Question
Two masses 10 kg and 20 kg respectively are connected by a massless springs as shown in the figure. A force of 200 N acts on the 20 kg mass. At the instant shown is a figure the 10 kg mass has an acceleration of 12 m/s2. The value of the acceleration of 20 kg mass is
4 m/s2
10 m/s2
20 m/s2
30 m/s2
Solution
A.
4 m/s2
The equation of motion of m1 = 10 kg mass is
F1 = m1a1 = 10 x 12 = 120 N
Force on 10 kg mass is 120 N to the right. As action and reaction are equal and opposite, the reaction force F- on 20 kg mass F = 120 N to the left.
therefore, equation of motion of mass m2 = 20 kg is
200 - F = 20 a2
200-120 = 20a2
80 = 20a2
a2 = 80 /20 = 4 m/s2
