1) A 50.0 kg block is moving up theincline that is sloped upward and to the left

Question

1)      A 50.0 kg block is moving up theincline that is sloped upward and to the left.   Theincline is angled at 30 degrees to the horizontal. Thecoefficient of kinetic friction is 0.5.

a)      What is the acceleration of theblock ?

b) Would the acceleration of the block be different if it weremoving down instead of up (yes or no). EXPLAIN.

Explanation / Answer

The equation of motion along the horizontal direction is                F = mg sin + fk                   = mg sin + kN           .........1              Along the vertical direction we have              N = mgcos                        ......2 From eq 1 and 2 we have       F = mg sin + k mgcos ==> m a = mg sin + k mg cos ==> a = g ( sin + k cos )            = 9.8 * (sin 30 + 0.5 * cos30)            = 9.143 m/s2 Yes. acceleration a = g ( sin - k cos)                                = 9.8 * (sin 30 - 0.5 * cos30)                  = 0.656 m/s2

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