# Plank and torque, problem with finding center mass

• paul11
In summary, the problem involves a 5.0 m plank with a weight of 212 N and a person weighing 433 N walking on the overhanging part of the plank. The person can walk up to a distance of 1.09 m before the plank begins to tip, with the right support acting as the fulcrum point. The correct calculation involves finding the midpoint of the plank (2.5 m from each end) and subtracting the distance of the plank hanging over the right support (1.41 m) to get a distance of 1.09 m. This is different from initially adding the overall length of the plank and the distance between supports. It is important to draw a diagram and clearly understand the
paul11

## Homework Statement

A uniform plank of length 5.0 m and weight 212 N rests horizontally on two supports, with d = 1.41 m of the plank hanging over the right support. To what distance, x, can a person who weighs 433 N walk on the overhanging part of the plank before it just begins to tip?

Tnet = 0
T = r * F

## The Attempt at a Solution

Torque of plank = Torque of person
212N * 1.09m = 433N * distance

The right support is the fulcrum point.

What I don't understand is why the plank's weight acts on is 1.09m. I know the idea to get the midpoint from the two supports then subtract by the plank that is hanging over the right support, 5.00m / 2 - 1.41m = 1.09m, but I don't understand why this is the case.

This is what I initially did, 5.00m + 1.41m = 6.41m, then I divided this value by 2 to get 3.205m, and this is the center point of the plank from either end point. This point will be 1.795m from the right support, and I used this to calculate the torque of the plank. Could someone enlighten me why this was wrong? And why the correct way is .. correct?

The beam is 5.0 m in overall length. The distance between supports is 3.59 m. You have misinterpreted the beam as being 6.41 m long and the distance between supports as being 5 m. This is not what is given.

ah thank you, I need to read it more clearly.

It is a good idea to draw a diagram showing all the forces acting.
The plank is uniform so the weight of 212N is acting at the centre of the plank (2.5m from each end). This should help to see the distancesa from forces and pivots.

I can understand your confusion about the distance at which the plank's weight acts. This is because the center of mass, or the point at which the weight of an object can be considered to act, is not always at the geometric center of the object. In the case of the plank, the weight is distributed evenly along its length, but the overhanging portion has a greater distance from the right support, causing the center of mass to shift towards the left support. This is why the correct distance to use in your calculation is 1.09m, as it represents the distance from the right support to the center of mass of the plank. This concept is important in understanding the stability and balance of objects, and it is crucial to consider the location of the center of mass when analyzing forces and torques. I hope this explanation helps to clarify the issue for you.

## 1. What is a plank?

A plank is a long, flat piece of wood or other material that is used as a support or as a building material.

## 2. What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis.

## 3. How do you calculate torque?

Torque is calculated by multiplying the force applied to an object by the distance from the point of rotation to the point where the force is applied.

## 4. What is the problem with finding center mass of a plank?

The problem with finding the center mass of a plank is that it is not a uniform object, so its mass is distributed unevenly. This makes it difficult to determine the exact point where the weight of the plank is evenly balanced.

## 5. Why is finding the center mass of a plank important?

Finding the center mass of a plank is important because it is essential for determining the stability and balance of the plank. It is also necessary for calculating the torque and understanding how the plank will behave when subjected to external forces.

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