Alex is asked to move two boxes of books in contact with each other and resting

Question

Alex is asked to move two boxes of books in contact with each other and resting on a frictionless floor. He decides to move them at the same time by pushing on box A with a horizontal pushing force F_p = 8.2 N. Here box A has a mass m_A = 11.1 kg and box B has a mass m_B = 7.0 kg. The contact force between the two boxes is F_c and N denotes the normal force. What is the acceleration of the two boxes? What is the force exerted on m_B by m_A? If Alex were to push from the other side on the 7.0 kg box, how would your answer to part (b) change?

Explanation / Answer

given that Fp (force exerted on MA) = 8.2 N

MA = mass of block A = 11.1 kg

MB = mass of block B = 7 kg

a) common acceleration of two boxes , a = Fp / MA + MB                                                   ( F = m*a , a = F/ m)

                                      a = 8.2 / 11.1 + 7

                                      a = 0.453 m/s2

b ) force exerted on MB by MA ( ie contact force Fc) = MB *a

                                                                                   = 7*0.453

                                                                                   = 3.171 N

c) Now Fp = 8.2 N ( force exerted on MB)

force exerted on MA by MB ( ie contact force) = MA*a

                                          = 11.1*0.453

                                           = 5.028 N

every action is equal an opposite reaction. So force exerted on MB = 5.028 N

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