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Help with Newtons laws and tension?

The block of mass M in the following figure slides on a frictionless surface.

Find an expression for the tension in the string.

Express your answer in terms of the variables m, M, and appropriate constants.

I tried starting with F=ma to get:

T=Ma <------ for block M

T=ma-mg <-- for Block m

But I can't figure out how to get a single expression out of them, and I can't see any other way to solve this. Can someone please help me?

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Your 2nd equation is wrong: It should be

T+ma = mg

Substitute a on the equation of m from the equation for M.

You will get:

T=mg - m*T/M

=>T(1-m/M) = mg

=>T= mg/(1-m/M)

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you did your algebra wrong. it is actually T= mg/(1+m/M)

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