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 rough floor. He decides to move them at the same time by pushing on box A with a horizontal pushing force F_p = 8.9 N. Here A has a mass m_A = 10.6 kg and B has a mass m_B = 7.0 kg. The contact force between the two boxes is F_C. The coefficient of kinetic friction between the boxes and the floor is 0.04. (Assume F_p acts in the +x direction.) What is the magnitude of the acceleration of the two boxes? What is the force exerted on m_B by m_A? In other words what is the magnitude of the contact force F_C? If Alex were to push from the other side on the 7.0-kg box, what would the new magnitude of F_C be?

Explanation / Answer

here,

Fp = 8.9 N
Ma = 10.6 Kg
Mb = 7.0 Kg
Fc = Contact Force
u = 0.04
Ff = Frictional Force = u * N

Part A:

as F = mass * acceleration
Ff = Frictional forceacting opposite to applied force,therefore

Fp -Ff = m*a
8.9 -uN = ( 10.6 ) * a

as
N = Normal Force
N = mg = ( 10.6+7)*9.8
N = 172.48 N

8.9 - (0.04 * 172.48) = (10.6+7.0) * a
a = 0.113 m/s^2
The Magnitude of acceleration of the two boxes is 0.113 m/s^2

Part B:
as Force = mass * acceleration
Fc= Mb*a = 7* 0.113
Fc= 0.791 N

the magnitude of the contact force Fc is 0.791 N

part C:
as Force = mass * acceleration
Fc= Ma*a = 10.6* 0.113
Fc= 1.197 N

the new magnitude of Fc is 1.197 N

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