Kgg Name: _____________________ Period: _____________________ Momentum and Impulse Momentum Momentum is how hard it is to stop something and is a product of an object’s mass and its velocity. Momentum is increased if either the mass or velocity is increased. Increasing mass increases momentum. Momentum is a vector p = mv m = 30 kg v = 4 m/s Velocity (in m/sec) v = 5 m/s p = 40 kgm/s 2 kg v = 3 m/s p = 0 kgm/s v = -3 m/s p = -6 kgm/s If a vector is at an angle, you can find its components. If in one dimension, just add or subtract. Net momentum can be negative. Sum of all Momentum 2 kg pnet = Σp Σp = p1 + p2 + … 8 kg v = 3 m/s p = 6 kgm/s p= py = 12(sin30º) = 6 kgm/s 12 kgm /s Net momentum can be zero. 6 kg v = -3 m/s p = -24 kgm/s pnet = Σp = 6 – 24 = –18 kgm/s Add up all of the momentums v = 3 m/s p = 18 kgm/ 9 kg v = -2 m/s p = -18 kgm/s Net momentum can be also be zero if all of the objects are at rest. pnet = Σp = 18 – 18 = 0 kgm/s An impulse is a force acting over time. Impulse is like work: an impulse causes a change of momentum, just like work causes a change of energy. Impulse Force (in N) I = Ft I I = ∆p Time (in sec) An impulse changes momentum. +I 3 sec 8N = pafter v = 8 m/s m= 3 kg pbefore + Impulse = pafter 0 kgm/s + 24 kgm/s = 24 kgm/s JI = ∆p = 8(3) = 24 kgm/s cstephenmurray.com 30º Together multiple objects have a net momentum. Net momentum is easy to calculate. Calculate each individual momentum and add them together. Net Momentum m= 3 kg px = 12(cos30º) = 10.4 kgm/s You add momentum vectors like all other vectors: find components; find total x and y; etc. (See “Adding Vectors”) ptotal = +8 kgm/s pbefore v = 0 m/s direction Being a vector, momentum must have magnitude and direction and must be treated like all vectors. It can have components and can be added or subtracted. p2 = -4 kgm/s Impulse (in kgm/sec) Momentum can be negative. 2 kg p1 = +12 kgm/s sit p = mv = (30kg)(4m/s) = 120 kgm/s Something must be moving to have momentum. 8 kg v = 3 m/s p = 24 kgm/s v = 3 m/s p = 6 kgm/s Momentum (in kgm/sec) Increasing velocity increases momentum. 8 kg 2 kg Net Momentum Ex. Calculate the momentum of a 30 kg object going 4 m/s? Mass (in kg) Ex. Calculate the impulse of a 4 N force acting for 6 seconds. F=4N t = 6 sec I = _____ I = Ft = (4)(6) = 24 kgm/s = ∆p A positive impulse causes a positive change of momentum. before 2 kg vB = 3 m/s pB = 6 kgm/s after +6N 2 sec 2 kg vA = 9 m/s pA = 18 kgm/s ∆p = pf – pi = 18 – 6 = 12kgm/s = 6(2) = Impulse It sets Force ≠ impulse. A small force can cause the same impulse as a big force if it acts for enough time. 100 N (1 sec) = 100 kgm/s 1 N (100 sec) = 100 kgm/s A negative impulse causes a negative change of momentum. before 2 kg vB = -1 m/s pB = -2 kgm/s after -4N 1 sec 2 kg vA = -3 m/s pA = -6 kgm/s ∆p = pf – pi = -6 – (-2) = -6+2 = -4kgm/s = -4(1) = Impulse Copyright © 2009, C. Stephen Murray Name: _____________________ Period: _____________________ 10. Can an object have momentum in space? 1. Momentum A. pf – pi. 2. Impulse B. Equal to Σp. 3. ∆p C. It is important to know how big and in what direction. 11. If you increase a moving object’s mass, how does its momentum change? 4. Vector D. How an object changes momentum. 5. Magnitude E. The “25” in 25 kgm/s. 12. If an object changes momentum there must be a change of ___________ or __________. 6. pnet velocity mass F. The product of mass and velocity. Which has more momentum? velocity is negative 14. How can an object have the same speed and mass, but change its momentum? 0 7. A bowling ball at rest or a bowling ball going 1 m/s? 8. A fast baseball or a slow bowling ball? 13. How can momentum be negative? Direction changes 15. How can multiple objects have a net momentum of zero? O 9. A 1000 kg object at rest or a 1 kg object moving 0.2 m/s? Ifall objects are at rest A. B. C. D. 3 kg 3 kg 3 kg 3 kg Mass A Mass B Mass C Mass D v = 0 m/s v = -4 m/s 6 kg 4 kg 1 kg 6 kg v = 0 m/s v = -2 m/s v = 5 m/s v = 2 m/s Above shows an object at different positions. v = 5 m/s v = 3 m/s 16. Calculate the object’s momentum at position A. ISkgints 19. Calculate pnet of A and B above. 42kgm s 17. Calculate ∆v between positions A and B. 20. Calculate pnet of B and D . m s Okays 18. Calculate ∆p between positions B and D. 6 125 6kgm 21. Calculate pnet for all four objects. s 22. 6 N pushes to the right on a 3 kg mass for 8 seconds. A. Calculate the impulse. 30kgm s 24. Draw the net momentum for the following: p2 848 B. How much momentum was gained by the object? 23. A 15 N force pushes on an object for 10 seconds. How much momentum did it gain? is p3 p1 25. Find the px and py of the following object. 26. A 4 kg object is moving 2 m/s to the right. A 6 N force pushes to the left for 3 seconds. A. Calculate pbefore. 8kg s /s m N kg θ = 42º 6 Peel 8kg.ms Py 16.1kgms 27. A 20 kg object is at rest. A 6 N force pulls to the right on the object for 10 seconds. A) Find the impulse on the object. 18 C. What is ∆p for this object? Go What is it’s 60 final velocity? B) Find the final momentum of the object. 10h8m1s D. What is its final momentum (pf )? cstephenmurray.com = i B. Calculate the impulse. 10kg v 4 s C) Girls Copyright © 2009, C. Stephen Murray