CHAPTER 7 Impulse and Momentum

Objective Define and calculate momentum. Describe changes in momentum in terms of force and time. Source: Wikimedia Commons

Linear Momentum

When we think of a massive object moving at a high velocity, we often say that the object has a large momentum. A less massive object with the same velocity has a smaller momentum. On the other hand, a small object moving with a very high velocity has a large momentum.

Linear Momentum The faster an object moves, the more momentum the object has and the more difficult it is for it to come to a stop. The more massive an object is, the more force it will exert on another object (during a collision) because of its momentum.

Examples: Momentum A 21 kg child is riding a 5.9 kg bike with a velocity of 4.5 m/s to the northwest. What is the momentum of the child alone? What is the momentum of the bike alone? What is the momentum of the bike and child together? What velocity would a child with a mass of 42 kg need in order to have the same momentum?

Examples: Momentum (a)

Examples: Momentum (b)

Examples: Momentum (c)

Examples: Momentum (d)

Impulse

7.1 The Impulse-Momentum Theorem

final momentuminitial momentum IMPULSE-MOMENTUM THEOREM When a net force acts on an object, the impulse of this force is equal to the change in the momentum of the object impulse

7.1 The Impulse-Momentum Theorem Example 2 A Rain Storm Rain comes down with a velocity of -15 m/s and hits the roof of a car. The mass of rain per second that strikes the roof of the car is kg/s. Assuming that rain comes to rest upon striking the car, find the average force exerted by the rain on the roof.

7.1 The Impulse-Momentum Theorem Neglecting the weight of the raindrops, the net force on a raindrop is simply the force on the raindrop due to the roof.

7.1 The Impulse-Momentum Theorem Conceptual Example 3 Hailstones Versus Raindrops Instead of rain, suppose hail is falling. Unlike rain, hail usually bounces off the roof of the car. If hail fell instead of rain, would the force be smaller than, equal to, or greater than that calculated in Example 2?

Example: A force of 2 N applied over a period of 4 s delivers an impulse of 8 Ns 2 N The impulse is a vector. It has the same direction as the applied force. Impulse

Impulse – momentum theorem Impulse-momentum theorem state that: A change in momentum takes force and time Force x (change in time) = change in momentum Change in momentum is proportional to force Change in momentum is proportional to time interval

Impulse – momentum theorem uses Used to determine stopping time and safe following distances for cars and trucks. Used to design safety equipment that reduces the forces exerted on a human body during collisions

On a trampoline, jumpers are protected from injury because the rubber reduces the force of the collision by allowing it to take place over a longer period of time. Increasing time of impact

Egg Impulse Demo

Impulse Graphically, the impulse is the area under a force vs. time graph. F (N) t (s) J

Impulse Even if the force varies, the same principle should hold: impulse is the area under the force vs. time curve. t (s) F (N) J

Example Problem 1: Force and momentum A 1400kg car moving westward with a velocity of 15m/s collides with a utility pole and is brought to rest in 0.30s. Find the magnitude of force exerted on the car during the collision?

Example Problem 1: Force and momentum

Example Problem 2: Stopping time and distance How long does it take to stop a car with a mass of 2400 kg travelling at 20 m/s, if the stopping force is 8000N? How far does the car travel in that time?

Example Problem 2: Stopping time and distance

Trebuchet project Trebuchet project Clarifications: The cover page, bibliography, pictures, sketches do not count towards the 4 pg. max. You may include a picture or a sketch of your decorated golf ball

DUE IN CLASS Assignment

DUE IN CLASS Assignment

CONSERVATION OF MOMENTUM SECTION 2

Conservation of Momentum In its most general form, 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 forces between the objects Regardless of the nature of the forces between the objects, Momentum is conserved in collisions

Conservation of Momentum

The diagram below shows the velocity and momentum of each soccer ball both before and after the collision. The momentum of each ball changes due to the collision, but the total momentum of the two balls together remains constant

Conservation of Momentum In other words, the momentum of ball A plus the momentum of ball B before the collision is equal to the momentum of ball A plus the momentum of ball B after the collision. when you use conservation of momentum to solve a problem or to investigate a situation, it is important to include all objects that are involved in the interaction.

Conservation of Momentum

Practice problem 1 A 44 kg student on in-line skates is playing with a 22 kg exercise ball. The student, starting at rest, throws the ball, causing the student to glide back at 3.5 m/s. How fast was the ball moving away from the student?

Example Problem 1: conservation of momentum

Practice Problem 2 An 85.0 kg fisherman jumps from a dock into a 135 kg rowboat at rest on the west side of the dock. If the velocity of the fisherman is 4.30 m/s to the west as he leaves the dock, what is the final velocity of the fisherman and the boat?

Example Problem 2: conservation of momentum

7.2 The Principle of Conservation of Linear Momentum Example 6 Ice Skaters Starting from rest, two skaters push off against each other on ice where friction is negligible. One is a 54-kg woman and one is a 88-kg man. The woman moves away with a speed of +2.5 m/s. Find the recoil velocity of the man.

7.2 The Principle of Conservation of Linear Momentum

Applying the Principle of Conservation of Linear Momentum 1. Decide which objects are included in the system. 2. Relative to the system, identify the internal and external forces. 3. Verify that the system is isolated. 4. Set the final momentum of the system equal to its initial momentum. Remember that momentum is a vector.

Assignment Worksheet

Section 3: Collisions in One Dimension Collisions are normally classified according to the changes in the total KE during the collision 1.Elastic collision: Objects bounce off each other after collision. KE before and after collision is the same (conserved) 2.Inelastic collision: Objects stick together after collision. KE before collision is not equal to the KE after collision

ELASTIC AND INELASTIC COLLISION SECTION 3

Collisions There are 2 major types of collisions: Perfectly inelastic collisions – when 2 objects collide and move together as one mass (coupled). Elastic collisions – 2 objects collide and return to their original shapes with no change in total kinetic energy. After the collisions, the objects move off separately.

Perfectly Inelastic Collisions

Elastic Collisions

a.A moving ball strikes a ball at rest. b.Two moving balls collide head-on, and move on in opposite directions, momentum is conserved c.Two balls moving in the same direction collide.

7.3 Collisions in One Dimension The total linear momentum is conserved when two objects collide, provided they constitute an isolated system. Elastic collision -- One in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. Inelastic collision -- One in which the total kinetic energy of the system after the collision is not equal to the total kinetic energy before the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.

Practice Problem – Inelastic collision

Practice Problem – Elastic collision A kg marble moving to the right at m/s makes an elastic head-on collision with a kg shooter marble moving to the left at m/s. After the collision, the smaller marble moves to the left at m/s. Assume that both marbles are moving on a frictionless surface. What is the velocity of the kg marble after the collision? Show that the change in KE is 0J

ASSIGNMENT Worksheet