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The figure shows a small object of mass m = 1kg can slide without friction on a wedge of mass M = 3kg inclined at angle [tex]\delta[/tex]=30 degree . What horizontal force F must be applied to the wedge if the small block is not to move with respect to the wedge?

I do it in this way:

By newton`s 3rd law: the small object will exert a same force F to the wedge, so

mgsin30 = Fcos30

F = 5.66N

But my answer is wrong. Can anyone teach me how to solve it?

Thanks.

I do it in this way:

By newton`s 3rd law: the small object will exert a same force F to the wedge, so

mgsin30 = Fcos30

F = 5.66N

But my answer is wrong. Can anyone teach me how to solve it?

Thanks.