Linear MomentumChapter 7

Momentum and its Relation to Force

• How do we define momentum?

• How is momentum related to force?

• How can we apply the conservation of momentum?

Momentum

• http://www.youtube.com/watch?v=0LnbyjOyEQ8&feature=related

Momentum

• Linear Momentum: the product of an objects mass and its velocity

• Symbol is p

• Units are kg·m/s

Momentum

• Since v is a vector, …

• A big truck can have the same momentum as a small car if…

• Stopping force?

• Damage?

Momentum

• A smaller football player can have the same momentum as a larger one, if…

• Application?

• Direction change?

Relation to Newton’s 2nd

• Rate of change of momentum is equal to net force:

• Newton originally wrote the second law in terms of momentum

• Proof Page 168

Force of a tennis serve

• For a top player, a tennis ball may leave the racket on the serve with a speed of 55 m/s (about 120 mph). If the ball has a mass of 0.060 kg and is in contact with the racket for about 4 x 10-3 s, estimate the average force on the ball.

• Would this force be large enough to lift a 60 kg person?

Water

• Water leaves a hose at a rate of 1.5 kg/s with a speed of 20 m/s and is aimed at the side of a car, which stops it. What force is exerted by the water on the car?

Conservation of Momentum

• During a collision, measurements show that the total momentum does not change

Conservation of Momentum

• Since mass doesn’t change, the velocities change

The total momentum of an isolated system remains constant

Railroad cars

• A 10,000 kg railroad car, A, traveling at a speed of 24.0 m/s strikes an identical car, B, at rest. If the cars lock together as a result of the collision, what is their common speed just afterward?

Systems

• Only applies to an isolated system

• Only forces are between objects in the system

• System of rock falling by itself will not conserve momentum, because an external force, gravity

• If we expand the system to include the Earth, then we can conserve momentum

Systems

• Momentum conservation works for a rocket as long as we consider the rocket and its fuel to be one system, and account for the mass loss of the rocket.

Homework

• Read Sections 7.1 and 7.2• Do Problems # 1 – 12, Page 188