Step-by-step explanation:
Draw a free body diagram. There are four forces acting on the block:
Weight force Mg pulling straight down,
Normal force N pushing normal to the incline,
Friction force μN pushing down the incline,
and applied force P (100 N) pulling up the incline.
Choose +x to be up the incline and +y to be normal to the incline.
Sum of forces in the +y direction:
∑F = ma
N − Mg cos θ = 0
N = Mg cos θ
Sum of forces in the +x direction:
∑F = ma
P − μN − Mg sin θ = 0
P = μN + Mg sin θ
Substitute:
P = μMg cos θ + Mg sin θ
P = Mg (μ cos θ + sin θ)
Plug in values and solve for M:
100 N = M (9.8 m/s²) (0.28 cos 30° + sin 30°)
M = 13.7 kg