Torque Equilibrium on a Pivot

[JamesEarl]

Homework Statement

The two objects in the figure below are balanced on the pivot, with m = 2.4 kg. What is the distance d?

http://www.webassign.net/knight/p13-27alt.gif

Homework Equations

T=rf

The Attempt at a Solution

2.4kg + 4.0 kg= 6.4kg
6.4kg/2= 3.2kg on each side of pivot
Looking at the right half, 1.2kg+4kg= 5.2kg.
3.2kg/5.2kg * 1m = 0.615 m from right side
So 1.38 m from left side = d...THIS ANSWER IS WRONG

Basically, I understand all the main concepts, I got everything else on my homework right, but for some reason this problem has me stuck. Any help would be appreciated!

 

[rl.bhat]

Find the torque by the center of masses about the left end.
From the left end center of masses produce clockwise torque.
The reaction of the center of masses on pivot produce counterclockwise torque. Equate them to find d.

 

[tomcue]

To solve this problem, we must consider the principle of torque equilibrium. This principle states that for an object to be in rotational equilibrium, the sum of the clockwise torques must be equal to the sum of the counterclockwise torques.

In this case, we have two objects on a pivot, with the pivot acting as the fulcrum. The weight of each object creates a torque, with the clockwise direction being positive and the counterclockwise direction being negative. The torque created by an object is equal to its weight multiplied by its distance from the pivot.

Therefore, we can set up the equation:

(m1 x d1) + (m2 x d2) = 0

Where m1 and m2 are the weights of the objects, and d1 and d2 are the distances from the pivot.

In this problem, we know that m1 = 2.4 kg and m2 = 4.0 kg. We also know that the total distance from the pivot is 1.0 m (since the objects are balanced). So we can rewrite the equation as:

(2.4 kg x d1) + (4.0 kg x d2) = 0

Now, we need to find the values of d1 and d2. We can rearrange the equation to solve for d1:

d1 = -(4.0 kg x d2) / 2.4 kg

Substituting this value into the equation, we get:

(2.4 kg x [-(4.0 kg x d2) / 2.4 kg]) + (4.0 kg x d2) = 0

Simplifying, we get:

-4.0 kg x d2 + 4.0 kg x d2 = 0

This equation holds true for any value of d2, so we can choose any value for d2. Let's choose d2 = 1 m for simplicity.

Plugging this value into the equation, we get:

-4.0 kg x 1 m + 4.0 kg x 1 m = 0

Simplifying, we get:

-4.0 kg + 4.0 kg = 0

Therefore, we can conclude that d1 = -1 m. This means that the distance d is 1 m from the pivot on the left side, and 0 m on the right