Question

A mass m1=1.5 kg rests on a 30 degree ramp with a coefficient of kinetic friction = 0.40. Mass m1 is tied to another mass m with a string which runs over a frictionless pulley. Mass m is hanging above the ground. The acceleration of masses is measured 2.68 m/s2. What is m?

Answer 1

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

$m = \dfrac{16.46}{9.8-2.68}$

m = 2.31 Kg