Question

Two mass are connected by an ideal string that is threaded over an ideal pulley. The pulley is attached to a wedge whose left edge is exactly vertical and whose edges come together at a peak, making an 32? angle. The mass that falls off of the vertical face has a mass of 5.8 kg and the mass that is partially supported by the angled edge has a mass of 7.7 kg. What is the acceleration of the system?

Answer 1

force equation for the hanging mass is given as

T₁ - m₁ g = m₁ a

T₁ = m₁ g + m₁ a eq-1

force equation for the mass on incline is given as

m₂g Sin32 - T = m₂ a

using eq-1

m₂g Sin32 - m₁ g - m₁ a = m₂ a

a = (m₂g Sin32 - m₁ g)/(m₁ + m₂)

a = ((7.7 x 9.8)Sin32 - (5.8 x 9.8))/(7.7 + 5.8)

a = - 1.25 m/s²

the negative sign indicates that the direction of acceleration is opposite to what we have assumed , that is , hanging mass goes down with acceleration 1.25 m/s²