The piece of furniture shown in the diagram below has a mass of 80 kg. Determine

Question

The piece of furniture shown in the diagram below has a mass of 80 kg. Determine its acceleration and the normal reaction under the legs A and B if the force, P= 250 N, is applied at the position shown. The coefficients of static and kinetic friction between the cabinet and the ground are s=0.2 and k= 0.15, respectively. The cabinet’s center of gravity is located at G.

Forces and Moments on Rigid Bodies: The piece of furniture shown in the diagram below has a mass of 80 kg. Determine its acceleration and the normal reaction under the legs A and B if the force, P = 250 N, is applied at the position shown. The coefficients of static and kinetic friction between the cabinet and the ground are 0.2 and ,-0.15, respectively. The cabinet's center of gravity is located at G. 0.3 m0.3 m 14 m 1.2 m

Explanation / Answer

let normal force at A and B are Fa and Fb.

assume that acceleration of the system is a m/s^2.

kinetic friction at A=0.15*Fa, to the left

kinetic friction at B=0.15*Fb, to the left

balancing forces in vertical direction,

Fa+Fb=weight of the furniture=80*9.8=784 N…(1)

balancing total moment about A:

P*1.4=80*9.8*0.3+Fb*0.6

==>Fb=(250*1.4-80*9.8*0.3)/0.6=191.33 N

then from equation 1, Fa=784-191.33=592.67 N

total force in horizontal direction=P-0.15*Fa-0.15*fb

=250-0.15*191.33-0.15*592.67=132.4 N

acceleration of the system=total force in horizontal direction/mass

=132.4/80=1.655 m/s^2

hence acceleration of the system is 1.655 m/s^2.

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