Can someone explain CoE in this example?

[Baby Astronaut]

I'd liek to understand how conservation of energy applies when using a lever. For example, you didn't put that much work in when using a lever to hoist up something heavy.

 

Layman's terms please

[D H]

I'd liek to understand how conservation of energy applies when using a lever. For example, you didn't put that much work in when using a lever to hoist up something heavy.

You did undeed "put that much work in when using a lever to hoist up something heavy". What you put in was a reduced force, but at the expense of having to apply that force over a larger distance.

 

Work is, in layman's terms, force times distance. To lift a 100 kg object 10 centimeters directly without the aid of a simple machine means you have to apply a 980.665+ Newton force as you lift the object the requisite 10 centimeters. When you have lifted that 100 kg object the 10 centimeters off the ground you will have performed 98.0665 joules of work.

 

Suppose instead you use a lever with a 10:1 mechanical advantage. Now you can raise the same object by applying a 98.0665+ Newton force, but you have to apply that force over a 1 meter span of distance. When you have lifted that 100 kg object 10 centimeters off the ground you will have still performed 98.0665 joules of work.

[swansont]

I'd liek to understand how conservation of energy applies when using a lever. For example, you didn't put that much work in when using a lever to hoist up something heavy.

 

Layman's terms please

 

D H has explained that your use of "work" is wrong. The term you should have used was "power" — you did the same amount of work, but did it slower, allowing a smaller force to complete the task.

[Baby Astronaut]

You did undeed "put that much work in when using a lever to hoist up something heavy". What you put in was a reduced force, but at the expense of having to apply that force over a larger distance.

 

Work is, in layman's terms, force times distance. To lift a 100 kg object 10 centimeters directly without the aid of a simple machine means you have to apply a 980.665+ Newton force as you lift the object the requisite 10 centimeters. When you have lifted that 100 kg object the 10 centimeters off the ground you will have performed 98.0665 joules of work.

 

Suppose instead you use a lever with a 10:1 mechanical advantage. Now you can raise the same object by applying a 98.0665+ Newton force, but you have to apply that force over a 1 meter span of distance. When you have lifted that 100 kg object 10 centimeters off the ground you will have still performed 98.0665 joules of work.

Thank you, and bear with me please. Maybe I'm using the wrong terminology, as swansont revealed, it's power not work.

 

So to rephrase, there seems toi be less power being depleted by using the lever. It might be a machine, but it doesn't need batteries. Let's use a robot instead of a human. If robot A were using its humanoid body to lift 100 kilogram crates all day, and an identically constructed robot B were lifting the same but using a lever with a 10:1 mechanical advantage, it seems like robot A would be recharging its batteries more often.

 

Here's my confusion about it. More energy/power seems to have been depleted/expended in one case more than another. How was the extra/less energy or power conserved?

 

It seems as if the non-renewable energy going into robot B's system isn't matched by the output of potential or kinetic energy created if it were to suddenly drop its crate onto something else.

[swansont]

Here's my confusion about it. More energy/power seems to have been depleted/expended in one case more than another. How was the extra/less energy or power conserved?

 

It seems as if the non-renewable energy going into robot B's system isn't matched by the output of potential or kinetic energy created if it were to suddenly drop its crate onto something else.

 

 

Power is the rate at which energy is transferred. Energy is power*time.

 

The robot running at half-power takes twice as long to do the task. The energy is the same.

[D H]

Power isn't conserved a conserved quantity. Why should it be? Power is a process variable. An object doesn't hold a certain amount of power. An object holds stored energy. A more powerful object can release more stored energy per unit time than can a less powerful object.

 

Let's use your example of two robots, one of which is more powerful than the other. The more powerful robot simply lifts 100 kilogram crates directly. The less powerful robot uses mechanical advantage to overcome the lack of power. Both robots perform the same amount of work (and thus use the same amount of energy) in lifting a 100 kilogram weight to some specified height.