How Should a Plank Be Supported for Balance with Unequal Weights at Its Ends?

[alexo]

Homework Statement

I think I'm being a bit dull today but I seem to be having real trouble understanding this question...

Two children wish to make a see-saw from a 5m plank of wood, the children weigh 25kg and 20kg. They wish to sit right on the ends of the plank. Where should the plank be supported in order for it to balance...

Homework Equations

t=RF

The Attempt at a Solution

I know that Net ACWM should = CWM...
I found the weight in Newtons of the kids...196N and 245N..
I added the two forces together to get the opposing force of the pivot, 441N

But now I'm stuck... and have no idea where to take it from here :(

Thanks :) Alexo.

 

[LBloom]

I don't think the question is dealing with the pivot (in many of these problems the means of rotation, like the pulley is deemed massless and frictionless.)
the question is about torque, so ask yourself, how can the plank be placed so there is no torque? the only equation you need you already have.

 

[tomcue]

Hello Alexo,

Don't worry, rotational equilibrium can be a bit tricky to understand at first. Let's break down the problem and see if we can figure out the solution.

First, we need to understand what rotational equilibrium means. In simple terms, it means that the forces acting on an object are balanced and there is no net torque (or rotational force) acting on the object. In other words, the object is not rotating or turning.

In this case, we have two forces acting on the plank of wood: the weight of the children on either end and the support force at the pivot point. In order for the plank to be in rotational equilibrium, the net torque must be zero. This means that the clockwise torque must be equal to the counterclockwise torque.

Now, let's look at the equation you provided: t=RF. This is known as the torque equation, where t is the torque, R is the distance from the pivot point, and F is the force. In this case, we can use this equation to calculate the torque of each force acting on the plank.

For the children on the ends of the plank, the torque is equal to their weight multiplied by the distance from the pivot point. Since the distance from the pivot point to each child is 2.5m (half of the plank's length), the torque for the 25kg child is 196N x 2.5m = 490Nm, and the torque for the 20kg child is 245N x 2.5m = 612.5Nm.

Now, let's look at the support force at the pivot point. Since we want the plank to be in rotational equilibrium, the torque from the support force must be equal to the torque from the children. This means that the support force must be located at a distance that will create an equal torque.

To find this distance, we can rearrange the torque equation to solve for the distance: R = t/F. Plugging in the values we found for the torque and the force of the children, we get R = 490Nm/441N = 1.11m. This means that the support force must be located 1.11m from the pivot point in order for the plank to be in rotational equilibrium.

I hope this helps you understand rotational equilibrium a bit better. Keep practicing and don't be afraid to ask for help if you get stuck again. Good luck with