Physics 6A Practice Final fall 2009 solutions

# Physics 6A Practice Final fall 2009 solutions - Physics 6A...

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Physics 6A Practice Final (Fall 2009) solutions Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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1. A locomotive engine of mass M is attached to 5 train cars, each of mass M. The engine produces a constant force that moves the train forward at acceleration a. If 3 of the cars are removed, what will be the acceleration of the shorter train? We just use Newton’s 2 nd law here: Net force = (total mass) x (acceleration) Initially, the total mass is 6M (5 cars, plus the engine) After removing 3 cars the total mass is 3M (2 cars, plus the engine) In both cases the Net force is the same (the engine didn’t change). Here is the formula in both cases: Initial F = (6M)(a) Final F = (3M)(a final ) Setting these equal gives a final = 2a Another way to think about this one is that since the mass is cut in half, the acceleration must double. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
We can think of this as a single box with total mass 4kg. Then using F = ma we get the acceleration of the whole system. A B 2 s m system system kg N 2 a a 4 8 = = 2. Two boxes are placed next to each other on a smooth flat surface. Box A has mass 1 kg and Box B has mass 3 kg. A constant horizontal force of 8 N is applied to Box A. Find the force exerted on Box B. Now we do the same thing, but just for box B: Remember – Box B has a mass of only 3kg N B s m kg B 6 F 2 3 F 2 = = Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

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We can think of this as a single box with total mass 4 kg . Then using F = ma we get the acceleration of the whole system. We need to account for friction, so first find the maximum force of static friction: B ( ) ( ) N 68 . 15 8 . 9 4 4 . 0 N 2 max static max , static m kg F s F = = µ = 3. Two boxes are placed next to each other on a flat surface. Box A has mass 1kg and Box B has mass 3kg. The coefficients of friction are 0.3 and 0.4 for kinetic and static friction, respectively. A constant horizontal force of 8N is applied. Find the acceleration of Box B. A , s 8N F static This friction force is more than the 8 N force trying to move the boxes, so they are held in place by friction. Thus the acceleration of both boxes is 0. *Note that the actual force of friction holding the boxes in place is only 8 N – just enough to keep them from moving. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
A 0.2 kg piece of wood is being held in place against a vertical wall by a horizontal force of 5 N. Find the magnitude of the friction force acting on the wood. 5N N F friction From the force diagram, we can see that the friction force must equal the weight of the piece of wood to keep it from falling. ( ) ( ) N

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## This note was uploaded on 12/09/2009 for the course PHYS PHYS 6a taught by Professor Geller during the Spring '09 term at UCSB.

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Physics 6A Practice Final fall 2009 solutions - Physics 6A...

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