motion says that the force one object applies to another object is the same
as the force the other object applies to the first but in the opposite direction.
In equation form, it is
!
!
Ffrom A on B = −Ffrom B on A
These two forces are call a Newton’s third law pair.
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