Calculating Tray and Food Weight: Torque Question Help Requested

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In summary, the problem involves finding the forces exerted by the thumb and the four fingers in holding a lunch tray with a plate of food and a cup of coffee. Using the equation T=Fl, the forces T and F were calculated, and then the net forces were determined to be in equilibrium. The weights of the objects were also calculated to verify the results.
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Student3.41
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Homework Statement



A lunch tray is being held in one hand, as the drawing below illustrates.
The mass of the tray itself is 0.218 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.28-kg plate of food and a 0.255-kg cup of coffee. Assume L1 = 0.0590 m, L2 = 0.109 m, L3 = 0.242 m, L4 = 0.373 m and L5 = 0.398 m. Obtain the force T exerted by the thumb (enter first) and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

Attached picture.

Homework Equations



T=Fl

The Attempt at a Solution



I first solved for F.

I have subtracted L1 all the other L values because I have started from the thumb.

Tcup = Fl = (0.255kg*9.8m/s^2)(0.373m-0.0590m) = 0.785N*m

Tfood = (1.28kg)(9.8m/s^2)(0.183m) = 2.30N*m

I am not sure about this one but I am thinking I use the CG as the L because it is uniform. Therefore;

Ttray = (0.218kg)(9.8m/s^2)(0.200m(CG)-0.0590m) = 0.301N*m

TF = Fl = F(0.05m)

T[/SUB]NET[/SUB] = 0 - - - > Static Equilibrium


TF = Ttray+Tfood+Tcup
F(0.05m) = 0.301+2.30+0.785

F(0.05m)= 3.39N*m
F=3.39/0.05
F=67.8N


F[/SUB]NET[/SUB] = 0 ------> Equilibrium, Calulate the Weights of the objects.

W[/SUB]tray[/SUB]W[/SUB]cup[/SUB]W[/SUB]food[/SUB]F[/SUB]f[/SUB]
(2.14N) + (12.5N) + (2.50N) + (-67.8N) = T
T=-51.0N (-) indicates direction.

Did some work and need help.. thanks.
 

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  • #2
Your work approach looks very good. To be sure you did not make a math error, it is always a good idea to sum moments about the other unknown force (about the fingers) to see if you get the same result for T. Good work.:approve:
 

Related to Calculating Tray and Food Weight: Torque Question Help Requested

1. What is torque?

Torque is a measure of the twisting force applied to an object. It is commonly used to describe the force required to rotate an object around an axis.

2. How is torque calculated?

Torque is calculated by multiplying the force applied to an object by the distance from the axis of rotation. The equation for torque is T = F x d, where T is torque, F is force, and d is the distance from the axis of rotation.

3. What are the units of torque?

Torque is typically measured in units of newton-meters (Nm) in the metric system, or foot-pounds (ft-lb) in the imperial system.

4. What is the difference between torque and force?

While torque and force are related, they are not the same thing. Force is a push or pull on an object, while torque is a twisting force that causes an object to rotate around an axis. Torque is dependent on both the force applied and the distance from the axis of rotation.

5. How is torque used in everyday life?

Torque is used in many everyday situations, such as turning a key in a lock, tightening a bolt with a wrench, or pedaling a bicycle. It is also important in more complex systems, such as engines and machines, where precise control of rotation is necessary.

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