Three boxes are connected by a strings of constant length. an applied force F ac

Question

Three boxes are connected by a strings of constant length. an applied force F acts as shown in the figure. you are given that Mc=5kg,Mb=2Mc, and Ma=2Mb. the boxes move across a frictionless, horizontal surface, and the position of any fixed point on the boxes or the strings joining them varies with time as x=(0.100m/s^3)t^3+(10.0m/s)t for t>or equal to 0. i) calculate the magnitude of the applied force at t=2.0 seconds. ii) calculate the magnitude of the tension in the string joining A and B at t=5.00 seconds

Explanation / Answer

i) calculate the magnitude of the applied force at t=2.0 seconds.

a = d2x/dt2 = 2*3*0.1 t

F = m a = (5+10+20)*(2*3*0.1 t)

==> F = (5+10+20)*(2*3*0.1*2) = 42 N

ii) calculate the magnitude of the tension in the string joining A and B at t=5.00 seconds

a = d2x/dt2 = 2*3*0.1 t

==> a = 2*3*0.1*2 = 1.2 m/s2

T = mA a = 20 * 1.2 = 24 N

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