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Momentum and Impulse Chapter 9

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Standards SP3. Students will evaluate the forms and transformations of energy. c. Measure and calculate the vector nature of momentum. d. Compare and contrast elastic and inelastic collisions. e. Demonstrate the factors required to produce a change in momentum.

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**Momentum is a commonly used term in sports.**

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Momentum A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop. Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum.

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**What is momentum? Momentum is a property of moving matter.**

Momentum describes the tendency of objects to keep going in the same direction with the same speed. A force is required to change momentum.

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**p = m v Momentum Equation p = momentum vector m = mass**

v = velocity vector

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How do I find momentum? The momentum of a ball depends on its mass and velocity. Ball B has more momentum than ball A.

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**When could the truck and rollercoaster have equal momentum vectors?**

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Equivalent Momenta Car: m = 1800 kg; v = 80 m /s p = 1.44 ·105 kg · m /s Bus: m = 9000 kg; v = 16 m /s p = 1.44 ·105 kg · m /s Train: m = 3.6 ·104 kg; v = 4 m /s p = 1.44 ·105 kg · m /s

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Objects at Rest Momentum can be thought of as mass in motion An object at rest has NO momentum at all

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**Difference Between Momentum and Inertia**

Inertia is another property of mass that resists changes in velocity; however, inertia depends only on mass. Inertia is a scalar quantity. Momentum is a property of moving mass that resists changes in a moving object’s velocity. So momentum is a vector quantity.

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**Units The SI unit of momentum is kg * m/s**

Mass times velocity Anything that is a measure of mass times a measure of velocity is acceptable though Grams * Miles/hour Cg * cm/s

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Path of an Object Ball A is 1 kg moving 1m/sec, ball B is 1kg at 3 m/sec. A 1 N force is applied to deflect the motion of each ball. What happens? Does the force deflect both balls equally? Ball B deflects much less than ball A when the same force is applied because ball B had a greater initial momentum.

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**Kinetic Energy and Momentum**

Kinetic energy and momentum are different quantities, even though both depend on mass and speed. Kinetic energy is a scalar quantity. Momentum is a vector, so it always depends on direction. Two balls with the same mass and speed have the same kinetic energy but opposite momentum.

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**A Force is Required to Change Momentum**

The relationship between force and motion follows directly from Newton's second law. Force (N) F = D p D t Change in momentum (kg m/sec) Change in time (sec)

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Impulse The product of a force and the time the force acts is called the impulse. Impulse is a way to measure a change in momentum because it is not always possible to calculate force and time individually since collisions happen so fast.

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**Impulse Changes Momentum**

A force sustained for a long time produces more change in momentum than does the same force applied briefly. Both force and time are important in changing an object’s momentum. When you push with the same force for twice the time, you impart twice the impulse and produce twice the change in momentum.

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**Impulse is Equal to Change in Momentum**

The quantity force × time interval is called impulse. impulse = F × t The greater the impulse exerted on something, the greater will be the change in momentum. impulse = change in momentum Ft = ∆(mv) This is called the Impulse - Momentum Theorem!

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**Impulse Changes Momentum**

If the change in momentum occurs over a long time, the force of impact is small.

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**Impulse Changes Momentum**

If the change in momentum occurs over a short time, the force of impact is large.

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**Impulse Changes Momentum**

When you jump down to the ground, bend your knees when your feet make contact with the ground to extend the time during which your momentum decreases. A wrestler thrown to the floor extends his time of hitting the mat, spreading the impulse into a series of smaller ones as his foot, knee, hip, ribs, and shoulder successively hit the mat.

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**Impulse Changes Momentum**

The impulse provided by a boxer’s jaw counteracts the momentum of the punch. a. The boxer moves away from the punch.

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**Impulse Changes Momentum**

The impulse provided by a boxer’s jaw counteracts the momentum of the punch. a. The boxer moves away from the punch. b. The boxer moves toward the punch. Ouch!

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**Padded gloves are worn to reduce the effect of the impulses**

Padded gloves are worn to reduce the effect of the impulses. The padding increases the time over which the force is experienced. This reduces the force (and thus the hurt on the hand. Boxers often ride the punch when they know they are going to be hit. They allow their head to continue backwards with the gloved fist in order to increase the time over which the fist is brought to a stop. This in turn decreases the force.

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**Safety net for acrobats is a good example.**

Impulse Changes Momentum A glass dish is more likely to survive if it is dropped on a carpet rather than a sidewalk. The carpet has more “give.” Since time is longer hitting the carpet than hitting the sidewalk, a smaller force results. The shorter time hitting the sidewalk results in a greater stopping force. Safety net for acrobats is a good example.

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Cassy imparts a large impulse to the bricks in a short time and produces considerable force. Her hand bounces back, yielding as much as twice the impulse to the bricks.

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Bouncing The impulse required to bring an object to a stop and then to “throw it back again” is greater than the impulse required merely to bring the object to a stop.

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**Suppose you catch a falling pot with your hands. **

Bouncing Suppose you catch a falling pot with your hands. You provide an impulse to reduce its momentum to zero. If you throw the pot upward again, you have to provide additional impulse.

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Bouncing If the flower pot falls from a shelf onto your head, you may be in trouble. If it bounces from your head, you may be in more serious trouble because impulses are greater when an object bounces. The increased impulse is supplied by your head if the pot bounces.

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Try this In a physics demonstration, two identical balloons (A and B) are propelled across the room on guide wires. The motion diagrams (depicting the relative position of the balloons at time intervals of 0.05 seconds) are shown below. Which balloon (A or B) has the greatest acceleration? Which balloon (A or B) has the greatest final velocity? Which balloon (A or B) has the greatest momentum change? Which balloon (A or B) experiences the greatest impulse?

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Momentum is Conserved The law of conservation of momentum states when a system of interacting objects is not influenced by outside forces (like friction), the total momentum of the system cannot change. Initial Momentum = Final Momentum

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**Conservation of Momentum**

The momentum before firing is zero. After firing, the net momentum is still zero because the momentum of the cannon is equal and opposite to the momentum of the cannonball.

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**Conservation of Momentum**

Momentum has both direction and magnitude. It is a vector quantity. The cannonball gains momentum and the recoiling cannon gains momentum in the opposite direction. The cannon-cannonball system gains none. The momenta of the cannonball and the cannon are equal in magnitude and opposite in direction. No net force acts on the system so there is no net impulse on the system and there is no net change in the momentum.

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**Conservation of Momentum**

Equation:

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Cart and Brick In the collision between the cart and the dropped brick, total system momentum is conserved. Before the collision, the momentum of the cart is 60 kg*cm/s and the momentum of the dropped brick is 0 kg*cm/s; the total system momentum is 60 kg*cm/s. After the collision, the momentum of the cart is 20.0 kg*cm/s and the momentum of the dropped brick is 40.0 kg*cm/s; the total system momentum is 60 kg*cm/s. The momentum of the cart-dropped brick system is conserved. The momentum lost by the cart (40 kg*cm/s) is gained by the dropped brick.

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**Collisions in One Dimension**

A collision occurs when two or more objects hit each other. During a collision, momentum is transferred from one object to another. Collisions can be elastic or inelastic.

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

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Collisions A moving ball strikes a ball at rest.

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**Collisions A moving ball strikes a ball at rest.**

Two moving balls collide head-on.

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**Collisions A moving ball strikes a ball at rest.**

Two moving balls collide head-on. Two balls moving in the same direction collide.

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Elastic Collision

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**Collisions Inelastic Collisions**

A collision in which the colliding objects become distorted and generate heat during the collision is an inelastic collision. Momentum conservation holds true even in inelastic collisions. Whenever colliding objects become tangled or couple together, a totally inelastic collision occurs.

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Collisions In an inelastic collision between two freight cars, the momentum of the freight car on the left is shared with the freight car on the right.

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Collisions The freight cars are of equal mass m, and one car moves at 4 m/s toward the other car that is at rest. net momentum before collision = net momentum after collision (net mv)before = (net mv)after (m)(4 m/s) + (m)(0 m/s) = (2m)(vafter) Twice as much mass is moving after the collision, so the velocity, vafter, must be one half of 4 m/s. vafter = 2 m/s in the same direction as the velocity before the collision, vbefore.

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Collisions The initial momentum is shared by both cars without loss or gain. Momentum is conserved. External forces are usually negligible during the collision, so the net momentum does not change during collision.

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8.5 Collisions do the math! Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch?

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8.5 Collisions do the math! Consider a 6-kg fish that swims toward and swallows a 2-kg fish that is at rest. If the larger fish swims at 1 m/s, what is its velocity immediately after lunch? Momentum is conserved from the instant before lunch until the instant after (in so brief an interval, water resistance does not have time to change the momentum).

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8.5 Collisions do the math!

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8.5 Collisions do the math! Suppose the small fish is not at rest but is swimming toward the large fish at 2 m/s.

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8.5 Collisions do the math! Suppose the small fish is not at rest but is swimming toward the large fish at 2 m/s. If we consider the direction of the large fish as positive, then the velocity of the small fish is –2 m/s.

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8.5 Collisions do the math! The negative momentum of the small fish slows the large fish.

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8.5 Collisions do the math! If the small fish were swimming at –3 m/s, then both fish would have equal and opposite momenta. Zero momentum before lunch would equal zero momentum after lunch, and both fish would come to a halt.

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**8.5 Collisions do the math! Suppose the small fish swims at –4 m/s.**

The minus sign tells us that after lunch the two-fish system moves in a direction opposite to the large fish’s direction before lunch.

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Elastic collisions Two kg billiard balls roll toward each other and collide head-on. Initially, the 5-ball has a velocity of 0.5 m/s. The 10-ball has an initial velocity of -0.7 m/s. The collision is elastic and the 10-ball rebounds with a velocity of 0.4 m/s, reversing its direction. What is the velocity of the 5-ball after the collision?

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Elastic collisions You are asked for 10-ball’s velocity after collision. You are given mass, initial velocities, 5-ball’s final velocity. Diagram the motion, use m1v1 + m2v2 = m1v3 + m2v4 Solve for V3 : (0.165 kg)(0.5 m/s) + (0.165 kg) (-0.7 kg)= (0.165 kg) v3 + (0.165 kg) (0.4 m/s) V3 = -0.6 m/s

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**Inelastic collisions You are asked for the final velocity.**

A train car moving to the right at 10 m/s collides with a parked train car. They stick together and roll along the track. If the moving car has a mass of 8,000 kg and the parked car has a mass of 2,000 kg, what is their combined velocity after the collision? You are asked for the final velocity. You are given masses, and initial velocity of moving train car.

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Inelastic collisions Diagram the problem, use m1v1 + m2v2 = (m1v1 +m2v2) v3 Solve for v3= (8,000 kg)(10 m/s) + (2,000 kg)(0 m/s) (8, ,000 kg) v3= 8 m/s The train cars moving together to right at 8 m/s.

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**Collisions Summarized**

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