Two boxes are connected by a light string that passes over a massless, frictionl

Question

Two boxes are connected by a light string that passes over a massless, frictionless pulley. One box of mass m_1 rests on a frictionless ramp that rises at an angle theta above the horizontal (see figure). The other box hangs and has mass m_2. The system is released from rest. Call the acceleration of the hanging box "a" in the downwards direction i.e. if a is positive number then m_2 accelerates downwards. The acceleration a of the two boxes is expressed as follows (where this is the acceleration down-wards for the hanging box and the acceleration up along the incline for m1) A a = (m_2 g + m_1 g)/(m_1 - m_2) B. a = g C. a = m_2 g - m1 g cos theta D. a = 0

Explanation / Answer

the two blocks are attached using string, then the acceleration of the two blocks along the string will be same.

In the situation given, there can be only one acceleration and that is along the rope only. Hence both block will have one common acceleration.

The value of acceleration can be found writting the equation of motions for both.

For the hanging block:

m2g - T = m2a ---------(i)

for the second block,

T - m1 g sin(theta) = m1a -----------(ii)

Adding both equation we get,

a = (m2-m1 sin(theta))*g/(m1+m2)

this is the expression of the acceleration.

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