1. Energy Momentum, Collisions, Impulse

2. Momentum A measure of how hard it is to stop a moving object A measure of how hard it is to stop a moving object Momentum = Momentum = (MASS) (VELOCITY) (MASS) (VELOCITY)

3. Momentum Equation p= m v Units p= mv = (kg)(meter) = kg·m second s second s

4. Momentum animations http://physics.weber.edu/amiri/director/M omentum.html http://physics.weber.edu/amiri/director/M omentum.html http://physics.weber.edu/amiri/director/M omentum.html http://physics.weber.edu/amiri/director/M omentum.html

5. Momentum Example 1 What is the momentum of an orange with a mass of 0.5kg thrown with a velocity of 5.0 m/s? thrown with a velocity of 5.0 m/s? m = 0.5kg v = 5.0 m/s p = mv = (0.5kg)(5.0 m/s) = 2.5 kg·m s s

6. Momentum Example 2 An object with a mass of 3.0 kg is traveling at a velocity of 4.0 m/s. What is its momentum? What is its momentum?

7. More momentum examples http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary1.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary1.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary1.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary1.html

8. Conservation of Momentum Newton’s Third Law For every action there is an equal and opposite reaction! To accelerate an object, we must apply force To accelerate an object, we must apply force

9. Conservation of Momentum Force(s) must be external Force(s) must be external Internal forces do not apply Internal forces do not apply E.g. to accelerate a car, E.g. to accelerate a car, do you push do you push on the dashboard? on the dashboard?

10. Conservation of Momentum http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary3.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary3.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary3.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary3.html

11. Collisions Net momentum before collision = Net momentum after the collision

12. Elastic Collisions http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm

13. Inelastic Collisions http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm http://id.mind.net/~zona/mstm/physics/m echanics/momentum/solvers/momentumS olvers1.htm

14. Impulse = force exerted over time  Impulse changes momentum

15. Impulse Equation J = (Force) (time) J = Ft = mΔv = Δp = m (v 2 -v 1 ) = Δp m (v 2 -v 1 ) = Δp (mass)(change in velocity) = (mass)(change in velocity) = change in momentum change in momentum

16. Impulse Units J= (Newton) (seconds) J = N·s J = N·s Force is in Newtons Force is in Newtons Time is in seconds Time is in seconds

17. Impulse Example An 8N force acts on a 5 kg object for 3 seconds. If the initial velocity of the object was 25 m/s, what is its final velocity? F= 8 Nm= 5 kg t= 3 s v 1 = 25 m/s v 2 = ? J = Ft =(8N)(3s) = 24 N·s BUT we need to find v 2 ……… BUT we need to find v 2 ………

18. Impulse Example J = mΔv = m (v 2 -v 1 ) = 24 N·s = 5 kg(v 2 - 25 m/s) = 24 = 5 v 2 - 125 m/s = 24 = 5 v 2 - 125 m/s = 125+24= 5 v 2 = 149/5 = v 2 = 29.8 m/s

19. Impulse problems http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary2.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary2.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary2.html http://id.mind.net/~zona/mstm/physics/m echanics/momentum/introductoryProblem s/momentumSummary2.html