To be able to set up and analyze the freebody diagrams and e

To be able to set up and analyze the free-body diagrams and equations of motion for a system of particles. Consider the mass and pulley system shown Mass m_1 = 35 kg and mass mo = 15 kg the angle of the inclined plane is given, and the coefficient of kinetic friction between mass m_2 and the inclined plane is mu_k. = 0.19 Assume the pulleys are massless and frictionless. Finding the acceleration of the mass on the inclined plane What is the acceleration of mass m_2 on the inclined plane? Take positive acceleration to be up the ramp Finding the speed of the mass moving up the ramp after a given time If the system is released from rest, what is the speed of mass m_2 after 3 s?

Solution

Part A:

As Value of friction factor is given so Frictional force (F_f) will come in to picture. Formula to Calculate Accelaration concidering Friction factor is

a= (m₂.g - F_f - m₁.g.Sin (theta)) / (m₁ + m₂)

m₁ = 15 Kg

m₂ = 35 Kg

theta = angle between the line perpendicular to the inclined plane and verticle component of (m₂.g)

        = cos^-1(12/13) = 22.62⁰

mu = coeffitient of friction = 0.19

F_f = mu.m₂.g.cos(theta) = 0.19*35*9.81*cos(22.62) = 60.21 N

a = {(35*9.81) - 60.21 - (15*9.81*sin(22.62))} / (35+15)

   = 4.531 m/s² (upwards)

PART B:

Speed = a*time

time = 3Sec.

Speed = 4.531*3 = 13.593 m/s