Momentum and Collisions

Momentum ►F►F►F►From Newton’s laws: force must be present to change an object’s velocity (speed and/or direction) MMMMethod to describe is to use concept of linear momentum scalar vector Linear momentum = product of mass velocity Golf ball initially at rest, so some of the KE of club transferred to provide motion of golf ball and its change in velocity

Momentum ► Vector quantity, the direction of the momentum is the same as the velocity ’ s ► Applies to two-dimensional motion as well Size of momentum: depends upon mass depends upon velocity

Impulse ► In order to change the momentum of an object (say, golf ball), a force must be applied

Impulse Cont’d  Gives an alternative statement of Newton ’ s second law  (F Δt) is defined as the impulse  Impulse is a vector quantity, the direction is the same as the direction of the force

Finding Impulse using F-t Graph ► Usually force is not constant, but time- dependent ► If the force is not constant, use the average force applied

Graphical Interpretation of Impulse ► 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 If force is constant: impulse = F  t

Example: 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 ► Ways to increase the time  Seat belts  Air bags  The air bag increases the time of the collision and absorbs some of the energy from the body

To Do…. In the first section of the Momentum chapter in your SNAP (Impulse and Momentum): ► Read Example problems ► Do Practice Exercises (odds) ► Next: 2-D collisions; Elastic vs. Inelasctic Collisions

ConcepTest1 Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare? 1. It takes less time to stop the ping-pong ball. 2. Both take the same time. 3. It takes more time to stop the ping-pong ball.

ConcepTest1 Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare? 1. It takes less time to stop the ping-pong ball. 2. Both take the same time. 3. It takes more time to stop the ping-pong ball. Note: Because force equals the time rate of change of momentum, the two balls loose momentum at the same rate. If both balls initially had the same momenta, it takes the same amount of time to stop them.

Problem: Teeing Off A 50-g golf ball at rest is hit by “ Big Bertha ” club with 500-g mass. After the collision, the golf ball leaves with velocity of 50 m/s. a)Find impulse imparted to ball b)Assuming club in contact with ball for 0.5 ms, find average force acting on golf ball

Problem: teeing off Given: m ball = 50 g = kg v = 50 m/s Find: Impulse = ? F average = ? 1. Use impulse-momentum relation: 2. Having found impulse, find the average force from the definition of impulse: Note: according to Newton ’ s 3 rd law, that is also a reaction force to club hitting the ball: of club CONSERVATION OF MOMENTUM