UNDERSTANDING MOMENTUM
Momentum is the “quantity of motion” that an object has, or how much motion is “in”
an object. For example a moving car has some quantity of motion, but a parked car has
no quantity of motion. Momentum is found by multiplying an object’s mass times its
speed. Unlike force, there is no special unit like a Newton. So the units are kg x m/s.
Here is the formula:
Momentum = kg x m/sec.
Try these momentum problems:
1. A ball’s mass is 30 kg and rolls at 20 m/sec. What is its momentum?
30 kg x 20 m/s = 600 kg ∙ m/s
2. A boy’s mass is 50 kg and he runs at 3 m/sec. What is his momentum?
50 kg x 3 m/s = 150 kg ∙ m/s
3. A comet’s mass is 3 x 1012 kg and has a terminal velocity of 1000 m/sec as it enters
the atmosphere. What is its momentum?
3 x 1012 x 103 = 3 x 1015
4. Do these objects possess any force? (the ball, the boy, the comet) Explain.
No; momentum is mass x speed, not mass x acceleration. Force = mass x acceleration
5. Are force and momentum the same thing? Explain.
Force and acceleration are different. Force = kg x m/s2, Momentum = kg x m/s
Remember that force is defined as F = kg x m/sec2 (mass x acceleration). But
momentum is defined as momentum = kg x m/second (mass x speed).
Momentum is not force. Objects moving at constant speed have no force until they
accelerate (or decelerate). Consider that you feel no force in a car moving at a constant
speed, but if the car speeds up or slows down you feel this force of acceleration. And you
know that as the Earth travels through space you do not feel this motion, as the speed of
the earth through space is constant or, it’s not accelerating. Actually it is changing speed
in many ways, but this acceleration happens too slowly over a human lifetime to notice!
Conservation of Momentum
When a moving object collides with another object (moving or not) there is a transfer of
momentum. The transfer is such that the total momentum before and after the collision
remains equal. For example, if a moving car hits a parked car (with the brake off and of
equal mass) the parked car will get all the momentum of the first car ideally. In other
words, the first car stops and the parked car moves away at the speed that the first car
had. Since momentum = kg x m/sec. it’s easy to solve conservation of momentum
problems. Here’s an example:
Car A (mass 50 kg, moving 10 m/sec) hits car B (50 kg, 0m/sec.) the total momentum
before is (50 kg x 10 m/sec.) + (50 kg x 0m/sec) = 500 kg x m/sec. What is the
momentum afterwards? It is always equal to the momentum before so it must be
500 kg x m/sec. afterwards!
(Turn the paper over!)
Now, if the car B moves off at 10 m/sec., what is the speed of car A after the collision?
Since the momentum is the same before and after, divide the total momentum (500 kg x
m/s) by the momentum of car B after the collision (50 kg x 10 m/s). Note that to figure
out the momentum of car B after the collision you must multiply its mass by its new
speed. You will see that all the momentum was transferred to Car B, since the total
momentum afterwards (500kg x m/s) divided by the new momentum of car B (500 kg x
m/s) = 1. The number 1 tells you that car B took all the momentum, or the momentum
is wholly transferred to car B. Therefore car A has 0 speed, since its mass x 0 would
equal 0 (it has no momentum after the collision).
Draw a picture to illustrate the just described transfer of momentum. Label the masses
and speeds of the cars and show the total momentum before and after.
Car A before: 50 kg x 10 m/s = 500 kg ∙ m/s
Car B before: 50 kg x 0 m/s = 0 kg ∙ m/s
Total momentum before = 500 kg ∙ m/s + 0 kg ∙ m/s = 500 kg ∙ m/s
Car A after: 50 kg x 0 m/s = 0 kg ∙ m/s
Car B after = 50 kg x 10 m/s = 500 kg ∙ m/s
Total momentum after = 0 kg ∙ m/s + 500 kg ∙ m/s = 500 kg ∙ m/s It’s the same!
Now try these problems:
A toy train car A (mass 10 kg, moving 5 m/sec.) hits a toy train car B (mass 5 kg, moving
10 m/sec.). What is the total momentum before and after the collision, and what is the
speed of car A if car B moves away after the collision at 5 m/sec.?
(10 kg x 5 m/s) + (5 kg x 10 m/s) = 100 kg ∙ m/s This is the total mom. before & after!
100 kg ∙ m/s – (5 kg x 5 m/s) = 75 kg ∙ m/s (Total mom. – the new mom. of Car B)
(75 kg ∙ m/s)/10 kg = 7.5 m/s By dividing the remainder (new mom. Car A) by the mass
of Car A, we have found its new speed (7.5 m/s)
A toy train car (mass 10 kg, speed 5m/sec.) hits a toy train car B (mass 10 kg, 0 m/sec.)
and they couple (their masses combine!). What is the total momentum before and after
the collision and what is their coupled speed after the collision?
(10 kg x 5 m/s) + (10 kg x 0 m/s) = 50 kg ∙ m/s This is the total mom. before & after!
(50 kg ∙ m/s)/(10 kg + 10 kg) = 2.5 m/s By dividing the total mom. by the combined
mass (20 kg), we get the speed for the combined cars (2.5 m/s)
Which has more momentum, a cannonball with mass 100 kg moving at 1 m/sec. or a ping
pong ball with mass 0.001 kg moving at 109 m/sec.? The ping pong ball. cannonball =
100 kg x 1 m/s2 = 100 kg ∙ m/s ping pong ball = 10-3 kg x 109 m/s = 106 kg ∙ m/s
Write the units of momentum and the units of force. Describe how mass and momentum
are different. momentum = kg ∙ m/s, force = kg ∙ m/s2 Momentum has no force.