section%202%20soln - is mv 2 2 + 2 Mv 2 c 2 . At the...

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Friday, November 07, 2008 10:25 AM Midterm 2 Prob 1 Page 1
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1 Solution for Problem 2 1) Before the collision the total momentum is mv 0 + Mv 0 . The total mo- mentum should be conserved, since there are no external forces in x-direction. Also since there is no force in x-direction acting on the block m (no friction) during the collision, the momentum of the block won’t change (just after the collision). Then we can find the velocities of the block and carts: the velocity of the block v 0 the velocity of two carts after the collision Mv 0 = 2 Mv c and therefore v c = v 0 2 2) To find the height we can use the conservation of energy. The energy just after the collision (we can’t use the initial energy, since the collision is inelastic)
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Unformatted text preview: is mv 2 2 + 2 Mv 2 c 2 . At the maximum height the relative velocity of the block (respect to carts) is zero, so the block and the carts move as a whole system. To nd this velocity we again can use the conservation of momentum (this velocity is not equal to v c ). ( m + M ) v = ( m + 2 M ) v f v f = m + M m + 2 M v The conservation of energy gives us: mv 2 2 + 2 Mv 2 c 2 = mgh + ( m + 2 M ) v 2 f 2 mv 2 + 2 M v 2 2 = 2 mgh + ( m + M ) 2 (2 M + m ) v 2 h = Mv 2 4 g (2 M + m )...
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This note was uploaded on 10/17/2011 for the course PHYSICS 7A taught by Professor Lanzara during the Spring '08 term at University of California, Berkeley.

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section%202%20soln - is mv 2 2 + 2 Mv 2 c 2 . At the...

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