A box at rest on a ramp is in equilibrium, as shown. What is the force of static friction acting on the box? Round your answer to the nearest whole number. N What is the normal force acting on the box? Round your answer to the nearest whole number. N

Answer

Ffs = 251 N

Fn = 691 N

Explanation

Take the y direction to be normal to the ramp and the x direction to be parallel to the ramp. The angle of the ramp is 20°, so the angle that the weight vector makes with the normal is also 20°. Therefore:

Fgx = Fg sin 20°

Fgy = Fg cos 20°

Sum of the forces in the x direction (parallel to the ramp):

∑F = ma

Ffs - Fgx = 0

Ffs = Fgx

Ffs = Fg sin 20°

Ffs = 735 sin 20°

Ffs ≈ 251

Sum of the forces in the y direction (normal to the ramp):

∑F = ma

Fn - Fgy = 0

Fn = Fgy

Fn = Fg cos 20°

Fn = 735 cos 20°

Fn ≈ 691