A 5kg box is sitting at an angle of 40 degrees above the horizontalwith a wire c

Question

A 5kg box is sitting at an angle of 40 degrees above the horizontalwith a wire connecting it to a 10 kg box which is hanging over theedge. A frictionless pulley is holding the wire up between the twocrates. Find the acceleration of the 5kg crate and tension in thestring?

From the free body diagram for M2, as the block of mass m2 goesdownward, T + 10a=98. Then, as the m1 block moves upward, theequation was shown to be T-5a=31.5. However, can someoneexplain how you put these two equations together to findacceleration and tension? Thanks.

Explanation / Answer

A 5kg box is sitting at an angle of 40 degrees above the horizontalwith a wire connecting it to a 10 kg box which is hanging over theedge. A frictionless pulley is holding the wire up between the twocrates. Find the acceleration of the 5kg crate and tension in thestring? From the free body diagram for M2, as the block of mass m2 goesdownward, T + 10a=98. Then, as the m1 block moves upward, theequation was shown to be T-5a=31.5. However, can someoneexplain how you put these two equations together to findacceleration and tension? Thanks. T + 10a=98 T- 5a=31.5. multiply second eq by 2 it becomes 2T-10a=63 now T + 10a=98 2T-10a=63 adding these two equations we get 3T+0=161 T=53.66N substituting the value of T in the above equation T + 10a=98 we get 10a=98-T=98-53.66=44.33 now a =44.33/10=4.433m/sec2

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