Answer:
m = 2.31 Kg
Explanation:
given,
m₁ is the mass rest on the inclined plane = 1.5 Kg
inclination of plane = 30°
Kinetic friction = μ = 0.4
acceleration of the body = 2.68 m/s²
mass m is hanging = ?
using equation to solve
T - m₁g sin θ - μ m₁g cos θ = m₁ a
on the block on inclined plane there will be acting tension T on the string,
mg sin θ will be the force acting opposite to the tension on the string and a frictional force will be acting which will oppose moment which will be equal to μ m₁g cos θ
T = m₁(g sin θ + μ g cos θ + a )
T = 1.5 (9.8 x sin 30° + 0.4 x 9.8 x cos 30°+ 2.68 )
T = 16.46 N
now, forces on the other side of pulley
m g - T = m a
m (g - a ) = T
m = 2.31 Kg