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are not. The changes in velocities of each are proportionate to the separate
bodies. As the horse continues to apply an increasing force, a point is arrived at
whereby the inertia of the load is overcome and the cart moves forward.
The example of a cannonball being shot from a cannon is a good illustration
of this concept. The forces on both cannon and cannonball are equal and
result in equal actions, but as a result of the explosion within the cannon, the
velocities of each object, cannon and cannonball, are different. The forward
motion of the cannonball is far greater than the velocity of the backward
motion of the cannon as a consequence of the difference in mass between
the two. The cannon may move a few feet backward, whereas the cannonball
will be projected over a much greater distance. If the mass of both objects
were the same, the velocity would be the same for both objects.
FIG 2.10 A cannonball moves
forward more quickly than the cannon
only because it possesses less mass.
The velocity of a rocket ship's exhaust as it is expelled from the rear of the rocket
during liftoff is far greater than the upward motion of the rocket, even though
the forces on both the thrust and the rocket are the same. The velocities of each
object are directly proportional to the object's mass, given that there are no
other factors involved, such as friction acting on one object and not the other.
FIG 2.11 The gasses shooting out
from a rocket move more quickly than
the rocket because they possess less
mass than the rocket.
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