Calculating Torque & Lever Arm for a Lunch Tray

In summary, the conversation discusses the force exerted by the thumb while holding a lunch tray with a mass of 0.201 kg. The tray also contains a 1.33 kg plate of food and a 0.285 kg cup of coffee, with their respective lever arms. The force T exerted by the thumb was calculated to be -133 Newtons, but the accuracy was questioned. The conversation ends with a request for clarification on the axis of rotation and direction of moments of force.
  • #1
drewfus
2
0
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?
 
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  • #2
torque is T=F * D

just take the moment of all forces at one point and then use statics equations to find the rections
 
  • #3
From which axis of rotation the arms are measured. Check axis of rotation you have taken and the directions of the moments of force
 
  • #4
thanks guys i appreciate it.
 

1. What is torque and lever arm?

Torque is a measure of the force that can cause an object to rotate around an axis. Lever arm is the distance between the axis of rotation and the point where the force is applied.

2. Why is it important to calculate torque and lever arm for a lunch tray?

Calculating torque and lever arm for a lunch tray is important because it helps determine the stability and balance of the tray, which is crucial for preventing spills and accidents.

3. How do I calculate the torque and lever arm for a lunch tray?

To calculate the torque, multiply the force applied to the tray by the distance from the axis of rotation. To calculate the lever arm, simply measure the distance from the axis of rotation to the point where the force is applied.

4. What units are used to measure torque and lever arm?

Torque is typically measured in Newton-meters (Nm) or foot-pounds (ft-lb), while lever arm is measured in meters (m) or feet (ft).

5. How can I use torque and lever arm calculations to improve the stability of a lunch tray?

By calculating the torque and lever arm, you can determine the best location to apply force on the tray to increase its stability. You can also adjust the amount of force applied or the distance from the axis of rotation to achieve a more balanced and stable tray.

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