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A lunch tray is being held in one hand, as the figure illustrates. The mass of the tray itself is 0.169 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.13-kg plate of food and a 0.270-kg cup of coffee. Obtain (a) the force exerted by the thumb and (b) the force exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

Explanation / Answer

Balancing forces,

F=T+0.169*9.8+1.13*9.8+0.27*9.8

F-T=15.376N

Balancing moments about left end of tray,

F*0.1-T*0.06-0.169*9.8*0.2-1.13*9.8*0.24-0.27*9.8*0.38=0

Solving both simultaneously,

b)F=76.8N

a)T=61.4N

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