Impulse-Momentum

1. Impulse-Momentum

2. Impulse • Impulse, J, is the product of average force and the time interval during which force acts • J=Ft • Impulse is a vector in same direction as force • Unit= Ns • When a large force is applied for a long time, get good velocity leaving the bat- a solid hit

3. Momentum • Momentum, p, is product of object’s mass and velovity • p=mv • Units: kg m/s • Vector that points in same direction as v • Think- if you hit a softball vs. a baseball- softball has more mass and thus less velocity after leaving the bat

4. Impulse-Momentum Theorem • When net force acts on object, the impulse of this force equals the change in momentum • Ft=mvf-mv0 • Impulse=change in momentum • J=p

5. Example • A baseball, mass=0.14kg, has an initial velocity of -38m/s as it approaches a bat. The direction of approach is considered negative. The bat applies an average force, F, that is much larger than the weight of th ball and the ball departs from the bat with a velocity of 58m/s. Determine the impulse applied to the ball by the bat.

6. Example continued • J=p • J=mv0+mv0 • J=(0.14kg)(58m/s) + (0.14kg)(-38m/s) • J=13.4kgm/s • Now- if the time of contact is 1.6x10-3s, what is the average force on the ball?

7. Example continued • J=Ft • F=J/t = 13.4/1.6x10-3 • F=8400N

8. Conservation of momentum • Momentum of a system is conserved • An isolated system has Fexternal=0 • pi=pf • Or sum of momentum of objects in internal system =0 (the pushing off problem)- think of the recoil of a gun/cannon

9. Problem-solving using conservation of momentum • Choose an isolated system- include objects involved so net external forces=0 • ID internal forces and external forces • Equate initial momentum to final momentum or sum of momentum of objects in system =0

10. Example • An astronaut is floating in space near her shuttle when she realizes that her tether cord that is supposed to attach her to the ship has come loose. Her total mass is 90kg. She reaches into her pocket and finds a 1kg tool and throws it out into space with a v=9m/s directed directly away from the ship. If the ship is 10m away, how long will it take her to reach it?

11. Ex- solution • What is the system of interacting objects where total momentum will remain constant? • Astronaut + tool • pastronaut+ptool=0 • mastronautvastronaut+mtoolvtool=0

12. Ex- solution continued • vastronaut=1kg(-9m/s) / 90kg = 0.1m/s • t=d/v t=10m/0.1m/s= 100s

13. Analyzing collisions • Conservation of momentum is used to analyze collisions- objects that collide form the system • Momentum before=momentum after

14. Elastic and inelastic collisions • Elastic collisions conserve kinetic energy (this is ideal since there is always some K lost to heat, deformation, etc) • Inelastic collisions do not conserve kinetic energy • Regardless- all collisions have conservation of momentum

15. Collisions in 1D- example • Two balls roll toward each other. The red ball has a mass of 0.5kg and a speed of 4m/s just before the collision. The green ball has a mass of 0.0kg and a speed of 2 m/s just before the collision. The collision is completely inelastic (they stick together). Determine the velocity of the composite object after the collision.

16. Ex- solution • Total p before= total p after • mredvred+mgreenvgreen=(mred+mgreen)vr+g • Vr+g=1.8m/s

17. What about collisions in 2D? • Same concept but since momentum is a vector, you will need to resolve into x and y components • Momentum in x direction is conserved • Momentum in y direction is conserved • Beware direction- need to use appropriate signs…just like projectiles

18. 2D example…find vc and  if they stick together