a person is pushing a stationary box of mass 'M' against the ceiling with a force 'F' at angle 'a'. show that the magnitude of the normal force exerted on the box from the ceiling is 'Fp sin a -MG' ?
To show that the magnitude of the normal force exerted on the box from the ceiling is equal to 'Fp sin a - MG', we need to break it down step by step.
1. Start with the free-body diagram of the box:
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Fp|
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| M |
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The forces acting on the box are the force of gravity (mg), the applied force (Fp), and the normal force (N). The vertical component of the applied force is Fp sin a, and the gravitational force is Mg, where g represents the acceleration due to gravity.
2. Resolve the forces along the vertical direction (y-axis):
ΣFy = N - Mg - Fp sin a = 0
We know that the box is stationary, so the net force along the y-axis must be zero.
3. Rearrange the equation to solve for the normal force (N):
N = Mg + Fp sin a
Therefore, the magnitude of the normal force exerted on the box from the ceiling is given by N = Fp sin a + MG, as desired.