# Laws of motion/static friction problem

1. Oct 18, 2009

### Leesh09

1. The problem statement, all variables and given/known data

Two astronauts are unloading scientific equipment from the space ship that has just landed on the Moon surface. To prevent a box from sliding down an inclined ramp, astronaut A pushes on the box in the direction parallel to the incline, just hard enough to hold the box stationary. In an identical situation astronaut B pushes on the box horizontally. Regard as known the mass m of the box, the coefficient of static friction s between box and incline, and the inclination angle . (a) Determine the force A has to exert. (b) Determine the force B has to exert. (c) If m = 2.00 kg, = 25.0°, and s = 0.160, who has the easier job? (d) What if s = 0.380? Whose job is easier? The acceleration of gravity on the Moon is 1.625 m/s2.

2. Relevant equations

fstatic= coefficient of friction * normal force

3. The attempt at a solution
For A, the applied force is on the x plane so the forces in play are the applied force, the static friction force, and the x component of the normal force/mg. Both the static friction force and applied force are working against gravitational force to keep the box in place and there is no movement, so mg*sin theta = applied force + static friction force so the applied force= mg*sin theta - (coefficient of friction)(gravitational constant)??
I don't know how to tackle B though, since the applied force is neither parallel nor perpendicular to the incline.

2. Oct 18, 2009

### rl.bhat

In the first case what is the frictional force?
The applied force is in the upward direction along the inclined plane. What is the direction of the frictional force and mgsinθ?
In the case of B, resolve the force in to components. One along the inclined plane and the other normal to the inclined plane. Then identify the directions of mgsinθ, frictional force and the component of applied force.

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