Momentum: Is the inertia of an object in motion. Momentum is a vector quantity. Remember this means it has a magnitude and direction. An object must have a velocity to have momentum. An object at rest has a momentum of zero.
The formula for momentum is the mass of the object x the velocity of the object or simply put (m)(v) The mass should be in kg and the velocity in m/s. There are no special units for momentum. See example below.
What is the momentum of a 200 kg motorcycle moving at 10 m/s?
Answer = 200 kg x 10 m/s = 2000 kg-m/s.
Does a more massive object always have more momentum?
1.) How about if a bowling ball and a tennis ball are moving
across a table at the same speed?
The bowling ball has more momentum because it has more mass
2.) What about a bowling ball moving across a table or a Tennis ball served by Venus Williams?
In this case the tennis ball probably has more momentum. Why? The bowling ball has a lot more mass but the tennis ball is moving at a much greater speed. Therefore, the tennis ball probably has more momentum. Remember it is the PRODUCT of the mass x the velocity. So a small object can have a lot of momentum if it is moving at a high velocity
According to Newton's first law, an object in motion will stay in motion unless an outside force acts on it. So to change the momentum of an object we must supply an outside force. Remember this force has to be applied over a time frame. For example you can stop your car by slamming on the brakes or by slamming in a tree. Which situation requires more time to stop? Which situation do you think applied the greater force?
This brings us to IMPULSE
The impulse is the product of the force x the time it takes to act. (F x t) To change the momentum of an object, you must supply an impulse. See equation below:
change in momentum = impulse or change in mv=Ft
When changing the momentum of an object you have two ways of doing it. You can
1.) apply a large force over a short time or
2.) apply a small force of a large time.
REMEMBER IN EACH CASE THE IMPULSE IS THE SAME ( the product of the force x the time)
Remember the egg toss that we did in class. You can either stop the egg by throwing it a blanket, or you can stop an egg by letting it land on the floor.
In which case was the force greater? ( the egg on the floor)
In which case was the time to stop greater? (the egg in the blanket)
In which case was there a larger Impulse applied? ( THE SAME FOR BOTH)
Remember this is why air bags in cars are so effective. If you can double the time it takes to stop your head moving forward then the force required to stop it will be cut in half. If you increase the time, you decrease the force but the product must always be the same.
This also applies when trying to increase the momentum of an object. Remember the two blow guns that we looked at in class.
Which tube could I blow through harder? (both are the same you can only blow so hard)
Which tube applied the larger impulse ( the long tube because the dart is in the barrel longer and as long as it is in the barrel there is a force acting on it)
Which tube did the dart have a higher velocity? ( the long tube because it had a greater impulse and thus could provide a greater change in momentum to the dart)
When is there a greater momentum change when an object bounces or sticks in a collision?
An elastic collision is when there is a perfect bounce. Think of when a super ball hits the floor and bounces back. It is an elastic collision because there is a bounce and not a stick.
An inelastic collision is when the two objects stick together when they collide. When you throw a dart into a dart board that is an inelastic collision because the dart sticks in the board.
In which case is there a greater change in momentum?
Conservation of momentum
Whether the collision is elastic or inelastic the total momentum of the system is always conserved! What does this mean? Lets look at two examples:
1.) Car A has a mass of 4 kg and is moving east at 2 m/s. It collides in an elastic collision with car B of mass 4 kg that is initially at rest. After the collision, car A stops and car B moves off with a velocity of 2 m/s. Was momentum conserved?
momentum before = Car A (4 kg)(2 m/s) = 8 kg-m/s Car B = (4 kg)(0 m/s) = 0 kg-m/s Total momentum before = 8+0=8
momentum after =Car B (4 kg)(2 m/s) = 8 kg-m/s Car A = (4 kg)(0 m/s) = 0 kg-m/s Total momentum after = 8+0=8
Momentum before = momentum after
2. Car A has a mass of 4 kg and is moving east at 5 m/s. It collides with car B in an inelastic collision (stick together) with car B of mass 6 kg that is initially at rest. After the collision the stuck together cars move off with a velocity of 2 m/s. Was momentum conserved?
momentum before = Car A (4 kg)(5 m/s) = 20 kg-m/s Car B = (6 kg)(0 m/s) = 0 kg-m/s Total momentum before = 20+0=20
momentum after =Car B and A are stuck together so the total mass is (10 kg)(2 m/s) = 20 kg-m/s Total momentum after = 20
Momentum before = momentum after
Here is a website that can help you to visualize these collisions
Can you use this information to solve the velocity of a car after a collision? Try these two examples: ( look at the calculation corner on page 79 of your text if you need help)
1.) Car A has a mass of 6 kg and is moving east at 2 m/s. It collides with car B of mass 2 kg that is initially at rest. After the collision, car A stops and car B moves off with a new velocity. What is the velocity of car B? (answer = 6 m/s)
2.) Car A has a mass of 7 kg and is moving east at 3 m/s. It collides in a collision with car B of mass 2 kg that is initially at rest. After the collision, car A moves with a velocity of 1 m/s. What is the velocity of car B? Was momentum conserved? (answer = 7 m/s)
3.) Car A has a mass of 10 kg and is moving east at 3 m/s. It collides with car B in an inelastic collision (stick together) with car B of mass 5 kg that is initially at rest. After the collision the stuck together cars move off with what velocity? (answer = 2 m/s)
Having fun with toys that show momentum..
video one, video two, video three, video four, video five, video six
