A small block of mass m rests on the sloping side (45°) of a triangular block of

Question

A small block of mass m rests on the sloping side (45°) of a triangular block of mass M which itself rests on a horizontal table..
Assuming all surfaces are frictionless, determine the force P that must be applied to M so that m remains in a fixed position relative to M (that is, m doesn’t move on the incline).

I tried to solve 2.23 = (1.00 + x)*9.8*tan(45), to no avail. What am I doing wrong?

Here is a Free-body diagram for ramp (triangular block)

and here is a Free-body diagram for small block

THANKS!

Explanation / Answer

F = (M+m)g tan

mg is the weight

So, 2.23 N = Mg tan +mg tan

2.23 N = (1.00 N ) tan 45 0 + mg tan 45 0

2.23 N = 1.00 N + mg

1.23 N = mg

mg (1.23 N) is the weight of the block with mass 'm'. This should be the answer.

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