Momentum The secret of collisions and explosions

Who Pushes Who Rin Tin Tin and the Refrigerator meet at the 50 yard line Mass 20 Kg Speed 17 m/s Mass 160 Kg Speed 2 m/s Who pushes who over the 50 yard line?

Momentum = Mass x Velocity Whoever has the most momentum = mv wins Mass 20 Kg Speed 17 m/s Mass 160 Kg Speed 2 m/s Momentum = 340 Kg m/s Momentum = 320 Kg m/s

Momentum = mv Mass times velocity! Velocity is a vector but here we can usually think of it as speed Example: A speeding car has a mass of 1000 Kg and a speed of 20 m/s. What is its momentum? mv = 1000kg x 20 m/s = 20,000 kg m/s

Unit of Momentum Kg m/s No nickname like “Newton;” maybe it could have been called an “Isaac.” Jump to conservation

Momentum is a Vector p = mv Force is required to change the momentum of an object. Newton stated his 2 nd law:  F =  p/  t  The rate of change of momentum of a body equals the net force exerted on it  Equivalent to F = ma

Proof of equivalence of two forms of Newton’s 2 nd Law  F =  p/  t = (mv –mv 0 )/  t = m(v - v 0 )/  t = m  v/  t = ma Q: Which form of the law is more general? (which includes the possibility that the mass could change?)

Example Water leaves a hose at a rate of 1.5 kg/s with speed 20 m/s and hits a car without splashing back. What force is exerted by the water on the car? F =  p/  t = (p final - p initial )/  t = (0 – 30kg m/s)/1sec = -30N

Momentum is Conserved The total momentum of an isolated system of bodies remains the same “isolated” means net external force is zero Momentum before = momentum after m 1 v 1 + m 2 v 2 = m 1 v 1 ’ + m 2 v 2 ’ Applies to all interactions, especially collisions, explosion-like events, and “dumpings” Closely related to Newton’s 3 rd law

Law of Conservation of Momentum Momentum before = momentum after m 1 v 1 + m 2 v 2 = m 1 v 1 ’ + m 2 v 2 ’ Apostrophe thingee is pronounced “prime”

Two Kinds of Collision Inelastic - sticking Examples: glue balls fly into each other,air track gliders with clay Elastic – bouncing Examples: hard balls or protons collide Courtesy St. Mary College Physics Department Courtesy Deer Vally HS Espace Academy

Two Kinds of Collision(video) Inelastic - sticking Examples: glue balls fly into each other,air track gliders with clay Elastic – bouncing Examples: hard balls or protons collide Courtesy St. Mary College Physics Department Courtesy Stephanie Wong

Video Full Screen

New Vocabulary Momentum Conserved Isolated Elastic collision Inelastic collision Mass times velocity Stays the same By itself, net force on it is zero Objects bounce Objects stick

Objects moving toward each other If two carts of equal mass approach each other with equal speed what is the total momentum before collision? Answer: zero

Dumping Example A 10 kg cart rolls on a frictionless track at speed v. Suddenly 10 kg of rocks are dropped straight down into the cart. What happens to its speed? How come? Answer v/2 ; momentum mv is conserved, m doubled so v must go in half. Courtesy Easyhaul Cart Inc.

Explain This A rock falls to earth. Is momentum conserved? Include earth in your explanation Does the earth really come up to meet the rock?

You Predict Glider moving with speed v hits glider of equal mass at rest. They stick. What will be speed of stuck together gliders after the collision? Answer: v/2

Railroad Cars Collide Inelastically(stick) A 10,000 kg railcar moving 2.4 m/s hits and sticks with an identical car at rest. What is the final speed of the two cars? m 1 v 1 + m 2 v 2 = (10,000 kg) (2.4 m/s) + 0 = 2.4 x 10 4 kg m/s = (m 1 + m 2 )v’ v’= 2.4 x 10 4 kg m/s /2.0 x 10 4 kg = 1.2 m/s

New example A 3 kg glider moves to the right at 4.0 m/s and collides inelastically with a 1 kg glider at rest. What is the final speed of the two joined together gliders? 12 kg m/s = 4kg x v f v f = 3 m/s

Next example A 3 kg glider moves to the right at 4.0 m/s and collides inelastically with a 1 kg glider moving to the right at 1.0 m/s. What is the final speed of the two joined together gliders? 12 kg m/s + 1kg x 1 m/s = 13 kg m/s = 4.0 kg v f v f = 3.25 m/s

Next example A 3 kg glider moves to the right at 4.0 m/s and collides inelastically with a 1 kg glider moving to the right at 2.0 m/s. What is the final speed of the two joined together gliders? 12 kg m/s + 1kg x 2 m/s = 14 kg m/s = 4.0 kg v f v f = 3.50 m/s

Next example A 3 kg glider moves to the right at 4.0 m/s and collides inelastically with a 1 kg glider moving to the left at 1.0 m/s. What is the final speed of the two joined together gliders? 12 kg m/s - 1kg x 1 m/s = 11 kg m/s = 4.0 kg v f v f = 2.75 m/s

Next example A 3 kg glider moves to the right at 4.0 m/s and collides inelastically with a 1 kg glider moving to the left at 5.0 m/s. What is the final speed of the two joined together gliders? 12 kg m/s - 1kg x 5 m/s = 7 kg m/s = 4.0 kg v f v f = 1.75 m/s

Next example A 3 kg glider moves to the right at 4.0 m/s and collides inelastically with a 1 kg glider moving to the left at 20.0 m/s. What is the final velocity of the two joined together gliders? 12 kg m/s - 1kg x 20 m/s = -8 kg m/s = 4.0 kg v f v f = m/s

Sled Collision Kids on a sled, total mass 100kg move to the right at 4.0 m/s. They collide inelastically with other kids, mass 150 kg, moving to the left at 2.5 m/s. Find the final velocity of the two sleds.

solution m 1 v 1 + m 2 v 2 = m 1 v 1 ’ + m 2 v 2 ’ 100Kg x 4m/s –150Kg x 2.5m/s = 400 Kg m/s – 375 Kg m/s = 25 Kg m/s = 250 Kg x v f V f = 0.1 m/s

Sled Collision in reverse Kids on a sled, total mass 100kg move to the right at unknown speed v. They collide inelastically with other kids, mass 150 kg, moving to the left at 2.5 m/s. The final velocity of the two sleds is 0.2 m/s. Find v V = 4.25 m/s

Explosion like Event If a stationary student on a skateboard throws a rock with momentum 10 kg m/s, what momentum will the student get? Answer; -10 kg m/s

Recoil of a pistol(explosion- like event) What is the recoil velocity of a 1 kg pistol that shoots a.02 kg bullet at 400 m/s? Initial momentum = 0 = m B v B +m p v p = (0.02kg x 400 m/s) + 1kg x v p v p = - 8 m/s Q: Does the shooter recoil too? Skip think and explain # 8

Think and Explain 8) m 1 v 1 + m 2 v 2 = m 1 v 1 ’ + m 2 v 2 ’ Let mass of flat car = m Then mass of diesel engine = 4m V 1 = 5 km/hv 2 = 0 4m * 5 km/h + 0 = 5 m V f 20 m = 5m V f V f = 4 km/h

9) A) 5 kg * 1 m/s + 0 = 6 kg V f V f = 5/6 m/s B) 5 kg * 1 m/s – 1 kg * 4 m/s = 6 kg * V f 5 kg * m/s – 4 kg * m/s = 6 kg * V f 1 Kg * m/s = 6kg V f V f =1/6 m/s

“Impulse” Why should you Bend your knees when you land? Pull back when the baseball enters your mitt? Follow through when you swing? Not walk into a punch? (like Mike Tyson did)

Impulse Impulse = F  t =  p Impulse is product of force and time during which force acts Impulse equals change of momentum F is usually non uniform and time interval is usually short

You Predict Two gliders of equal mass collide elastically. The first is moving with speed v. The second is at rest. What happens? First one stops, second moves off at speed v But why? Find the answer yourself and get extra credit

Energy Conservation in Elastic and Inelastic Collisions Elastic – kinetic energy is conserved as well as momentum and total energy Inelastic – kinetic energy is not conserved – some energy turns into heat Elastic – bounce Completely inelastic - stick

Ballistic Pendulum A bullet of mass m is fired into a block of wood of mass M suspended from a string. The bullet remains in the block which rises a height h. What was the speed of the bullet? Show that v = (2gh) 1/2 (m + M)/m h

Collisions in Two Dimensions Remember momentum p is a vector x and y components are conserved separately What is the total vertical momentum? 11 22