# Plank problem/Center of Gravity/Torque/Level Arm(p.26)

• gcombina
In summary: I'm sorry I didn't catch that earlier. But I thought that was the only problem. Why didn't you ask for help when you still had more work to do?In summary, a 10-m plank weighing 100 N rests on two supports, 1.0 m from each end. The task is to determine how close to one end an 800-N person can stand without tipping the plank. Using the equation T = F x L, and taking into account the center of mass at 4.5 m, the proper torque calculation for the left side of the plank is [ (90N)(9.8) ] ( 4.5 m ) = FL. This is because the plank's mass is
gcombina

## Homework Statement

A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.0 m from each end as shown in the figure. How close to one end can an 800-N person stand without causing the plank to tip?
(a) 0 m (d) 0.7 m

(b) 0.3 m (e) 0.9 m

(c) 0.5 m

## Homework Equations

T = Force x level arm

## The Attempt at a Solution

T = F x L

mg x (center of gravity of the plank) = mg x level arm
[ (90N)(9.8) ] ( 4.5 ) = [ (800N)(9.8) ] ( l )

level arm = .5

My question is why do "center of mass" needs to be used?

I originally did 90N but didn't work so I had to do 4.5 for the center of mass

Thanks!

#### Attachments

• q26.png
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gcombina said:
[ (90N)(9.8) ] ( 4.5 ) = [ (800N)(9.8) ] ( l )
You've forgotten the rest of the plank.
gcombina said:
My question is why do "center of mass" needs to be used?
As opposed to using what? Or do you mean why is the centre of mass at 4.5?
gcombina said:
I originally did 90N but didn't work so I had to do 4.5 for the center of mass
I've no idea what you mean. How exactly did you "do" 90N?
If there's some approach you took that didn't work, please post all the working, and explain how you know it did not work.

because i did the torque from the left side which is 9.0 meters

I am doing the torque on the left = torque on the right

the torque on the left starts from the second fulcrum to the left

see belowI did mg x length
[ (90N)(9.8) ] ( 9.0 m ) = FL

And this way did NOT work

I had to change it to

[ (90N)(9.8) ] ( 4.5 m ) = Fl

Hello and welcome back! non-Shouting contest misunderstanding ironed out, I hope :)

I completely agree with the anti-clockwise torque (torque on the left).
The 4.5 m is the average distance of the wood to the left of the pivot point to that pivont point
Now the right-hand side.

And if you want do do some checking of the way you obtain your answer: have the support in the center and check that the person has to be 5m from the right end of the plank.

:)

gcombina said:
I did mg x length
[ (90N)(9.8) ] ( 9.0 m ) = FL

And this way did NOT work

I had to change it to

[ (90N)(9.8) ] ( 4.5 m ) = Fl
Right, so you want to know why the second is correct?
If all of the mass of the 9m of plank were at 9m from the fulcrum then of course the torque would be 90*9*9.8. But it is spread evenly from zero distance to 9m. If you think of the plank as made of mass elements ##\rho dx## at distance x, the torque of an element is ##\rho x dx##. On average, an element is at distance 4.5, so treat it as though the whole mass is at that distance.

Now, as BvU said, let's move on the the other side of the equation. You had that wrong in the OP, as I mentioned in my first comment of post #2.

## 1. What is the Plank problem?

The Plank problem is a physics problem that involves finding the point of balance, or center of gravity, of a plank placed on two supports. This problem is used to demonstrate the concept of torque and how it relates to the distribution of weight on an object.

## 2. What is the center of gravity?

The center of gravity is the point where the entire weight of an object is concentrated. It is the point around which an object will balance in any orientation. In other words, it is the point where the force of gravity acts on an object.

## 3. What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation to the point of application of the force. Torque is responsible for causing objects to rotate.

## 4. How does the level arm affect torque?

The level arm, also known as the moment arm, is the distance between the point where the force is applied and the axis of rotation. The longer the level arm, the greater the torque will be. This is because a longer level arm increases the distance over which the force is applied, resulting in a greater rotational force.

## 5. How is torque related to the Plank problem?

In the Plank problem, the distribution of weight on the plank affects the torque acting on the plank. The further away the center of gravity is from the axis of rotation, the greater the torque will be. This is why the plank will tip towards the heavier side, as the heavier side has a greater distance from the axis of rotation.

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