Two small carts of masses 8 kg and 12 kg are connected by a light inextensible string and placed on a smooth horizontal track as shown in the figure. A constant horizontal force of 50 N is applied to the 12 kg cart, pulling the system. What is the magnitude of the tension in the string connecting the two carts?

Step-by-step solution

Let the common acceleration of the two carts be a . Considering both carts as a single system, the total mass is M = 8 + 12 = 20 kg . The net external force acting on the system is F = 50 N . Using Newton's second law, the acceleration of the system is: a = F M = 50 20 = 2.5 m/s ^2 Let T be the tension in the string connecting the two carts. Considering the free body diagram of the 8 kg cart, the only horizontal force acting on it is the tension T . Applying Newton's second law to the 8 kg cart: T = m₁ a = 8 2.5 =