How Far Can a Person Stand on a Plank Without It Tipping?

[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?

Homework Equations

The Attempt at a Solution

This is kind of difficult to me, please help me understand this

I know the person weighs 800 and there is X distance

so I have 800N from the weight of the person plus 10 N from the weight of the plank on the right side of the fulcrum

800X + 10 N = 90 N (the weight of the rest of the plank)

 

[jedishrfu]

Isn't the formula F x Dist so that for this case (800 + 10) * X and the length on the other side would be?

 

[gcombina]

Isn't the formula F x Dist so that for this case (800 + 10) * X and the length on the other side would be?

the length of the other side would be 90 meters which equates to 90N

 

[BvU]

Not good.
On the left we have 90 N * 4.5 m (as we had in October...)
On the right we have
from the person: 800 * (1-X) if X is the distance from the end of the plank
from the plank: 10 N * 0.5 m (Haru's "the rest of the plank")

Now balance the lot and you're done.

Good luck with the exam :)

 

[HalfLostAndSearching]

To solve this problem, we need to use the principle of moments. This principle states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments. In this case, the clockwise moments are caused by the weight of the person and the plank on the right side of the fulcrum, while the counterclockwise moments are caused by the weight of the plank on the left side of the fulcrum.

Using this principle, we can set up the following equation:

(800N * x) + (100N * 1m) = (100N * 9m)

Where x is the distance from the left end of the plank to the person's position. We know that the weight of the person and the plank on the right side must be equal to the weight of the rest of the plank on the left side in order for the plank to be in equilibrium.

Solving for x, we get:

800x + 100 = 900

800x = 800

x = 1m

Therefore, the person can stand up to 1m from the left end of the plank without causing it to tip. Any closer, and the clockwise moments would be greater than the counterclockwise moments, causing the plank to tip.