# Rigid Objects in Equilibrium &amp; Center of Gravity

• tem_osu
In summary, the force T exerted by the thumb is 63.7 N downward and the force F exerted by the four fingers is 79.086 N upward.
tem_osu
[SOLVED] Rigid Objects in Equilibrium &amp; Center of Gravity

## Homework Statement

http://img149.imageshack.us/img149/8568/0968lr6sc4.gif

A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.220 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00 kg plate of food and a 0.350 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.

T = ___N (downward)
F = ___N (upward)

## Homework Equations

Torque = force * distance

## The Attempt at a Solution

Mug 0.350*9.8* 0.300= 1.029 Nm
Plate 1.00*9.8*0.140= 1.372 Nm
Tray 0.220*9.8*0.100= 0.2156 Nm
Total Clockwise torque = 2.6166 Nm

2.6166 = 0.04T
T = 65.415 N - wrong answer

Last edited by a moderator:
tem_osu said:
Mug 0.350*9.8* 0.300= 1.029 Nm
Check that distance.

And I have no idea how to solve for F.
You can chose another pivot point to calculate torques or you can consider the sum of vertical forces.

Doc Al said:
Check that distance.

Do I use the distance between the thumb & the mug? = 0.320 m

You must measure all distances from the same point when calculating torques. Based on your other calculations, I thought you were using the point of application of force F as your pivot point.

Using distance measure from the same spot:

Mug: 0.350 x 9.8 x 0.380 = 1.3034
Plate: 1.00 x 9.8 x 0.240 = 2.352
Tray: 0.220 x 9.8 x 0.400 = 0.8624

Total = 4.5178 Nm
4.5178Nm / 0.06 m = 75.297 N for T?

tem_osu said:
Using distance measure from the same spot:

Mug: 0.350 x 9.8 x 0.380 = 1.3034
Plate: 1.00 x 9.8 x 0.240 = 2.352
Tray: 0.220 x 9.8 x 0.400 = 0.8624

Total = 4.5178 Nm
4.5178Nm / 0.06 m = 75.297 N for T?
For some reason, you changed your pivot point to be the left side of the tray. In that case: (1) T also provides a clockwise torque; (2) You need to include the torque from F (which would be counterclockwise).

Combine this torque equation (once you correct it) with an equation for the total force on the tray. Solve them together to find T and F.

Your original choice of using the point of application of force F as your pivot point was a good one, since it eliminates force F and allows you to immediately calculate T. (Your only error was using an incorrect distance for one of the forces.) You'd still need another equation to find F.

Thank you for your explanation. I understood it now.

Solve for T:
Mug 0.350*9.8* 0.280= 0.9604 Nm
Plate 1.00*9.8*0.140= 1.372 Nm
Tray 0.220*9.8*0.100= 0.2156 Nm
Total Clockwise torque = 2.548 Nm

2.548 = 0.04T
T = 63.7 N

Solve for F:
F is the upward force so it must be equal to the sum of the down forces
Mug 0.35*9.8 = 3.43 N
Plate 1.00*9.8 = 9.8 N
Tray 0.220*9.8 = 2.156 N
Upward force = 63.7 N

F = 3.43 + 9.8 + 2.156 + 63.7
F = 79.086 N

## What is a rigid object?

A rigid object is an object that does not deform or change shape when forces are applied to it. It maintains its shape and size, and all points within the object move together when the object is subjected to external forces.

## What is equilibrium?

Equilibrium refers to a state in which an object is at rest or moving at a constant velocity with no net force acting on it. In other words, the forces acting on the object are balanced, resulting in a stable state.

## How is center of gravity defined?

The center of gravity of an object is the point at which the weight of the object can be considered to act. It is the point around which the object will balance in any orientation. In uniform objects, the center of gravity is located at the geometric center of the object.

## What factors affect the center of gravity of an object?

The center of gravity of an object is affected by its shape, size, and distribution of weight. The center of gravity can also be affected by the position of the object relative to the Earth's surface and the presence of external forces acting on the object.

## How is the center of gravity determined for an irregularly shaped object?

The center of gravity for an irregularly shaped object can be determined by suspending the object from different points and finding the point at which the object is perfectly balanced. This point will be the center of gravity for the object. Alternatively, mathematical calculations can also be used to determine the center of gravity for complex objects.

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