Goal: To understand momentum Objectives: To Learn about What momentum is To learn about how to calculate Momentum in 2 dimensions To understand How is momentum changed? To understand the Conservation of momentum To learn about Why momentum is useful to understand. Tomorrow: To learn about applications to the conservation of momentum

What is momentum In reality momentum is quite simply a measure of your ability to create change. Momentum = p = mv Lets do a quick sample: 1) A car with mass of 500 kg moves at a velocity of 20 m/s. What is the car’s momentum?

Another example: Two cars are headed towards one another. The first car has 700 kg of mass and moves at a velocity of 20 m/s North The 2nd car has 1400 kg of mass and moves at a velocity of 10 m/s South. What is the combined momentum of the cars (yes momentum has direction)?

Momentum in 2 dimensions… Each dimension has momentum. So, you have to find the total momentum for each dimension separately. Then at the end you can get a magnitude if you want, but usually it is more useful to keep them separate much like you keep a checking account separate from a savings account.

Straight Foreward 2 D question A car is heading North with a mass of 1000 kg and a velocity of 12 m/s. A 2nd car is heading East with a mass of 750 kg and a velocity of 20 m/s. Which car has a greater magnitude of momentum? What is the combined magnitude of momentum for both cars combined

Changing momentum How do you change momentum? You use what is called an “impulse”. Impulse = change in momentum Impulse = mass * change in velocity Impulse = F * t Note that F = ma So, Impulse = m * (a * t) What does acceleration * time equal?

Example: A car runs into a mailbox. The mass of the mailbox is 10 kg and the mass of the car is 800 kg. If the car imparts a 2000 N force to the mailbox for 0.4 seconds find: A) The impulse on the mailbox B) The new velocity of the mailbox (set impulse = to mass * change in velocity)? C) What is the impulse the mailbox imparts on the car? (What, you have forgotten about Newton’s 3rd law already?) D) How much does the car’s momentum change? E) What is the net change in momentum (i.e. if you add the changes in momentum of the car and mailbox what do you get)?

Conservation of momentum! Momentum is almost always conserved in a collision. In fact it is conserved for each dimension. Total p before = Total p after Quick question – will kinetic energy be conserved?

Energy? Sometimes kinetic energy is also conserved. Collisions that conserve kinetic energy are called elastic collisions. Collisions where energy is not conserved are called inelastic collisions.

“Oooh, oooh, fender bender” The pips from that car commercial In many collisions energy is transferred. Energy is transferred to sound energy, heat energy, and used to crumple a car. These collisions are always inelastic collisions. So, if you get hit by a car, you want it to be an elastic collision! You will fly faster and further, but the initial impact won’t use energy to bend and break things.

Rear end crash A speeding car of mass 800 kg attempting to elude the police crashes into a 600 kg car sitting parked at the intersection. Ignoring brakes and friction, if the initial velocity of the speeding car is 50 m/s forward and the final velocity of the speeding car is 10 m/s forward then what will the final velocity of the other car be? There are 2 ways to do this problem

Head on collision Car 1: 25 m/s East and a mass of 800 kg. Car 2: 30 m/s West and a mass of 900 kg. A) What is the net momentum of the two cars combined before the collision. C) After the crash Car 1 moves West at a velocity of 5 m/s. What will the final velocity of car 1 be? Hint, total momentum

T Bone! Car 1: mass of 650 kg and headed North at 10 m/s Car 2: mass of 750 kg and headed west at 5 m/s. Car 1 T Bones Car 2 and car 1 comes to a complete stop. A) Before the crash what are the momentums in the north and west directions? B) After the crash how much momentum will car 1 have? C) After the crash what is the north and west velocity of Car 2 (hint: will the west velocity change?) D) What is the magnitude of the final velocity for car 2?

If time: Ball off a wall You bounce a 0.15 kg ball off of the wall. The ball hits the wall at 20 m/s forward and when it bounces it returns (backward) at 80% of the SPEED of when it hit the wall. A) What is the change in velocity for the ball (remember direction)? B) What is the change in momentum? C) If the ball is in contact with the wall for 0.6 seconds then what is the average force that the wall imparts to the ball? D) What is the acceleration the wall gives the ball?

Conclusion Momentum = mass * velocity Momentum is conserved! Momentum is conserved in every direction! If you run into something – or it runs into you – at high velocity – don’t bounce!