Solve the Tray Forces Puzzle: Find T and 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!

 

[Chi Meson]

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.

 

[ogb p]

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.