A Classical Approach of Newtonian Mechanics

6 CONSERVATION OF MOMENTUM 6.6 Collisions in 1 - dimension

(^)
before
after
Figure 54: A collision in 1 - dimension.
The net change in momentum of an object subject to f(t) is
∆p = I. (6.36)
Finally, if t 2 − t 1 = ∆t, then the average force experienced by the object in the
time interval t 1 to t 2 is
̄f = I
∆t

. (6.37)

6.6 Collisions in 1 - dimension

Consider two objects of mass m 1 and m 2 , respectively, which are free to move

in 1-dimension. Suppose that these two objects collide. Suppose, further, that

both objects are subject to zero net force when they are not in contact with one

another. This situation is illustrated in Fig. 54.

Both before and after the collision, the two objects move with constant velocity.

Let vi1 and vi2 be the velocities of the first and second objects, respectively, before

the collision. Likewise, let vf1 and vf2 be the velocities of the first and second

objects, respectively, after the collision. During the collision itself, the first object

exerts a large transitory force f 21 on the second, whereas the second object exerts

an equal and opposite force f 12 = −f 21 on the first. In fact, we can model the

collision as equal and opposite impulses given to the two objects at the instant in

time when they come together.

We are clearly considering a system in which there is zero net external force

(the forces associated with the collision are internal in nature). Hence, the total

m 1

vf1

m 2

vf (^2)
m 1
vi1
m 2
vi2