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Lab3Momentum

# Lab3Momentum - Physics 2010 Laboratory 3 Momentum and...

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1 Physics 2010 Laboratory 3: Momentum and Energy NAME ___________________________ Section Day (circle): M Tu W Th F Section Time: 8a 10a 12p 2p 4p TA Name: ________________________ In this experiment you will use air tracks, gliders, and photogate timers to study the concepts of momentum and kinetic energy and how they behave when objects interact (that is, when they "collide"). These concepts are critical for many real-world issues, so are valuable even outside the sciences. Background Information Here we discuss the momentum and kinetic energy of an object. Imagine you are in a car stopped at a light. Prof. Dubson comes up behind you, his mind on some obscure physics problem, and rams into your rear bumper. Call his mass and his car’s mass, m 1 , the mass of you and your car m 2 , and the velocity with which he hit you v 1 i (i for "initial"). You started at rest, so v 2 i = 0. Immediately after the cars collide, both you and he will be moving at new velocities: he moving forward with velocity v 1 f and you moving with velocity v 2 f (f for "final"). During the very short time (call it Δ t ) that the cars were in contact, we know by Newton's third law that the force on Dubson’s car (car 1) by your car (car 2) is equal in magnitude and opposite in direction to the force on your car by Dubson’s car: F 21 = – F 12. (1) We also know, by Newton's second law, that F net = m a for each car, so that during the contact between the cars: m 1 a 1 = – m 2 a 2. (2) For constant acceleration a = Δ v/ Δ t = ( v f v i )/ Δ t, so we can rewrite Eq. (2) as: m 1 ( v 1 f - v 1 i )/ Δ t = – m 2 ( v 2 f - v 2 i )/ Δ t (3) Multiplying both sides by Δ t and moving things around (being careful with negative signs), we get m 1 v 1 i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f (4) Calling an object's momentum p = m v (note that it's a vector), we can see that the total momentum of the system before the collision, that is, the sum of the momenta of both cars, equals the total momentum of the system afterwards: hence momentum is conserved . (Note that the momentum of each car individually changes! Only the total momentum stays the same.) Another useful quantity is the kinetic energy. This is defined as KE = ½ mv 2 , so for example Prof.

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