# Solve the Tray Forces Puzzle: Find T and F

• shotgunbob
In summary, the conversation discusses a lunch tray being held in one hand with a mass of 0.2 kg and a center of gravity at its geometric center. On the tray are a 1 kg plate of food and a 0.25 kg cup of coffee. The goal is to calculate the force exerted by the thumb and the four fingers, which act perpendicular to the tray. To do so, the equation T=FX=Counterclockwise forces - clockwise forces = 0 is used, with the point of contact of the fingers as the pivot point. After finding T, the up and down forces are balanced to find F.
shotgunbob

## Homework Statement

A lunch tray is being held in one hand, as the Drawing illustrates. The mass of the tray is .2 kg and its center of gravity is located at its geometric center (the tray is .4m long). On the tray is a 1 kg plate of food and a .25 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.

## Homework Equations

T=FX=Counterclockwise forces - clockwise forces = 0

## The Attempt at a Solution

T= ((f)(.1)) - ( (t)(.06m) + (.2kg)(.2m)(10 m/s^2) + (1kg)(.24)(10) + (.25)(.38)(10m/s^2)) = 0

manipulated the equation so I got F= 625 + T

I Isolated T to be1656.25lbs of force, which is obviously wrong. Help!

#### Attachments

• physics.bmp
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shotgunbob said:
T=FX=Counterclockwise forces - clockwise forces = 0
no, ccw torques balance cw torques. "up" forces balance "down" forces.

T= ((f)(.1)) - ( (t)(.06m) + (.2kg)(.2m)(10 m/s^2) + (1kg)(.24)(10) + (.25)(.38)(10m/s^2)) = 0

looks like you're balancing torques, but what have you picked as a pivot point? I'd use the point of contact of the fingers, since that would make the torque there zero, leaving one unknown (T).

After finding T, go to balance the up and down forces to find F.

Last edited:

As a scientist, my response to this content would be to first clarify what units are being used for the forces (Newton, pounds, etc.) and to check the calculations and equations being used. It is important to use consistent units and to make sure all forces are accounted for in the equation. Additionally, it may be helpful to draw a free body diagram to visualize the forces acting on the tray and to double check the direction and magnitude of each force. It is also important to consider any assumptions being made, such as the assumption that the tray is being held perfectly level and that the forces are acting perpendicular to the tray. Further experimentation or analysis may be needed to accurately determine the forces T and F.

## 1. How do you solve the Tray Forces Puzzle?

To solve the Tray Forces Puzzle, you need to draw a free body diagram of the tray and identify all the forces acting on it. Then, use the equations of motion to find the unknown forces T and F.

## 2. What is the purpose of solving the Tray Forces Puzzle?

The Tray Forces Puzzle is a common problem used to illustrate the principles of static equilibrium and the concept of solving a system of equations. It is a useful way to practice applying these concepts to a real-life situation.

## 3. What are the forces that act on the tray in the puzzle?

The forces that act on the tray include the weight of the tray itself, the weight of the object on the tray, and the normal forces from the table and the block. There may also be frictional forces present depending on the surface and the angle of the tray.

## 4. Can you use the Tray Forces Puzzle to find the mass of the object on the tray?

No, the Tray Forces Puzzle only allows you to find the unknown forces T and F. To find the mass of the object, you would need to know at least one of the forces acting on it (such as its weight) and use Newton's second law.

## 5. Is there a specific method or formula for solving the Tray Forces Puzzle?

Yes, the Tray Forces Puzzle can be solved using the principles of static equilibrium and the equations of motion. There is no one specific method or formula, but the key is to accurately identify all the forces acting on the tray and set up and solve a system of equations to find the unknown forces T and F.

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