"A lunch tray is being held in one..." solved and explained

High School
Physics
Force, Motion and Energy
Acceleration Due to Gravity

Armorikam

Answered question

2020-10-23

A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.200 kg, and its center of gravity is located tits geometrical center. On the tray is a 1.00 kg plate of food and a 0.190 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.

Answer & Explanation

Jaylen Fountain

Skilled2020-10-24Added 169 answers

Since, the entire system is in equilibrium, the net torque about any point due to all forces acting on it must be zero.
Taking the net torque about the FOUR Fingers where F is acing upwards is,

(T \times 0.04 m) = (0.2 k g \times 0.1 m \times g) - (1 k g \times 0.14 m \times g) - (0.19 k g \times 0.32 m \times g) = 0

With

g = 9.8 \frac{m}{s^{2}}

Solving T = 52.2 Ndownwards.
Similarly net torque about the thumb,

(F \times 0.04 m) - (0.2 k g \times 0.14 m \times g) - (1 k g \times 0.18 m \times g) - (0.19 k g \times 0.32 m \times g) = 0

Solving, F = 65.9 N upwards.

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