Question

In the figure here, a box of Cheerios (mass mC = 1.3 kg) and a box of Wheaties (mass mW = 2.6 kg) are accelerated across a horizontal surface by a horizontal force applied to the Cheerios box. The magnitude of the frictional force on the Cheerios box is 2.7 N, and the magnitude of the frictional force on the Wheaties box is 4.5 N. If the magnitude of is 12.8 N, what is the magnitude of the force on the Wheaties box from the Cheerios box?

Answer 1

apply Newton's second law of motion, for the applied

force exerted on total system to the right side,

    

total force ΣF = F - f_total

                

(m_C + m_W)(a) = F - f_total

acceleration a = (F - f_total)/(m_C + m_W) ............ (1)

where, f_total = 2.7+4.5 = 7.2 N and F = 12.8 N

substitute the given data in above equation , we get

acceleration a = (12.8 - 7.2)/(1.3 + 2.6)          
                    a = 1.43 m/s²

the contact force:

              F_c - f_W = m_Wa

            F_c   = m_Wa + f_W

where f_W = 4.5 N

    F_c   = (2.6)(1.43) + 4.5

    F_c   = 8.23 N