Violation of Energy conservation by use of pulley

[Tony Stark]

A person has reached H height by 100J energy whereas by the use of pulley, the man can reach the height by a fraction of that energy. In this manner, it is reaching height H by giving off less energy than required by gravitational potential energy. So isn't the law of conservation of energy violated?

 

[Drakkith]

A person has reached H height by 100J energy whereas by the use of pulley, the man can reach the height by a fraction of that energy. In this manner, it is reaching height H by giving off less energy than required by gravitational potential energy.

Not true. Raising the person to height H would require 100 joules of work be done on them, regardless of the source. A pulley converts a smaller force into a larger force by having the smaller force act over a larger distance. So if it takes 100 Newtons to raise someone 1 meter, a force of 50 Newtons acting over 2 meters on one side of the pulley would be converted into 100 Newtons acting over 1 meter on the other side.

In both cases 100 joules are 'spent' to raise the person to height H.

 

[Dr. Courtney]

Using a pulley can decrease the force needed (say by a factor of 2 in a simple arrangement), but it increases the distance over which the force needs to be applied by the same factor, so the mechanical work (energy input needed) is the same. Thus, there is no violation of energy conservation.

For example, a man of mass 100 kg has a weight of 980 N. With a simple pulley, he can be lifted with a force (tension) of 490N, but you need to pull the rope a distance of 10 m to lift him 5 m. So, the work is equal to the increase in gravitational potential energy.

 

[Noctisdark]

You need 2 pullies, an Atwood machine (Machines using one or multiple pullies), they are very useful when it comes to manipulating force such as amplifying them or changing their direction, they serve alse for amplifying acceleration and I encourage you to take a serious look at them, you'll have fun when trying to derive their equation of motion and free-body diagrams, but they do not violate energy conservation, or else it'll be widely used as a free energy source, Cheers !,

 

[CWatters]

Using a pulley is like taking the long route up a mountain...

The direct route is shorter and steeper, the zig-zag route is longer but shallower. If humans were "ideal" then both routes would take the same energy = mgh.

 

[Tony Stark]

Its fine that even by the use of pulley, the work done preserves the conservation law. But the energy exerted would be the muscular force of the person (which is much less than required), whereas the pulley system cannot itself provide energy. Thus how is the law preserving its state in this case?

 

[Drakkith]

But the energy exerted would be the muscular force of the person (which is much less than required), whereas the pulley system cannot itself provide energy.

You're not even using the correct terminology. The force exerted by the person's muscles is amplified by the pulley and exerted on the object being lifted. The energy spent by the muscles is actually more than the energy needed to lift the object because the human body is not a perfectly efficient machine. You do not exert energy, you exert a force.

 

[Tony Stark]

You're not even using the correct terminology. The force exerted by the person's muscles is amplified by the pulley and exerted on the object being lifted. The energy spent by the muscles is actually more than the energy needed to lift the object because the human body is not a perfectly efficient machine. You do not exert energy, you exert a force.

But how does the pulley amplify force...

 

[Drakkith]

But how does the pulley amplify force...

Mechanical advantage: https://en.wikipedia.org/wiki/Mechanical_advantage

I'm not sure that's going to answer your question about 'how' it works. All I can say is that mechanical advantage works and then give you the rules by which it works.

 

[Tony Stark]

So isn't their any scientific reason as to why the Mechanical advantage is present..

 

[Drakkith]

So isn't their any scientific reason as to why the Mechanical advantage is present..

Oh I'm sure there is, but I don't know what that principle is.

 

[Noctisdark]

So isn't their any scientific reason as to why the Mechanical advantage is present..

There is, remember energy is conserved, so if you input work you should expect to output the same amount (case of an ideal machine) or less, in case of the ideal, if you exert a force F along a distance d then your work is F.d, the pully system amplify that force by a factor of a and the object on the other side will move a distance d', F.d = aF.d' which yields to d' = d/a, you can try this expirement yourself to check if d' = d/a, but again one single pully can only change the direction of the force, for mechanical advantage you need an atwood machine !.,

 

[Nugatory]

So isn't there any scientific reason as to why the Mechanical advantage is present..

Of course there is. The easiest way to see how it works is to consider the picture at the top of the wikipedia article, the one of the man pulling on the rope. If the man pulls on the rope hard enough to create a tension of 100 Newtons, what is the force on the bottom pulley? Well, there are TWO ropes attached to the bottom pulley, each applying a force of 100 Newtons, so the total upwards force on the bottom pulley is 200 Newtons. If we looped the rope around the pulleys more times, we get even more mechanical advantage.

(The downwards force on the upper pulley is 300 Newtons because there are three ropes pulling it down, each applying a force of 100 Newtons. This downwards force is offset by the upwards force from the pulley's mounting in the ceiling).

Energy is conserved in this setup because to raise the load by one meter the man has to pull the end of his rope two meters, so W=Fd=2*100=200 Joules if you're looking at the man applying 100 Newtons for two meters and W=Fd=1*200 Joules if you're looking at the two ropes applying 200 Newtons for one meter.

 

[CWatters]

I think you can have a mechanical advantage with one pulley (eg if it's mounted on the object being lifted).

 

[Nugatory]

I think you can have a mechanical advantage with one pulley (eg if it's mounted on the object being lifted).

Yes, you can, and anyone who has a worked a small sailboat will have seen many examples.