The figure below shows one object of mass m_1 on a frictionless laeline at angle

Question

The figure below shows one object of mass m_1 on a frictionless laeline at angle theta _l connected by a cord of negligible mass to another of mass m _2 on a frictionless incline at angle theta _2 Assume that the pulley at the top of the incllnes is trictionless and has negligible mass. Assume the acceleration due to gravity as g and objects move to the right. Set up equations accordingly. Draw a clear free-body diagram showing all the forces acting on the block. Make sure every. thing is clearly labeled. Find the acceleration of the object 1 (a _1) algebraically using only the variables given above. Express the tension of the cord T algebraically using only the variables given above.

Explanation / Answer

Let T be the tension in the string and a be the acceleration of the system

m2gsin(theta2) - T = m2a

T - m1gsin(theta1) = m1a

Add above eqn

(m2sin(theta2) - m1sin(theta1))*g / (m1+m2) = a

T= m2gsin(theta2) + m2a = m2gsin(theta2) + m2[(m2sin(theta2) - m1sin(theta1))*g / (m1+m2) ]

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