Blocks A and B each have a mass of 0.4 kg and block C has a mass of 1.2 kg. The

Question

Blocks A and B each have a mass of 0.4 kg and block C has a mass of 1.2 kg. The coefficient of friction between the blocks and the plane is uk = 0.30. Initially, block A is moving at a speed of vo = 3 m/s and blocks B and C are at rest (see figure below). After A strikes B and B strikes C, all three blocks come to a stop in the positions shown in part (2) of the figure. Determine (a) the coefficients of restitution between A and B and between B and C, and (b) the displacement x of block C. Chegg wont let me upload the diagram so here is an imgur link: http://i.imgur.com/rsvxY.png

Explanation / Answer

x=285 mm.

e=0.245 b/w A and B

for X

all the kinetic energy goes into work done against friction when all blocks are under rest...

uk Na Da + uk Nb Db + uk Nc Dc = 0.5 mass of A (velocity of A^2)

Na is weight of A,

Da is displacement of A

only unknown in Dc ie the displacement of C

to calculate coefficient of restitition we want velocities of A and B after and before collision

for A before collision friction decreases its energy by doing work in moving 300mm and after collision A has that much K.E that it can slip 75 mm more.

Va before collision=2.689m/s

VA after collision=0.66m/s

same analogy for B and C

after collision coefficient off restitution=(Va after- Vb after)/(Va before- Vb before)

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