Question for maths/physics/mechanics students

[MarkDavis]

If you imagine a see saw, what's the equation that I use to calculate the balance point if I add weights at different lengths along the see saw.

For example, if I add 5kg 1m from the pivot point, how much weight do I add at the other end say at 5m from the pivot to maintain the original balance?

Does the equation differ if the pivot and equal balance point is not exactly half way in the middle of the see saw?

Ta.

 

[Edward01]

Remembering my mechanics from years ago, isn't it distance x weight.

So if 5kg x 1m = Y x 5m therefore isn't Y = to 1kg?

 

[Spyhop]

I've forgotten a shameful amount of the maths I've done, but..

5*g*1 - x*g*5 = 0

?

 

[whitecrook]

Remembering my mechanics from years ago, isn't it distance x weight.

So if 5kg x 1m = Y x 5m therefore isn't Y = to 1kg?

I think that's right.

As for if the pivot point isn't exactly in the middle I think you just have to do 2 calculations there, in terms of the weights the calculation is the same, i.e. distance is from the pivot point, but ou also need to calculate the weight of the 'beam', so if the beam was 10 metres long and weighed 10 KG, then ofseting the pivot point by 2 metres will increase the weight of one side by 2KG and lessen the weight on the other side by 2 kg.

i'm thinking some kind of curve, but I think it's literally straight forward like that as it cancels out. (i.e the negative curve + the positive curve = a straight line / linear relationship ?)

 

[exhashdotdot]

Whenever a system wants to rotate around a pivot. Torque is required in order to cause this rotation.

The equation for torque is

Which in the linear one dimensional case would be
τ = r F

where r is the distance from the pivot point, and F is the force acting on the pivot.

Since the see saw is balanced, the torque on one side will need to balance the torque on the other side.

So in your case. It would be

5g * 1 = 5* Mg

5g*1 / 5g = M

1 = M

M = 1[kg]

If the see saw were not in equilibrium, one side would go down and another side would g up.

 

[rdizzle]

pfft too slow!

 

[rypt]

Is today the ask simple maths questions day on OCUK or something?

 

[JonJ678]

It's normally described as "equilibrium of moments", a condition for static equilibrium. Exhashdotdot is correct.

A possible addition is that if the torques are not balanced, the angular acceleration that results is proportional to the net torque. The constant of proportionality is called the moment of inertia, and is analogous to mass in linear motion.

 

[BigglesPiP]

Convert the mass into force using F=ma where a is g (9.81).

Work out the torque at the pivot using Torque = Force x distance.

Reverse the equations to work out the mass or distance on the other side such that an equal and opposite torque is produced, then you have a balanced see-saw.

 

[Pestilence]

OK, the wife has demanded I add the following (not my text):

If you need to calculate the distance from the pivot for a second mass, you would use the principle of moments.

The principle of moments states that the sum of the anti-clockwise moments is the same is the sum of the clockwise moments.

A moment is defined as the turning effect of a force, and from Key Stage 3 onwards we use the equation "force * perpendicular distance from the pivot".

Force is calculated as the weight of the object, so you use its mass in kg, by the gravitational field strength (for ease you take mavity as = 10).

So, using anti-clockwise moments = clockwise moments.
Weight * Distance of objects on left = Weight * Distance of objects on right. This rearranges to give you Moment on the left / Weight of object on the right. Which gives you the distance from the pivot that the object needs to be for equilibrium.

Done.


She teaches A-level physics, so please do argue if necessary. NOT MY WORDS. I don't know **** about science.

 

[JonJ678]

She's being quite pretentious, or something is lost in translation. "Principle of moments" is a very grand term for a simple idea, and would be stated as "in static equilibrium, the sum of the anti-clockwise moments is equal in magnitude to the sum of the clockwise moments about every point". The rest I'll leave as it is applicable to this particular problem if inappropriate to more general problems.

 

[Pestilence]

She's being quite pretentious, or something is lost in translation. "Principle of moments" is a very grand term for a simple idea, and would be stated as "in static equilibrium, the sum of the anti-clockwise moments is equal in magnitude to the sum of the clockwise moments about every point". The rest I'll leave as it is applicable to this particular problem if inappropriate to more general problems.

Isn't that exactly what was described, though?

Confused.com.

 

[Destination]

, and from Key Stage 3 onwards we use the equation "force * perpendicular distance from the pivot".

That is the age 14-15 year old stuff isn't it? Or is keystage 3 earlier?

 

[Minto]

That is the age 14-15 year old stuff isn't it? Or is keystage 3 earlier?

year 9 (13-14yo), i taught it yesterday.

 

[p4radox]

I think it's all been covered, but I'll just follow up on this one:

I think that's right.

As for if the pivot point isn't exactly in the middle I think you just have to do 2 calculations there, in terms of the weights the calculation is the same, i.e. distance is from the pivot point, but ou also need to calculate the weight of the 'beam', so if the beam was 10 metres long and weighed 10 KG, then ofseting the pivot point by 2 metres will increase the weight of one side by 2KG and lessen the weight on the other side by 2 kg.

i'm thinking some kind of curve, but I think it's literally straight forward like that as it cancels out. (i.e the negative curve + the positive curve = a straight line / linear relationship ?)

If you assume that the bar is uniform then you can just treat its centre of mass as a point force applied to a weightless beam.

For example, if your see-saw weighs 10kg (100N) and is 10m long, but the pivot is 3m from one end, then the moment exerted by self-weight is 100N * 2m = 200Nm. Simples.