Question

Three packing crates of masses, M1 = 6 kg, M2 = 2 kg

and M3 = 8 kg are connected by a light string of
negligible mass that passes over the pulley as shown.
Masses M1 and M3 lies on a 30o
incline plane which
slides down the plane. The coefficient of kinetic friction
on the incline plane is 0.28.
Determine the acceleration of the system.

Answer 1

a = 2.5 m / s²

Step-by-step explanation:

This is an exercise of Newton's second law, in this case we fix a coordinate system with the x axis parallel to the plane with positive direction

Let's write the second law for bodies in the inclined plane

W₁ₓ + W₃ₓ - fr = (m₁ + m₃) a

N₁ -
`W_(1y)` + N₃- W_{3y} = 0

N₁ + N₃ = W_{1y} + W_{3y}

let's use trigonometry to find the weight components

sin 30 = Wₓ/ W

Wₓ = W sin 30

cos 30 = W_{y} / W

W_{y} = W cos 30

we substitute

N₁+ N₃ = W₁ cos 30 + W₃ cos 30

W₁ₓ + W₃ₓ - μ (m₁ + m₃) g cos30 = (m₁ + m₃) a

a = (m₁g sin 30 + m₃g sin 30 - μ (m₁ + m₃) g cos 30) / (m₁ + m₃)

a = g sin 30 - μ g cos30

let's calculate

a = 9.8 sin 30 - 0.28 9.8 cos 30

a = 4.9 - 2,376

a = 2.5 m / s²