A crate of mass m1 on a frictionless inclined plane isattached to another crate

Question

A crate of mass m1 on a frictionless inclined plane isattached to another crate of mass m2 by a massless rope. The ropepasses over an ideal pulley so the mass m2 is suspended in air. Theplane is inclined at an angle ? = 36.9'. Use conservation ofenergy to find how fast crate m2 is moving after m1 has traveled adistance of 1.4 m along the incline, starting from rest. The massof m1 is 10.6 kg and the mass of m2 is 21.2 kg. A crate of mass m1 on a frictionless inclined plane is attached to another crate of mass m2 by a massless rope. The rope passes over an ideal pulley so the mass m2 is suspended in air. The plane is inclined at an angle ? = 36.9'. Use conservation of energy to find how fast crate m2 is moving after m1 has traveled a distance of 1.4 m along the incline, starting from rest. The mass of m1 is 10.6 kg and the mass of m2 is 21.2 kg.

Explanation / Answer

Summing forces on m2 we have m2*g - T = m2*a or T= m2*g - m2*a

Summing forces along the ramp on m1 we get

T - m1*g*sin(?) = m1*a or T = m1*g*sin(?) + m1*a

So m2*g - m2*a = m1*g*sin(?) + m1*a

or (m1 + m2)*a = m2*g - m1*g*sin(?)

a = (m2*g - m1*g*sin(?))/(m1 + m2) = = (21.2*9.8 - 10.6*9.8*sin(36.9))/(10.6 + 21.2) = 4.57m/s^2

So use kinematic eqn v^2 = v0^2 + 2*a*x where v0 = 0

So v = sqrt(2*a*x) = sqrt(2*4.47*1.4) = 3.57 m/s

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