 Momentum 

1.  Momentum  A.K.A. The difference between moving and standing still.

2. Definition Mathematical Momentum = Mass (kg) x Velocity (m/s) Or p=mvThe units for momentum are kgm/s • Verbal • Momentum is “inertia in motion”. • Remember Newton’s 1st law. It’s analogous to Inertia.

3. Momentum = mass x velocity • Momentum is a true measure of how difficult it is to stop something. • A charging hippo can do some damage, a hippo charging twice as fast can do twice the damage. • Calculating momentum is easy, just find the mass and the velocity and multiply. p = mv • Notice that mass and velocity both affect momentum equally.

4. Momentum • How much momentum does Hulk Hogan have if he has a mass of 120 kg and runs at you with a velocity of 18 m/s? • 6.67 kgm/s • 2160 kgm/s • 138 kgm/s • 0 momentums

5. Momentum • A train has a mass of 7.22x107 kg and a momentum of 2.7x108 kgm/s. What is the velocity of the train? • 0.267 m/s • 3.42x108 m/s • 3.74 m/s • 0 m/s

6. Impulse – where momentum comes from! • Only a force can “give” something momentum (or take it away). • Lets say you are a member of a bobsled team. You push the sled to speed it up. The longer the you push the sled the greater the velocity and the greater the momentum you give it so time is also a factor. • Or think about the airbags in your car. They give you more time to slow down so less force is applied to your body. • So… a force applied for a certain time leads to a change in momentum. • Δp = (Force) x (time) This is called an impulse (I) I = Ft • Impulse is a change in momentum (∆mV)∆mV = Ft I = m∆V = Ft • The units for impulse are the same as momentum (kgm/s)

7. Impulse A stuntman jumps off a building while shooting “Die Hard VIII: Die Already!” If the airbag he lands on is able to catch him by applying a force of 1,500 N over 2.5 seconds, what is the impulse applied to the stuntman (how much does it change his momentum)? I = Ft

8. Impulse Jack throws a 0.5 kg basketball at Jill with a velocity of 12 m/s. How much force would Jill need to apply to stop the ball in 1.2 seconds?

9. Momentum is Conserved! Meaning: Once an object has momentum it is going to keep it OR give it to something else! IT does not just disappear! Conservation of momentum:The total amount of momentum in a system does not change!!! pi = pf

10. Collisions and Conservation of Momentum! • A.K.A… problems! • By finding the momentum of the “system” we can calculate the speeds (velocity) of the 2 objects after the collision. • Remember to GUESS! • Conservation of momentum: • For collisions… • pi = pfp1i + p2i = p1f + p2fm1v1 + m2v2 = m1v3 + m2v4(V3 is the final velocity of m1 and V4 is the final velocity of m2)

11. Collisions! • 2 types of collisions: • Elastic collision: • 2 objects collide and then they “bounce” off of each other with no loss of Kinetic Energy. • Inelastic collision: • 2 objects collide and then they “bounce” off of each other, but there is a loss of Kinetic Energy. • What’s another example? • Remember: In both situations momentum is always conserved!

12. Example 1 • You are playing pool with a friend and kicking butt. You hit the cue ball at 2.5 m/s towards the 8 ball which is at rest. After they collide elastically the cue ball continues at a velocity of 0.6 m/s. If the mass of both balls is 1.5 kg, what is the final velocity of the 8 ball? • 1.9 m/s • 0.6 m/s • 2.5 m/s • 0 m/s m1 = m2 = V1 = V2 = V3 = V4 =

13. Example 2 • Bill is out cruising in his brand new Kia until he hits some crazy traffic on IH-35. Ohh no! He just got rear-ended (in an elastic collision) by some jerk in a giant 2000 kg truck with an initial velocity of 17 m/s! Bill’s Kia has a mass of 850 kg and he was initially traveling at 0.75 m/s. If the jerk’s truck continued with a velocity of 10 m/s after the collision, what is his final velocity after the collision?

14. Momentum is a vector Victor!! • Direction is important! • 2 vectors in the opposite direction will subtract. • 2 vectors in the same direction add together. • Think about the velocities of the objects. Positive is to the right (or “east”), negative is to the left (or “west”). Example: 2 identical lumps of clay fly toward each other. They each have a mass of 2 kg. One is moving at 5 m/s and the other at 8 m/s. • What is the total momentum of the system? A) 26 kgm/s B) 6 kgm/s C) 10 kgm/s

15. Example 3 • Jimmy is playing with his Hotwheel cars! He has a truck that has a mass of 1.1 kg, and a sports car that has a mass of 0.75 kg. Jimmy wants them to crash in an elastic collision, so he gives the truck a velocity of 5.6 m/s to the right, and gives the car a velocity of 3.9 m/s to the left. If the velocity of the truck is 1.2 m/s to the right after the crash, what is the final velocity of the car after the collision?

16. Perfectly Inelastic Collisions and Conservation of Momentum! • Now we are also going to work problems with perfectly inelastic collisions. • Remember: in perfectly inelastic collisions two objects collide and “stick” together, due to this kinetic energy is lost. • You can look at the momentum of the “system” to figure out how fast they will be traveling after they collide! • Also, explosions are considered inelastic collisions, just backwards. So, reverse the formula! • Conservation of momentum: • For inelastic collisions… • pi = pfm1v1 + m2v2 = (m1 + m2)v3 • (V3 is the final velocity of the system)

17. Example 1 • The flash (100 kg) collides with the Blob (500 kg) at a velocity of 150 m/s and gets wedged into some of the Blob’s bellyfat so that they stick together. What will the new velocity of the blob/flash system be if the blob was initially at rest? • 9,000,000 m/s • 0.04 m/s • 25 m/s • 0 m/s • m1v1 + m2v2 = (m1 + m2)v3

18. Example 2 • Bill is out cruising in his new Mercedes until he hits some crazy traffic on Loop 360. Ohh no! He just got rear-ended again (in an inelastic collision) by the same jerk in 1000 kg corvette with an initial velocity of 17 m/s! If Bill’s Mercedes has a mass of 850 kg and he was initially traveling at 0.75 m/s, what is his final velocity after the collision? • m1v1 + m2v2 = (m1 + m2)v3

19. Explosions! • Explosions are another type of perfectlyinelastic collision. • They are simular to the types of inelastic collisions we have seen, but just backwards. Kinetic Energy is gained. • Two objects start as one mass, and after the “collision,” become two different masses. • Formula:pi = pf(m1 + m2)V3 = m1V1 + m2V20 = m1V1 + m2V2 (The initial momentum of the system is nearly always zero when the object starts from rest.)

20. Explosions! • Problem: A hand grenade is at rest when it explodes into two pieces that go flying in opposite directions. The mass of one piece is 2.3 kg and it flies to the right with a velocity of 54.9 m/s. What is the mass of the second piece if it flies to the left with at 78.1 m/s?

21. Unit 3 – Momentumformulas! • Momentum = mass x velocity • p = mv • Conservation of Momentum (CoM): • pi = pf • Inelastic and Elastic Collisions – objects “bounce” off each other. • m1v1 + m2v2 = m1v3 + m2v4 • Perfectly Inelastic Collisions – objects “stick” to each other. • m1v1 + m2v2 = (m1 + m2)v3 • ^ For explosions, reverse this formula! • Impulse – Change in momentum • I = ∆p = Ft

22. Hammer time • Thor successfully hits Doom in the chest with exactly the same amount of momentum that Doom had (but in the opposite direction). If the hammer sticks to Doom (inelastic collision) what must Doom and the hammer be doing after the collision? • Moving to the right. • Moving to the left. • They Stopped moving! • Could be any of the above.

23. Hammer time 4. Thor successfully hits Doom in the chest with exactly the same amount of momentum that Doom had (but in the opposite direction). If the hammer sticks to Doom (inelastic collision) which experiences an larger impulse? • Dr. Doom • The hammer • Both have the same • Depends on the velocity of the hammer

24. Two astronauts are floating at rest in space. One astronaut throws a tool to the other one, who catches it. What is their motion after transferring the tool? • Both at still at rest • They are now floating away from each other • They are now floating toward each other • The first astronaut is floating away while the second is at rest [Default] [MC Any] [MC All]