Momentum Momentum

A.K.A. The difference between A.K.A. The difference between moving and standing still.moving and standing still.

DefinitionDefinitionMathematical

Momentum Momentum = Mass (kg) x Velocity (m/s)= Mass (kg) x Velocity (m/s)OrOr

p=mvp=mv

The units for momentum are kgm/sThe units for momentum are kgm/s

Verbal

Momentum is “inertia in motion”. Momentum is “inertia in motion”.

Remember Newton’s 1Remember Newton’s 1stst law. It’s law. It’s analogous to Inertia.analogous to Inertia.

Momentum = mass x Momentum = mass x velocityvelocity

• MomentumMomentum is a true measure of how is a true measure of how difficult it is to stop something.difficult it is to stop something.– A charging hippo can do some damage, A charging hippo can do some damage,

a hippo charging a hippo charging twicetwice as fast can do as fast can do twicetwice the damage. the damage.

– Calculating momentum is easy, just find Calculating momentum is easy, just find the mass and the velocity and multiply.the mass and the velocity and multiply.

p = mvp = mv– Notice that mass and velocity both Notice that mass and velocity both

affect momentum affect momentum equallyequally..

MomentuMomentumm

• 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?

a) 6.67 kgm/sb) 2160 kgm/sc) 138 kgm/sd) 0 momentums

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?

a) 0.267 m/sb) 3.42x108 m/sc) 3.74 m/sd) 0 m/s

ImpulseImpulse – where momentum – where momentum comes from!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 = FtI = m∆V = Ft

• The units for impulse are the same as momentum (kgm/s)

ImpulseImpulse

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

ImpulseImpulseJack 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?

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

Collisions and Conservation Collisions and Conservation of Momentum!of Momentum!

– A.K.A… problems!A.K.A… problems!

– By finding the momentum of the By finding the momentum of the “system” we can calculate the “system” we can calculate the speeds (velocity) of the 2 objects speeds (velocity) of the 2 objects after the collision.after the collision.

– Remember to GUESS!Remember to GUESS!

Conservation of momentum:Conservation of momentum:For collisions…For collisions…

ppii = p = pff

pp1i1i + p + p2i2i = p = p1f1f + p + p2f2f

mm11vv11 + m + m22vv22 = m = m11vv33 + m + m22vv44

((VV33 is the final velocity of m is the final velocity of m11 and V and V44 is is

the final velocity of mthe final velocity of m22))

Collisions!Collisions!– 2 types of collisions:2 types of collisions:

• ElasticElastic collision collision: : – 2 objects collide and then they 2 objects collide and then they

“bounce” off of each other “bounce” off of each other with no loss of Kinetic Energy. with no loss of Kinetic Energy.

• InelasticInelastic collision collision::– 2 objects collide and then they 2 objects collide and then they

“bounce” off of each other, “bounce” off of each other, but there is a loss of Kinetic but there is a loss of Kinetic Energy. Energy.

– What’s another What’s another example??

• Remember: In both Remember: In both situations momentum is situations momentum is always conserved!always conserved!

• 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?

a) 1.9 m/sb) 0.6 m/sc) 2.5 m/sd) 0 m/s

Example 1

m1 =

m2 =

V1 =

V2 =

V3 =

V4 =

• 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?

Example 2

Momentum is a vector Momentum is a vector Victor!!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/sB) 6 kgm/s C) 10 kgm/s

• 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?

Example 3

Perfectly Inelastic Collisions Perfectly Inelastic Collisions and Conservation of and Conservation of

Momentum!Momentum!– Now we are also going to work Now we are also going to work problems with perfectly problems with perfectly inelasticinelastic collisions.collisions.

– Remember: in perfectly inelastic Remember: in perfectly inelastic collisions two objects collide and collisions two objects collide and “stick” together, due to this kinetic “stick” together, due to this kinetic energy is lost.energy is lost.

– You can look at the momentum of You can look at the momentum of the “system” to figure out how fast the “system” to figure out how fast they will be traveling after they they will be traveling after they collide!collide!

– Also, explosions are considered Also, explosions are considered inelastic collisions, just backwards. inelastic collisions, just backwards. So, reverse the formula!So, reverse the formula!

Conservation of momentum:Conservation of momentum:For inelastic collisions…For inelastic collisions…

ppii = p = pff

mm11vv11 + m + m22vv22 = (m = (m11 + m + m22)v)v33

(V(V33 is the final velocity of the system) is the final velocity of the system)

• 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?

a) 9,000,000 m/sb) 0.04 m/sc) 25 m/sd) 0 m/s

Example 1

mm11vv11 + m + m22vv22 = (m = (m11 + m + m22)v)v33

• 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?

Example 2

mm11vv11 + m + m22vv22 = (m = (m11 + m + m22)v)v33

– ExplosionsExplosions are another type of are another type of perfectlyperfectly inelasticinelastic collision. collision.

– They are simular to the types of inelastic They are simular to the types of inelastic collisions we have seen, but just collisions we have seen, but just backwards. Kinetic Energy is gained.backwards. Kinetic Energy is gained.

– Two objects start as one mass, and Two objects start as one mass, and after the “collision,” become two after the “collision,” become two different masses.different masses.

– Formula:Formula:ppii = p = pff

(m(m11 + m + m22)V)V33 = m = m11VV11 + m + m22VV22

0 = m0 = m11VV11 + m + m22VV22

(The initial momentum of the system is (The initial momentum of the system is nearly always zero when the object nearly always zero when the object starts from rest.)starts from rest.)

Explosions!Explosions!

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

Explosions!Explosions!

• 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

Unit 3 – Momentumformulas!

Hammer timeHammer time2. 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?

a) Moving to the right.

b) Moving to the left.

c) They Stopped moving!

d) Could be any of the above.

Hammer timeHammer time4. 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?

a) Dr. Doom

b) The hammer

c) Both have the same

d) Depends on the velocity of the hammer

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?A. Both at still at rest

B. They are now floating away from each other

C. They are now floating toward each other

D. The first astronaut is floating away while the second is at rest