1. Momentum and Collisions Unit 5, Presentation 1

2. Momentum  The linear momentum of an object of mass m moving with a velocity is defined as the product of the mass and the velocity SI Units are kg m / s Vector quantity, the direction of the momentum is the same as the velocity’s

3. More About Momentum  Momentum components p x = m v x and p y = m v y  Applies to two-dimensional motion  Momentum is related to kinetic energy

4. Impulse  In order to change the momentum of an object, a force must be applied  The time rate of change of momentum of an object is equal to the net force acting on it Gives an alternative statement of Newton’s second law

5. Impulse cont.  When a single, constant force acts on the object, there is an impulse delivered to the object is defined as the impulse Vector quantity, the direction is the same as the direction of the force

6. Impulse-Momentum Theorem  The theorem states that the impulse acting on the object is equal to the change in momentum of the object If the force is not constant, use the average force applied

7. Average Force in 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

8. Average Force cont.  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, the impulse is equal to the average force multiplied by the time interval,

9. Impulse Example Problem A golf ball with mass 5.0 x 10 -2 kg is struck with a club. The force on the ball varies from zero when contact is made up to some maximum value (when the ball is maximally deformed) and then back to zero when the ball leaves the club. Assume that the ball leaves the club face with a velocity of 44 m/s. (a) Find the magnitude of the impulse due to the collision. (b) Estimate the duration of the collision and the average force acting on the ball, assuming that the distance the ball travels on the face of the club is approximately 2.0 cm.

10. Example Problem (cntd) m = 5.0 x 10 -2 kg v = 44 m/s I=? d=0.02 m t=?

11. 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 This will reduce the chance of dying in a car crash  Ways to increase the time Seat belts Air bags

12. Typical Collision Values  Calculate the force and acceleration acting on a 75 kg person traveling at 27 m/s and coming to stop in 0.010 s

13. Survival  Increase time  Seat belt Restrain people so it takes more time for them to stop New time is about 0.15 seconds

14. Air Bags  The air bag increases the time of the collision  It will also absorb some of the energy from the body  It will spread out the area of contact Decreases the pressure Helps prevent penetration wounds