Two blocks of masses 4 kg and 2 kg are placed in contact with each other on a frictionless horizontal surface. A horizontal force F is applied to the 4 kg block, pushing the system forward. If the contact force between the two blocks is 12 N , what is the magnitude of the applied force F ?

Step-by-step solution

Let the applied force be F and the common acceleration of the system be a . The force F is applied to the 4 kg block, which in turn pushes the 2 kg block. The only horizontal force acting on the 2 kg block is the contact force N from the 4 kg block. Given N = 12 N , we can find the acceleration of the 2 kg block (and thus the whole system): a = N m₂ = 12 2 = 6 m s ⁻² Now, applying Newton's second law to the entire system to find the applied force F : F = (m₁ + m₂) a = (4 + 2) 6 = 6 6 = 36 N Answer: 36 N