How far from the left end should the fulcrum be placed?

  • Thread starter Mdhiggenz
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In summary, in order to balance a uniform bar with two small masses glued to its ends on a fulcrum, the fulcrum should be placed at a distance of 31.8 cm from the left end of the bar. This can be found by using the centres of mass for the bar and the two masses and setting the pivot at the far right to cancel out forces, or by taking into account the weight forces of all components in the static equilibrium equation.
  • #1
Mdhiggenz
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Homework Statement



A 0.105-, 48.7--long uniform bar has a small 0.055- mass glued to its left end and a small 0.150- mass glued to the other end. You want to balance this system horizontally on a fulcrum placed just under its center of gravity.

How far from the left end should the fulcrum be placed?


Homework Equations





The Attempt at a Solution



What I did was used the static equilibrium equation and set the pivot to be at the far right in order to cancel out those forces.
m2=mass of the bar
m1= mass of the ball to the far left
x the distance to the left from the Fulton
l= length of the bar
I set clockwise to be the positive direction

Ʃτ=0→ m1gx+m2g(l/2) solved for x and got

x=-m2(l/2)/m1

The answer I got was incorrect the correct answer is 31.8 cm and they used a different approach from mine.

Cheers
 
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  • #2
Mdhiggenz said:

Homework Statement



A 0.105-, 48.7--long uniform bar has a small 0.055- mass glued to its left end and a small 0.150- mass glued to the other end. You want to balance this system horizontally on a fulcrum placed just under its center of gravity.

How far from the left end should the fulcrum be placed?


Homework Equations





The Attempt at a Solution



What I did was used the static equilibrium equation and set the pivot to be at the far right in order to cancel out those forces.
m2=mass of the bar
m1= mass of the ball to the far left
x the distance to the left from the Fulton
l= length of the bar
I set clockwise to be the positive direction

Ʃτ=0→ m1gx+m2g(l/2) solved for x and got

x=-m2(l/2)/m1

The answer I got was incorrect the correct answer is 31.8 cm and they used a different approach from mine.

Cheers

I would use centres of mass.

The Centre of Mass for the Bar is clearly at its centre, and its mass is given.

You can find where the Centre of Mass of the two masses can also be found in the usual way.

You then find the Centre of Mass of those two Centres of Mass.
 
  • #3
Mdhiggenz said:

Homework Statement



A 0.105-, 48.7--long uniform bar has a small 0.055- mass glued to its left end and a small 0.150- mass glued to the other end. You want to balance this system horizontally on a fulcrum placed just under its center of gravity.

How far from the left end should the fulcrum be placed?


Homework Equations





The Attempt at a Solution



What I did was used the static equilibrium equation and set the pivot to be at the far right in order to cancel out those forces.
m2=mass of the bar
m1= mass of the ball to the far left
x the distance to the left from the Fulton
l= length of the bar
I set clockwise to be the positive direction

Ʃτ=0→ m1gx+m2g(l/2) solved for x and got

x=-m2(l/2)/m1

The answer I got was incorrect the correct answer is 31.8 cm and they used a different approach from mine.

Cheers

When doing the rotations as you did, you account for mass of Bar - at a distance half way out, the little mass all the way out [both anti-clockwise] and the fulcrum force equal to sum of both masses plus the bar. I think you have left some weight forces out.
 

1. How do I determine the distance of the fulcrum from the left end?

The distance of the fulcrum from the left end can be determined by using the formula: Distance of fulcrum = Load x Load arm ÷ Effort. The load arm is the distance from the fulcrum to the load, and the effort is the distance from the fulcrum to the effort.

2. What is the significance of the distance of the fulcrum from the left end?

The distance of the fulcrum from the left end is important because it determines the mechanical advantage of the lever. The closer the fulcrum is to the load, the greater the mechanical advantage and the easier it is to lift the load.

3. Can the distance of the fulcrum from the left end be adjusted?

Yes, the distance of the fulcrum from the left end can be adjusted depending on the desired mechanical advantage. Moving the fulcrum closer to the load will increase the mechanical advantage, while moving it further away will decrease it.

4. How does the weight of the load affect the placement of the fulcrum?

The weight of the load does not have a direct effect on the placement of the fulcrum. However, it does affect the amount of effort needed to lift the load. The heavier the load, the closer the fulcrum should be to the load to achieve a greater mechanical advantage.

5. Are there any safety precautions to consider when placing the fulcrum?

Yes, it is important to make sure that the fulcrum is securely placed and can handle the weight of the load. It is also important to evenly distribute the weight on both sides of the fulcrum to avoid any potential accidents or injuries.

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