How to calculate counterweight at a different height?

In summary, the conversation discusses finding the counterweights for two masses, m1 and m2, attached to two horizontal beams at different heights. The formula m1y=m2x is suggested for equilibrium, but the effects of h1 and h2 are questioned. It is clarified that the distance in the formula represents the distance from the pivot to the line of action of the force, and not the point of application. Finally, it is concluded that for equilibrium, h1 and h2 do not have any effect as they are not present in the expression.
  • #1
physicsodyssey
11
6

Homework Statement


m2=3kg, m1=?
the diagram has been attached

Homework Equations


I know that we find counterweights by equating equation mass x distance frm pivot but how do we find if it is at different height

The Attempt at a Solution


Is it m1yh1=m2xh2
is counterweight at all dependent on height?[/B]
 

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  • #2
Does the full problem statement mention that the two beams to which the masses are attached are horizontal ?

If yes, then your attempt looks good.
Mass x g is force
force x distance from pivot is torque
No net torque means no angular acceleration => balance. g divides out.

Advice: draw the forces in the diagram.
 
  • #3
That is basically m1y=m2x (in this case)
But what about the effects of h1 & h2 ?
The two beams are at different heights so will the approach change?
 
  • #4
Pity you don't show any equations. Your "Is it m1yh1=m2xh2" doesn't make sense to me. What does it represent ? A wild guess ? Is it a multiplication ? If so, I have no idea what y and x stand for. And the dimensions I don't recognize.

Time to read the guidelines and make better use of the template . . .

And completing the problem statement might be a good idea too: m1 can be anything if there are no restrictions. A restriction could be that the stuff is in equilibrium, but if you don't tell, nobody knows !

[edit] I am a bit too strict. Your "That is basically m1y=m2x (in this case)" is correct for equilibrium. It doesn't feature h1 or h2.
 
Last edited:
  • #5
BvU said:
force x distance from pivot is torque
To be precise (and this seems to be the crucial point here), the distance in that formula is the distance from the pivot to the line of action of the force, not to the point of application of the force.
 
  • #6
BvU said:
Pity you don't show any equations. Your "Is it m1yh1=m2xh2" doesn't make sense to me. What does it represent ? A wild guess ? Is it a multiplication ? If so, I have no idea what y and x stand for. And the dimensions I don't recognize.

Time to read the guidelines and make better use of the template . . .

And completing the problem statement might be a good idea too: m1 can be anything if there are no restrictions. A restriction could be that the stuff is in equilibrium, but if you don't tell, nobody knows !

[edit] I am a bit too strict. Your "That is basically m1y=m2x (in this case)" is correct for equilibrium. It doesn't feature h1 or h2.
Sorry for the inconvenience.
m1 & m2 are in equilibrium , y= 300mm & x=900 mm and hence m1y=m2x.
So, if m1 & m2 are in equilibrium, will different heights have any effect? h1=900mm & h2=913mm.
 
  • #7
"That is basically m1y=m2x (in this case)" is correct for equilibrium.

h1 and h2 are not present in the expression, so they have no effect !
 

1. How do you calculate the counterweight at a different height?

To calculate the counterweight at a different height, you will need to know the weight of the object you are trying to counterbalance, the distance between the object and the pivot point, and the desired height of the counterweight. You can then use the formula: Counterweight = (Object Weight * Object Distance) / Counterweight Distance.

2. What is a counterweight used for?

A counterweight is used to balance out the weight of an object in order to achieve stability and prevent it from tipping over. It is commonly used in cranes, elevators, and other machinery that require precise balancing.

3. How does the height of the counterweight affect its effectiveness?

The height of the counterweight directly affects its effectiveness in balancing the weight of an object. The higher the counterweight is positioned, the more leverage it has to balance out the weight of the object. However, the counterweight should not be too high, as it can create instability and potentially cause the object to tip over.

4. Is there a specific material that is best for making a counterweight?

The material used for a counterweight will depend on the specific application and the weight of the object it is balancing. Generally, dense and heavy materials such as steel or concrete are used for larger and heavier objects, while smaller objects may use lead or sand as a counterweight.

5. Can the counterweight be adjusted if the height of the object changes?

Yes, the counterweight can be adjusted if the height of the object changes. You will need to recalculate the counterweight using the new height and weight measurements to ensure proper balance and stability.

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