A lunch tray is being held in one hand, as the drawing illustrates. The mass of

Question

A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.220 kg, and its center of gravity is located at its geometrical center. On the tray is a1.00 kg plate of food and a 0.225 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

T = __________ N (downward)
F = __________ N (upward)

Explanation / Answer

here,

For the tray to be in balance:

a) The net sum of the upward and downward forces must be zero.

b) The net torque around a chosen axis must be zero.

Form two equations corresponding to conditions a and b.

Any point can be used to calculate the torques.

It makes sense to use the end of the tray since that is where all the measurements have been made from.

a) (0.22 + 1 + 0.225) * 9.8 + T = F

b) (0.2 * 0.22 + 0.24 * 1 + 0.38 * 0.225) * 9.8 + 0.06 * T = 0.1 * F

Then solving them simultaneously for T and F

F = 69.29 N

T = 55.13 N

the forces are T = 55.13 downwards and F = 69.29 N upwards

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