A 251-N force is directed horizontally as shown to push a 25.1-kg box up a ramp at a constant speed. There is friction between the box and the ramp. The angle of ramp is 30 degrees.

(a) Calculate the magnitude of the normal force of the ramp on the box.
(b) Calculate the coefficient of kinetic friction between the ramp and the box.

1 answer

sketching it:
normal force due to weight=mg*cosTheta
normal force due to pushing horizontal=251sinTheta
add them to get normal force.
b. coefficent of fk mu
net force=acceleration
net force has three components:
weight down the plane mgcosTheta
friction down the plane Normal force*mu
force up along the plane from pushing 251SinTheta
net force=251*sinTheta-mu(mgcosTheta+251*sinTheta)=zero (no acceleration)
251*sinTheta-mu(mgcosTheta+251*sinTheta)=0 solve for mu