Calculating Torque & Lever Arm for a Lunch Tray

[drewfus]

A lunch tray is being held in one hand. The mass of the tray itself is 0.201 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.33 kg plate of food and a 0.285 kg cup of coffee. Assume lever arm of the thumb is 0.0620 m, lever arm of the finger is 0.113 m, lever arm of the plate 0.231 m, lever arm of the coffee cup is 0.361 m and lever arm of the tray is 0.383 m. Obtain the force T exerted by the thumb. This force acts perpendicular to the tray, which is being held parallel to the ground.

The picture that I have (but could not upload for some reason) had the thumb on top of the tray have a force T exerted in the -y direction when drawn with a force diagram and the finger had a +y force.

I plugged into a force table and then calculated a torque table, and I substituted with the two equations and got an answer of -133 Newtons, but I checked it and it was wrong.

Any ideas on what I did wrong?

 

[mathmike]

torque is T=F * D

just take the moment of all forces at one point and then use statics equations to find the rections

 

[mukundpa]

From which axis of rotation the arms are measured. Check axis of rotation you have taken and the directions of the moments of force

 

[drewfus]

thanks guys i appreciate it.