Crazy hard Physics question below?

Question

A lunch tray is being held in one hand. The mass of the tray itself is 0.300 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00 kg plate of food and a 0.205 kg cup of coffee. The distance from the cup to the hand is 0.400 m, the distance from the center of the cup to the hand is 0.380 m, the distance from the center of the plate of food to the hand is 0.240 m, the distance from the tip of the four finger at the bottom of the lunch tray to the above thumb is 0.100 m, the distance from tip of the thumb to the palm of the hand is 0.0600 m.

Obtain the force T (downward)exerted by the thumb and the force F (upward) exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

Answer 1

Crazy hard?  Huh?

You've got two elements here, weight and torque.  The difference between the upward force of the fingers and the downward force of the thumb equals the weight.  The torque exerted by the tray (weight * moment) and all the items on it equals the torque exerted by the force couple between the thumb and fingers.

You don't even have to solve simultaneous equations because you can set the finger force to F(weight)+F(torque) and the thumb force to F(torque).  Boom, you're done.

Answer 2

Still not enough info! You have the distances from plate and cup to hand, but are they in the same or opposite directions? What is the distance from the center of the tray to the hand, or, what's the size of the tray? (How far and in which direction?) The thumb is hooked on the edge of the tray (I would think)? "The distance from the cup to the hand is 0.400 m, the distance from the center of the cup to the hand is 0.380 m": is this a contradiction or are we to infer from it the radius of the cup (a useless bit of data)?
Basically, once you have a complete picture, you find the weight and CM of the tray with its contents, and then you can compute the moment about the fingertips, which gives you the down force applied by the thumb. Then the up force from the fingers is the sum of the thumb force and the weight of the load.

Answer 3

The question will become easier if you drew a force diagram. The 4 fingers and the thumb exert anti-clockwise moment about the centre of the palm; while the food, tray and the coffee exert clockwise moments about the centre of the palm.

The two unknowns are T and F.
If you apply the principle of moments about the thumb, the F is the only unknown. So F can be found.

T + F = total downward weight (of tray, food and coffee)
If F is known, then T can be found.

Please try solving the question yourself: by first drawing a free body force diagram.

Answer 4

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