Topic 2.2 Momentum

Learning Outcomes 2.2.8State Newton’s second law of motion.1 Students should be familiar with the law expressed as: Solve problems involving Newton’s second law Define linear momentum and impulse Determine the impulse due to a time- varying force by interpreting a force–time graph State the law of conservation of linear momentum Solve problems involving momentum and impulse. 3

Momentum

Newton’s 2 nd law in terms of Momentum

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Newton’s second law Newton’s second law can be stated in two ways: The net force acting on an object is the: The net force acting on an object is the: Product of the mass of the object by the acceleration. Product of the mass of the object by the acceleration. Rate at which the momentum of the object is changing with time. Rate at which the momentum of the object is changing with time.

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Impulse

Impulse from Force-Time graph The impulse imparted by a force during the time interval Δt is equal to the area under the force-time graph from the beginning to the end of the time interval The impulse imparted by a force during the time interval Δt is equal to the area under the force-time graph from the beginning to the end of the time interval Or, to the average force multiplied by the time interval Or, to the average force multiplied by the time interval The average force can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval The average force can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval

Test your Knowledge! A ball of mass kg moves on a frictionless horizontal floor and hits a vertical wall with speed of 5.00 m.s -1. The ball rebounds with speed 4.0 m.s -1. If the ball was in contact with wall for 0.15 s: A ball of mass kg moves on a frictionless horizontal floor and hits a vertical wall with speed of 5.00 m.s -1. The ball rebounds with speed 4.0 m.s -1. If the ball was in contact with wall for 0.15 s: Determine the average force that acted on the ball. Determine the average force that acted on the ball. The force is assumed to vary with time as shown. Deduce the maximum force that acted on the ball The force is assumed to vary with time as shown. Deduce the maximum force that acted on the ball

Impulse Applied to Auto Collisions The most important factor is the collision time or the time it takes the person to come to a rest The most important factor is the collision time or the time it takes the person to come to a rest This will reduce the chance of dying in a car crash This will reduce the chance of dying in a car crash Ways to increase the time Ways to increase the time Seat belts Seat belts Air bags Air bags

Air Bags The air bag increases the time of the collision The air bag increases the time of the collision It will also absorb some of the energy from the body It will also absorb some of the energy from the body It will spread out the area of contact It will spread out the area of contact decreases the pressure decreases the pressure helps prevent penetration wounds helps prevent penetration wounds

Isolated system An isolated system will have no external forces. An isolated system will have no external forces. The example of colliding objects The example of colliding objects

Conservation of Momentum An isolated system will have no external forces An isolated system will have no external forces Momentum in an isolated system is conserved Momentum in an isolated system is conserved The principle of conservation of momentum states: The principle of conservation of momentum states: In the absence of external forces; the momentum of the system stays the same. (2 marks) In the absence of external forces; the momentum of the system stays the same. (2 marks)

Examples of Isolated Systems & conservation of Momentum

Two carts connected by a spring

Collision between 2 balls

Collision between two trucks

System of rocket and exhaust

Firecrackers

Firing a canon ball

Jumping off a boat

System of a fan and a sail

Conservation of Momentum, cont.

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Proof of momentum conservation

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Think again,

Now apply to the example of a helicopter