Answer:
17.6 kg
Explanation:
Newton's second law of motion says that the net force on an object is equal to its mass times its acceleration. By drawing a free body diagram for each block, we can balance the forces and solve for the unknown mass.
For the hanging mass, there are two forces:
Weight force m₂g pulling down,
Tension force T pulling up.
Sum of forces in the y direction:
∑F = ma
T − m₂g = 0
T = m₂g
For the sliding mass, there are four forces:
Weight force m₁g pulling down,
Normal force N pushing up perpendicular to the incline,
Friction force Nμ pushing up parallel to the incline,
Tension force T pulling up parallel to the incline.
Sum of forces in the perpendicular direction:
∑F = ma
N − m₁g cos θ = 0
N = m₁g cos θ
Sum of forces in the parallel direction:
∑F = ma
T + Nμ − m₁g sin θ = 0
T + m₁gμ cos θ − m₁g sin θ = 0
T + m₁g (μ cos θ − sin θ) = 0
Substitute:
m₂g + m₁g (μ cos θ − sin θ) = 0
m₂g = m₁g (sin θ − μ cos θ)
m₂ = m₁ (sin θ − μ cos θ)
m₁ = m₂ / (sin θ − μ cos θ)
Plug in values:
m₁ = (5.0 kg) / (sin 30° − 0.25 cos 30°)
m₁ = 17.6 kg
