Force of Ladies Push: Calculating Fpush & Normal Force on a Box

[colleenann]

Homework Statement

A woman pushes horizontally on a wooden box of mass 52.0 kg sitting on a frictionless ramp inclined at an angle of 30.0 degrees. Calculate the magnitude of all forces acting on the box under the assumption that the box is at rest.

Homework Equations

The Attempt at a Solution

I already calculated that the weight of the box is 510.12 N, I can't figure out the force of Fpush and Normal Force. Thanks!

 

[HallsofIvy]

Draw a picture. From the box, draw a vector straight downward representing its weight. Draw another vector perpendicular to the ramp to the tip of your first vector. You should see that you now have a right triangle in which one of the angles, the one at the ramp, has measure 60 degrees. The other, of course, has measure 30 degrees. The "length" of that vertical vector is, of course, the weight of the box and is the hypotenuse of that right triangle. Use trigonometry to find the lengths of the two legs, the components of force normal to and along the ramp. Notice that the vector along the ramp points down the ramp. If there were no other force, that would cause the vector to slide down the ramp.

Now draw a horizontal vector at the box representing the womans push. You don't know the "length" of this vector yet so just call it "f". Again, draw the vector perpendicular to the ramp to that horizontal vector and use trigonometry to find the components normal to and along the ramp. Notice that this component along the ramp points up the ramp. In order that the box not move the two components along the ramp must be the same (and in opposite directions). Set them equal and solve for f.