Impulse Momentum, and Collisions Physics

Topics to be covered Momentum & Impulse Linear momentum Conservation of Momentum Momentum is conserved Elastic and Inelastic Collisions Collisions Elastic Collisions

Overview What happens during a car crash? How do rockets work? my rocket Can physics improve our golf game? To answer these questions we introduce momentum EQ: Ultimately why is it hard to stop something that has a lot of momentum?

Momentum The concept of force and Newton’s laws can be used to calculate how the motion of an object changes when the object is struck. We will examine how the force and the duration of the collision between two objects affect the motion of an object.

Momentum A brontosaurus has a lot of momentum, but so does a piece of hot lead shot from a rifle. We should expect than that momentum has something to do with an objects mass and velocity. P = momentum, it is a vector quantity. px = mvx & py = mvy Related to kinetic energy Derive this equation

Pause for a Cause P = mv => 2250 kg * 25m/s = A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the momentum of the truck? Given: m =2250 kg v = 25 m/s to the east P = mv => 2250 kg * 25m/s = Practice A 5.6 x 104 kg*m/s

Pause for a Cause Compare the momentum of a 6160 kg truck moving at 3.00 m/s to the momentum of a 1540 kg car moving at 12.0 m/s.

Pause for a Cause A rubber ball with a mass of 0.30 kg is dropped onto a steel plate. The ball’s speed just before impact is 4.5 m/s and just after impact is 4.2 m/s. What is the change in the ball’s momentum?

Change in Momentum & Impulse A change is momentum take a force In fact Newton first expressed his second law not as… F = ma, but Solve for momentum This state a force over time changes an objects momentum

Impulse = Momentum Momentum is defined as “Inertia in Motion” Ns Consider Newton’s 2nd Law and the definition of acceleration Units of Impulse: Units of Momentum: Ns Kg x m/s Momentum is defined as “Inertia in Motion”

Pause for a Cause A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the force exerted on the car during the collision. 7.0 X 104 N to the east Practice B

Pause for a Cause A player at first base catches a throw traveling 22 m/s. The baseball, which has a mass of 0.21 kg, comes to a complete stop in the glove after 0.15 s. Assuming the force of the glove was uniform, what force did the glove exert on the ball?

Pause for a Cause A 65 kg trapeze artist falls straight down onto a safety net. The trapeze artist’s initial speed as she hits the net is 9.9 m/s, and the net stretches 1.5 m vertically as she comes to a stop. What average net force does the trapeze artist experience while the net breaks her fall? How many “g’s” of acceleration does she experience on average? (1 g = 9.81 m/s )

Pause for a Cause A 100 g ball is dropped from a height of h = 2.00 m above the floor. It rebounds vertically to a height of h'= 1.50 m after colliding with the floor. (a) Find the momentum of the ball immediately before it collides with the floor and immediately after it rebounds, (b) Determine the average force exerted by the floor on the ball. Assume that the time interval of the collision is 0.01 seconds.

Stopping Distance Highway safety engineers use the impulse-momentum theorem to determine stopping distances. Example Two identical trucks both traveling at the same speed Truck 1 is carrying a load of bricks doubling the mass of the truck. Therefore the mathematical expression for this would be Truck 1 = 2(Truck 2) Or double the momentum Truck 1: stopping distance is double Truck 2 Truck 1: stopping time is double Truck 2

Pause for a Cause A 2240 kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is 8410 N to the east? How far does the car travel during the deceleration? Unknown: Δt = ? Δx = ? m = 2240 kg vi = 20.0 m/s to the west, vi = −20.0 m/s vf = 5.00 m/s to the west, vf = −5.00 m/s F = 8410 N to the east, F = +8410 N = 4.00s = 4.00s

Pause for a Cause = -50.0 m = or 50.0 m to the west A 2240 kg car traveling to the west slows down uniformly from 20.0 m/s to 5.00 m/s. How long does it take the car to decelerate if the force on the car is 8410 N to the east? How far does the car travel during the deceleration? Unknown: Δt = ? Δx = ? m = 2240 kg vi = 20.0 m/s to the west, vi = −20.0 m/s vf = 5.00 m/s to the west, vf = −5.00 m/s F = 8410 N to the east, F = +8410 N Practice C = -50.0 m = or 50.0 m to the west

Impulse is the Area In real life the force on an object is rarely constant. Since I=Ft, Impulse is the AREA of a Force vs. Time graph.

Topics to be covered Momentum & Impulse Linear momentum Conservation of Momentum Momentum is conserved Elastic and Inelastic Collisions Collisions Elastic Collisions

Momentum is Conserved Ball A has velocity, ball B is sitting still After the collision ball A has transferred 97% of it’s momentum to ball b.

Conservation of Momentum For an isolated system, the law of conservation of momentum can be stated as follows: The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

Pause for a Cause = -4.2 to the right A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? Given: m1 = 76 kg m2 = 45 kg v1,i = 0 v2,i = 0 v1,f = 2.5 m/s to the right Unknown: v2,f = ? Practice D = -4.2 to the right

Pause for a Cause An astronaut with a mass of 85 kg is outside a space capsule when the tether line breaks. To return to the capsule, the astronaut throws a 2.0 kg wrench away from the capsule at a speed of 14 m/s. At what speed does the astronaut move toward the capsule? Practice D = 0.33 m/s

Pause for a Cause = 7.4x10-2 m/s A 65.0 kg ice-skater standing on frictionless ice throws a 0.15 kg snowball horizontally at a speed of 32.0 m/s. At what speed does the skater move backward? Practice D = 7.4x10-2 m/s

Topics to be covered Momentum & Impulse Linear momentum Conservation of Momentum Momentum is conserved Elastic and Inelastic Collisions Collisions Elastic Collisions

Collisions The total momentum remains constant in any type of collision. However, the total kinetic energy is generally not conserved in a collision because some kinetic energy is converted to internal energy when the objects deform.

Several Types of collisions Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved. When 2 objects collide and DON’T stick When 2 objects collide and stick together When 1 object breaks into 2 objects Elastic Collision = Kinetic Energy is Conserved Inelastic Collision = Kinetic Energy is NOT Conserved Perfectly Inelastic = Momentum is conserved kinetic energy is not, & two objects stick together. Vf = same.

Perfectly Inelastic Collisions When two objects, such as the two football players, collide and move together as one mass, the collision is called a Perfectly Inelastic Collision Vf = ? The final velocity is the same for both players The final velocity is the same for both players

Pause for a Cause A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision? Given: m1 = 1850 kg m2 = 975 kg v1,i = 0 m/s v2,i = 22.0 m/s to the north Unknown: vf = ? Practice E

Pause for a Cause A diver with a mass of 80.0 kg jumps from a dock into a 130.0 kg boat at rest on the west side of the dock. If the velocity of the diver in the air is 4.10 m/s to the west, what is the final velocity of the diver after landing in the boat? Practice E

Kinetic Energy & Perfectly Inelastic Collisions In an inelastic collision, the total kinetic energy does not remain constant when the objects collide and stick together. EQ: Where does some of the energy go? sound energy & internal energy as the objects deform during the collision. The decrease in the total kinetic energy during an inelastic collision can be calculated by using the formula for kinetic energy. It is important to remember that not all of the initial kinetic energy is necessarily lost in a perfectly inelastic collision.

Pause for a Cause An infant throws 5 g of applesauce at a velocity of 0.2 m/s. All of the applesauce collides with a nearby wall and sticks to it. What is the decrease in kinetic energy of the applesauce?

Pause for a Cause ΔKE = KEf − KEi Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.500 kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of 0.250 kg and an initial velocity of 3.00 m/s to the left. What is the decrease in kinetic energy during the collision? Given: m1 = 0.500 kg m2 = 0.250 kg v1,i = 4.00 m/s to the right, v1,i = +4.00 m/s v2,i = 3.00 m/s to the left, v2,i = −3.00 m/s Unknown: ΔKE = ? ΔKE = KEf − KEi

Pause for a Cause ΔKE = KEf − KEi Two clay balls collide head-on in a perfectly inelastic collision. The first ball has a mass of 0.500 kg and an initial velocity of 4.00 m/s to the right. The second ball has a mass of 0.250 kg and an initial velocity of 3.00 m/s to the left. What is the decrease in kinetic energy during the collision? ΔKE = KEf − KEi Unknown: ΔKE = ? Practice F

Pause for a Cause -ΔKE = KEf − KEi Two snowballs with masses of 0.40 kg and 0.60 kg, respectively, collide head-on and combine to form a single snowball. The initial speed for each is 15 m/s. If the velocity of the new combined snowball is 3.0 m/s after the collision, what is the decrease in kinetic energy? -ΔKE = KEf − KEi Practice F

Elastic Collisions In an elastic collision two objects collide and return to their original shapes with no loss of total kinetic energy. After the collision, the two objects move separately. In an elastic collision, both the total momentum and the total kinetic energy are conserved. Perfectly inelastic collisions rarely happen in the real world. Most collision are not elastic either. Some kinetic energy is lost. Ex: Collision Football & Foot Both are deformed and loss energy to sound. Any collision that makes sound can not by definition by elastic EX: the click of billiard balls. **Remember that v is positive if the object moves to the right and negative if the object moves to the left**

**Remember that v is positive if the object moves to the right and negative if the object moves to the left**

Pause for a Cause A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic headon collision with a 0.030 kg shooter marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 m/s. Assume that neither marble rotates before or after the collision and that both marbles are moving on a frictionless surface. What is the velocity of the 0.030 kg marble after the collision? Given: m1 = 0.015 kg m2 = 0.030 kg v1,i = 0.225 m/s to the right, v1,i = +0.225 m/s v2,i = 0.180 m/s to the left, v2,i = −0.180 m/s v1,f = 0.315 m/s to the left, v1,f = −0.315 m/s Unknown: v2,f = ? = 9.0 x 10-2 m/s to the right = 9.0 x 10-2 m/s to the right

Pause for a Cause Calculate the final KE and the initial KE. Practice G

Pause for a Cause

A) B)

C)

The End