Chapter 9:Linear Momentum 9-1 Momentum and Its Relation to Force 9-2 Conservation of Momentum 9-3 Collisions and Impulse 9-4 Conservation of Energy and Momentum in Collisions 9-5 Elastic Collisions in One Dimension 9-6 Inelastic Collisions 9-7 Collisions in Two or Three Dimensions

8-8 Power Example 8-14: Stair-climbing power. A 60-kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. (a) Estimate the jogger’s power output in watts and horsepower. (b) How much energy did this require?

8-8 Power Power is also needed for acceleration and for moving against the force of friction. The power can be written in terms of the net force and the velocity:

8-8 Power Example 8-15: Power needs of a car. Calculate the power required of a 1400-kg car under the following circumstances: (a) the car climbs a 10° hill (a fairly steep hill) at a steady 80 km/h; and (b) the car accelerates along a level road from 90 to 110 km/h in 6.0 s to pass another car. Assume that the average retarding force on the car is F R = 700 N throughout.

9-1 Momentum and Its Relation to Force Momentum is the property of a moving object to continue moving Momentum is a vector symbolized by the symbol, and is defined as The rate of change of momentum is equal to the net force: This can be shown using Newton’s second law.

Momentum, p Vector units: kgm/s Bowling Ball vs. Tennis Ball Mass7 kg57 g Speed9 m/s60 m/s momentum

9-2 Conservation of Momentum During a collision, measurements show that the total momentum does not change:

9-2 Conservation of Momentum Conservation of momentum can also be derived from Newton’s laws. A collision takes a short enough time that we can ignore external forces. Since the internal forces are equal and opposite, the total momentum is constant.

9-2 Conservation of Momentum Recall Newton’s third law v 1i v 2i v 1f v 2f m1 m2

9-2 Conservation of Momentum Newton’s third law implies that during an interaction momentum is transferred from one body to another. v 1i v 2i v 1f v 2f m1 m2 Momentum is a vector quantity!

9-2 Conservation of Momentum This is the law of conservation of linear momentum: when the net external force on a system of objects is zero, the total momentum of the system remains constant. Equivalently, the total momentum of an isolated system remains constant.

Question In these two cases, the work done in stopping the car is A.positive, with bricks doing more work B.positive, with bricks and balloon doing same work C.negative, with bricks doing more work D.negative, with bricks and balloon doing same work.

Momentum example A system consists of three particles with these masses and velocities: mass 3.0 kg moving west at 5.0 m/s; mass 4.0 kg moving west at 10.0 m/s; and mass 5.0 kg moving east at 20.0 m/s. What is total momentum of the system?

9-2 Conservation of Momentum Example 9-4: Rifle recoil. Calculate the recoil velocity of a 5.0- kg rifle that shoots a kg bullet at a speed of 620 m/s.

9-3 Collisions and Impulse During a collision, objects are deformed due to the large forces involved. Since, we can Write Integrating,

9-3 Collisions and Impulse This quantity is defined as the impulse, J: The impulse is equal to the change in momentum: This equation is true if F is the net impulsive force of the object that is much larger than any other force in a short interval of time.

9-3 Collisions and Impulse Since the time of the collision is often very short, we may be able to use the average force, which would produce the same impulse over the same time interval.

Question If the car now rebounds, with the same speed that it had before it hit: A.  p=0, W=0 B.  p is non-zero, W=0 C.  p=0, W is nonzero D.  p, W are both nonzero

9-3 Collisions and Impulse Example 9-6: Karate blow. Estimate the impulse and the average force delivered by a karate blow that breaks a board a few cm thick. Assume the hand moves at roughly 10 m/s when it hits the board.