# Torque, Equilibrium, and Center of Mass

• Lyphta
In summary, the conversation discusses a physics problem involving a painter standing on a board while painting a house. The question is how close to the end of the board can the painter stand without tipping it over. The attempted solution used the equation ##\taupainter = \tauboard## but the correct answer could not be determined without a picture showing the board's support. The conversation concludes by stating that the answer is likely incorrect.
Lyphta

## Homework Statement

While standing on a long board resting on a scaffold, a 70 kg painter paints the side of a house. If the mass of the board is 15 kg, how close to end can the painter stand without tipping the board over?
http://img146.imageshack.us/my.php?image=physicssl9.jpg

## Homework Equations

$$\tau$$painter = $$\tau$$board

## The Attempt at a Solution

$$\tau$$painter = $$\tau$$board
(rpainter) (70kg) = (1.5 m) (15kg)
70r = 22.5
r=.32 ft.

the answer was 1.2 m from left end of board.

Sorry, without a picture showing how and where the board is supported, we cannot figure out the correct solution. We are certain, however, that ##\tau## is an incorrect answer.

## What is torque and how is it calculated?

Torque is a measure of the force that causes an object to rotate. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point where the force is applied. The unit for torque is Newton-meters (Nm) in the metric system and foot-pounds (ft-lb) in the imperial system.

## What is equilibrium and how does it relate to torque?

Equilibrium is a state in which all forces acting on an object are balanced, resulting in no net change in the object's motion. In terms of torque, equilibrium occurs when the sum of all clockwise torques is equal to the sum of all counterclockwise torques. This means that the object will not rotate in either direction.

## What is the center of mass and why is it important?

The center of mass is the point at which the entire mass of an object can be considered to be concentrated. It is important because it helps us understand the motion of an object and how it responds to external forces. The center of mass also determines the stability and balance of an object.

## How does the center of mass change when an object is in motion?

The center of mass does not change when an object is in motion, unless external forces are acting on the object. In this case, the center of mass will shift in the direction of the applied force. However, the total mass of the object remains constant.

## What factors affect an object's center of mass?

The center of mass of an object is affected by its shape, mass distribution, and external forces acting on it. Objects with irregular shapes or uneven mass distribution will have a center of mass that is not located at the geometric center. External forces, such as gravity or applied forces, can also cause the center of mass to shift.

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