Question

Two crates, 3kg and 5 kg respectively, are connected with a thin rope.they are pulled up a rough plane which is inclined at 30degree to the horizontal.A force F is applied parallel to the plane as shown as in the diagram accelerating the system of crates at 2ms-2 up the slope.the frictional forces acting on 3kg and 5kg crates are 10N and 17N respectively. Draw a fully labeled free body diagram for each crate. calculate the component of the weight of each crate parallel l to the slope.calculate the magnitude of the applied force F and the tension T in the slope.

Answer 1

Answer:

F = 85.24 N

T = 30.84 N

Explanation:

The parameters given are

Mass of crates = m₁ = 3 kg and m₂ = 5 kg

Component of masses acting along the plane = mgsin(θ)

Which gives;

F - (3×9.81×sin(30) + 10 + 5×9.81×sin(30) + 17) = m×a

So that we have;

2 = (F - 66.24)(3 + 5)

F = 16 + 66.24 = 85.24 N

The tension T between the crates = F × m₁/(m₁+m₂) = 85.24 × 3/(3+5) = 30.84 N