Two masses, m1 = 100 kg and m2 = 200 kg, are connected by a massless rope, and are accelerated on a smooth (no friction) horizontal surface by a force F = 100 N.
a) What is the acceleration of the two masses?
b) What is the tension in the rope between m1 and m2 ?
Solution:
a) Consider the two masses as one system. Motion is in one dimension only.
F = ( m1+m2)a
a = F/( m1+m2) = 100N/(300 kg) = 0.33 m/s2
b) Consider free-body diagram for m2. The only force acting on it (in the horizontal direction - the normal force and the weight will cancel out in the y-direction) is the tension T, so we have
T = m2 a = (200 kg)(0.333 m/s2) = 66.7 N
since m2 must be moving with the same acceleration we found in part a)!
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