Answer:
15.7 N
Explanation:
Draw a free body diagram. The block has four forces acting on it. Gravity pulling down, normal force pushing perpendicular to the plane, friction pointing up the plane, and applied force F pushing up the plane.
Sum of the forces normal to the plane:
∑F = ma
N − mg cos θ = 0
N = mg cos θ
Sum of the forces parallel to the plane:
∑F = ma
Nμ + F − mg sin θ = 0
F = mg sin θ − Nμ
Substituting:
F = mg sin θ − mgμ cos θ
F = mg (sin θ − μ cos θ)
Given mg = 87.0 N, θ = 24.1°, and μ = 0.25 (because the block is not moving):
F = 87.0 N (sin 24.1° − 0.25 cos 24.1°)
F = 15.7 N
