Linear Momentum and Collisions
Answers to Even-numbered Conceptual Questions
Doubling an object’s speed increases its kinetic energy by a factor of four, and its
momentum by a factor of two.
For example, suppose object 2 has four times the mass of object 1.
In this case, the
two objects have the same kinetic energy if object 2 has half the speed of object 1.
other hand, it follows that the momentum of object 2 is twice the momentum of object 1.
Consider, for example, a system of two particles.
The total momentum of this system
will be zero if the particles move in opposite directions with equal momentum.
kinetic energy of each particle is positive, however, and hence the total kinetic energy is
The force due to braking – which ultimately comes from friction with the road –
reduces the momentum of the car.
The momentum lost by the car does not simply
Instead, it shows up as an increase in the momentum of the Earth.
As with braking, the ultimate source of the force accelerating the car is the force of static
friction between the tires and the road.
It is better if the collision is inelastic, because then the light pole gives your car only
enough impulse to bring it to rest.
If the collision is elastic, the impulse given to your car
is about twice as much.
This additional impulse – which acts over a very short period of
time – could cause injury.
The rate of change in momentum is the same for both objects.
As a result, the rate of
change in velocity for the less massive object (the pebble) must be greater than it is for the
more massive object (the boulder).
Alternatively, we know that the acceleration (rate of
change in velocity) of an object is proportional to the force acting on it and inversely
proportional to its mass.
These objects experience the same force, and therefore the less
massive object has the greater acceleration.
Just point the fan to the rear of the boat.
The resulting thrust will move the boat
Any collision between cars will be at least partially inelastic, due to denting, sound
production, heating, and other effects.
For example, we know that in a one-dimensional elastic collision of two objects of
equal mass the objects “swap” speeds.
Therefore, if one object was at rest before the
collision, it is possible for one object to be at rest after the collision as well.
See Figure 9-
The speed of the ball when it leaves the tee is about twice the speed of the club.
follows for two reasons:
(i) The collision is approximately elastic; and (ii) the mass of the
club and the arms swinging the club is much greater than the mass of the ball.