Three blocks M1, M2, M3 having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, T1 when they are moving upward with acceleration of 2ms–2 is ............... N (if g = 10 m/s2 )

Question

Find external force F so that block can move on inclined plane with constant velocity.

Answer 1

Fig.
The forces acting on each block will now be analyzed.

Considering the entire system (masses \(M_1\), \(M_2\), and \(M_3\) combined) accelerating upwards at \(a = 2 \, \mathrm{m/s^2}\):

The total mass is \(M = M_1 + M_2 + M_3 = 4 + 6 + 10 = 20 \, \mathrm{kg}.\)

The total weight is \(W = Mg = 20 \times 10 = 200 \, \mathrm{N}\)

As the system accelerates upwards, the net force \(F\) necessary for this acceleration is calculated as:

\(F = Ma = 20 \times 2 = 40 \, \mathrm{N}\)

Consequently, the tension \(T_1\) in rope 1 must counteract the combined weight and the force needed for acceleration:

\(T_1 = W + F = 200 + 40 = 240 \, \mathrm{N}\)

Correct Answer: 240