Question

The figure below shows an object of mass m1 = 1.0 kg on an inclined surface. The angle of the inclined surface is θ = 30° with the horizontal. The object m1 is connected to a second object of mass m2 = 2.5 kg on a horizontal surface below an overhang that is formed by the inclined surface. Further, an external force of magnitude Fext = 10 N is exerted on the object with mass m1. We observe both objects accelerate. Assuming the surfaces and the pulley are frictionless, and the pulley and the connecting string are massless, what is the tension in the string connecting the two objects?

Figure 4.71

Answer 1

Let the tension in the string = T
Now, Using Newton 2nd Law of Motion -

Fext - m₁*g*sin(30) - T = m₁*a
10 - 1.0*9.8*sin(30) - T = 1.0*a ----------1

For Block on Horizontal Surface
T = m₂*a
T =2.5*a

Equating the value of T in eq 1

a = (Fext-m₁ g sin30)/(m₁+m₂)
10 - 1.0*9.8*sin(30) /(1+2.5)
Solving for a
a = 1.45 m/s^2

Tension in the string, T = 2.5*1.45
Tension in the string, T = 3.625 N