Use work and energy to find an expression for the speed of the block in the foll

Question

Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor.

PART A: Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables M,m,h, mk(mu k) and free fall acceleration .

PART B: Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables M,m ,h , and free fall acceleration g.

Thank you so much!

Explanation / Answer

Acceleration = Net Force along Line of Motion/Total Mass in Motion

Therefore

Acceleration , a = (mg - µkMg)/(M+m)

Therefore

As we know

v^2 - u^2 = 2ah

Therefore

v = [2(mg - µkMg)h/(M+m)]

==============================

If there is No Friction

Acceleration = mg/(M+m)

Therefore

v = [(2mgh/(M+m)]

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