Momentum Chin-Sung Lin

Momentum A property of moving things Means inertia in motion Mass of an object multiplied by its velocity In equation form: momentum = mass  velocity p = mv Unit of momentum: kgm/s

Momentum Example What’s the momentum of a 1000 kg car moves at 20 m/s ?

Momentum Example What’s the momentum of a 1000 kg car moves at 20 m/s ? p = mv = 1000 kg x 20 m/s = 20000 kg m/s

Momentum Exercise Compare the momentum of a 2000 kg van moving at 30 m/s with a 5000 kg truck moving at 12 m/s.

Momentum Example: A moving boulder has more momentum than a stone rolling at the same speed A fast boulder has more momentum than a slow boulder. A boulder at rest has no momentum

When the speed of an object is doubled, its momentum remains unchanged in accord with the conservation of momentum doubles quadruples decreases B. doubles.

When the speed of an object is doubled, its momentum remains unchanged in accord with the conservation of momentum doubles quadruples decreases B. doubles.

Impulse If the momentum of an object changes, either the mass or the velocity or both change Since velocity change due to acceleration, and acceleration occurs due to net force we define impulse: impulse = net force x time J = Fnett Unit of impulse: Ns

Impulse Example A 300 N force applied to an object for 10 s. What’s the impulse?

Impulse Example A 300 N force applied to an object for 10 s. What’s the impulse? J = Fnet t = 300 N x 10 s = 3000 N s

Impulse Exercise A 40 N force applied to an object for 5 s. What’s the impulse?

Impulse Changes Momentum According to Newton’s second law and the definition of acceleration, a = Fnet / m and a = v / t so, Fnet / m = v / t or J = Fnet t = mv = (mv) = p impulse = change in momentum J = Fnett = p Units of impulse and momentum: kg m/s = Ns

Impulse Changes Momentum Example: A brief force applied over a short time interval produces a smaller change in momentum than the same force applied over a longer time interval If you push with the same force for twice the time, you impart twice the impulse and produce twice the change in momentum

Impulse Changes Momentum The greater the impulse exerted on something, the greater the change in momentum Fnet t = p

Impulse Changes Momentum When the force that produces an impulse acts for twice as much time, the impulse is not changed doubled quadrupled halved B. increased by twice.

Impulse Changes Momentum When the force that produces an impulse acts for twice as much time, the impulse is not changed doubled quadrupled halved B. increased by twice.

Impulse Changes Momentum Example A 0.144 kg baseball approaches a batter with a speed of 30 m/s. The batter lines the ball directly back to the pitcher with a speed of 40 m/s. Find the impulse exerted on the ball. If the bat and ball were in contact for 0.012 sec, find the average force exerted on the ball by the bat

Impulse Changes Momentum Example A 0.144 kg baseball approaches a batter with a speed of 30 m/s. The batter lines the ball directly back to the pitcher with a speed of 40 m/s. Find the impulse exerted on the ball. If the bat and ball were in contact for 0.012 sec, find the average force exerted on the ball by the bat Δp = Δ(mv) = 0.144 kg x (30 – (-40)) m/s = 10.08 kg m/s J = Fnet t = Δp = Fnet (0.012 s) Fnet = 840 N

Impulse Changes Momentum Exercise A 0.40-kg soccer ball approaches a player horizontally with a speed of 15 m/s. The player hits the ball with her head and causes it to move in the opposite direction with a speed of 15 m/s. What impulse was imparted to the ball by the player?

Impulse Changes Momentum Exercise A 30 kg block with velocity 50 m/s is encountering a constant 8 N friction force. What is the momentum of the block after 15 seconds?

Impulse Changes Momentum To increase the momentum of an object, you can apply the greatest force possible for as long as possible Since the force involved in impulses usually vary from instant to instant, when we speak of such impact forces, we mean the average force of impact Impact refers to a force and measured in newtons impulse is impact force x time and is measured in newton-seconds

Impulse Changes Momentum Case 1: Apply the greatest force possible and extend the time of contact Examples: Golfer swings a club and follows through Baseball player hits a ball and follows through

Impulse Changes Momentum A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater average force Impulse both of the above none of the above B. impulse.

Impulse Changes Momentum A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater average force Impulse both of the above none of the above B. impulse.

Impulse Changes Momentum Case 2: The impact time is the time during which your momentum is brought to zero. A longer impact time reduces the force of the impact and decreases the resulting deceleration Examples: Crash Cushion near the exit of a highway Airbag of a car

Impulse Changes Momentum A fast-moving car hitting a haystack or a cement wall produces vastly different results 1. Do both experience the same change in momentum? 2. Do both experience the same impulse? 3. Do both experience the same force? Yes for all three Yes for 1 and 2 No for all three No for 1 and 2 B. Yes for 1 and 2.

Impulse Changes Momentum A fast-moving car hitting a haystack or a cement wall produces vastly different results 1. Do both experience the same change in momentum? 2. Do both experience the same impulse? 3. Do both experience the same force? Yes for all three Yes for 1 and 2 No for all three No for 1 and 2 B. Yes for 1 and 2.

Impulse Changes Momentum When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? No, both are the same Yes, less if it lands on the carpet No, less if it lands on a hard floor No, more if it lands on a hard floor A. No, both are the same.

Impulse Changes Momentum When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? No, both are the same Yes, less if it lands on the carpet No, less if it lands on a hard floor No, more if it lands on a hard floor A. No, both are the same.

Impact Force vs. Impact Time Impact Force (F) Impact Time (t)

Impulse Changes Momentum Examples: When a car is out of control, it is better to hit a haystack than a concrete wall. Same impulse either way, but extension of hitting time reduces the force

Impulse Changes Momentum Example: In jumping, bend your knees when your feet make contact with the ground because the extension of time during your momentum decrease reduces the force on you

Impulse Changes Momentum Example: In boxing, ride with the punch

Impulse Changes Momentum Case 3: decreasing momentum over a short time short time interval produces large force Example: Karate expert splits a stack of bricks by bringing her arm and hand swiftly against the bricks with considerable momentum Time of contact is brief and force of impact is huge

Bouncing

Bouncing Impulses are generally greater when objects bounce Example: Catching a falling flower pot from a shelf with your hands. You provide the impulse to reduce its momentum to zero If you throw the flower pot up again, you provide an additional impulse This “double impulse” occurs when something bounces

Bouncing Pelton wheel designed to “bounce” water when it makes a U-turn on impact with the curved paddle

Bouncing Pelton wheel

Conservation of Momentum Change momentum To change momentum of an object, you need to exert an impulse on it The impulse must come from external source. Internal forces won’t work since they cancel each other out within the object. If no net force or net impulse acts on a system, the momentum of that system cannot change

Conservation of Momentum Law of conservation of momentum In the absence of an external force, the momentum of a system remains unchanged

Conservation of Momentum Law of conservation of momentum When no external force or external impulse is present, no change in momentum is possible

Conservation of Momentum Example: Cannon and Cannonball When a cannon is fired, the force on the cannonball inside the cannon barrel is equal and opposite to the force of the cannonball on the cannon The time the cannon and the cannonball interacting with each other is the same The cannonball gains momentum, while the cannon gains an equal amount of momentum in the opposite direction—the cannon recoils

Conservation of Momentum Examples: Internal molecular forces within a baseball come in pairs, cancel one another out, and have no effect on the momentum of the ball Molecular forces within a baseball have no effect on its momentum Pushing against a car’s dashboard has no effect on its momentum

Collisions

(net mv)before = (net mv)after Collisions Conservation of momentum: Whenever there is no external net force, the net momentum of both objects before collision equals the net momentum of both objects after collision net momentumbefore collision = net momentumafter collision (net mv)before = (net mv)after pbefore = Pafter

Conservation of Momentum Example A huge 20-kg rocket zooms upward at 5 meter/second. At the same exact time, 10-kg of water shoots downward. How fast does the water shoot out?

Conservation of Momentum Example A huge 20-kg rocket zooms upward at 5 meter/second. At the same exact time, 10-kg of water shoots downward. How fast does the water shoot out? 0 kg m/s = 20 kg x 5 m/s + 10 kg x v v = - 10 m/s

Collisions Elastic collision When objects collide without being permanently deformed and without generating heat, the collision is called an elastic collision Colliding objects bounce perfectly in perfect elastic collisions, and the sum of the momentum vectors is the same before and after the collision

Collisions Elastic collision Before Collision After Collision

Elastic Collisions Example A car (A) moving at 10 m/s collides with another car (B) of the same mass (m) at rest. If the collision is elastic, what is the new velocity of car (B)? From the conservation of momentum, (net mv)before = (net mv)after (m  10 m/s)before = (m  v)after v = 10 m/s

Elastic Collisions Exercise A 0.50 kg object traveling at 2.0 m/s east collides with a 0.30 kg object traveling at 4.0 m/s west. After the collision, the 0.30 kg object is traveling at 2.0 m/s east. What are the magnitude and direction of the velocity of the first object?

Elastic Collisions Exercise A toy 10-kg fire truck is rolling at 10 m/s when it hits a parked 5-kg toy car. After the collision, the car rolls at 4 m/s. What is the velocity of the fire truck?

Collisions Inelastic collision Whenever colliding objects become tangled or coupled together, a totally inelastic collision occurs Occurs when colliding objects result in deformation and/or the generation of heat

Collisions Inelastic collision m1v1 + m2•0= (m1 + m2)v v = m1v1 / (m1 + m2) v1 v2 = 0 m/s m1 m2 v m1 + m2

Collisions Inelastic collision m1v1 + m2•v2= (m1 + m2)v v = (m1v1 +m2v2) / (m1 + m2) v1 v2 m1 m2 v m1 + m2

Collisions Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is the same. half. twice. None of the above. B. half.

Collisions Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of freight car A, the speed of the coupled freight cars is the same. half. twice. None of the above. B. half.

Inelastic Collisions Example A car (A) moving at 10 m/s collides with another car (B) of the same mass (m) at rest. If the collision is inelastic and the cars couple together after collision, what is the new velocity of the cars? From the conservation of momentum, (net mv)before = (net mv)after (m  10 m/s)before = (2m  v)after v = 5 m/s

Inelastic Collisions Exercise A 4.0 kg mass is moving at 3.0 m/s toward the right, and a 6.0 kg mass is moving at 2.0 m/s toward the left on a horizontal, frictionless table. If the two masses collide and remain together after the collision, what is their final momentum?

Inelastic Collisions Exercise A 20. kg cart traveling east with a speed of 6.0 m/s collides with a 30. kg cart traveling west. If both carts come to rest after the collision, what was the speed of the westbound cart before the collision?

Inelastic Collisions Exercise A blue 10- kg box car rolls at 6 m/s and crashes into a 20-kg box car that is at rest. 6 m/s 0 m/s 10 kg 20 kg After the crash, both cars are stuck together. What is their velocity?

More Complicated Collisions Example: collision of two cars at a corner

More Complicated Collisions Momentum Vectors: Momentum is a vector quantity. Momentum is conserved even when interacting objects do not move along the same straight line Vector techniques will be used to analyze momentum in any direction In this case you create a parallelogram of the vectors describing each initial momentum to find the combined momentum

More Complicated Collisions Resolved Momentum: When an object bursts, the vector sum of the momenta of its fragments add up to the object’s momentum just before bursting mv m1v1 m2v2 mv