How do machines make work easier if it still requires the same amount of work to be done?

Answer 1

The reason for the apparent logical problem is the mushy word "easier". In a Physics

textbook, I don't think you'll ever see a description of simple machines that says that

they make work "easier". If somebody wants to say that about machines, then the

first thing they'll have to do is to give us the scientific definition of exactly what they

mean by "easy", and how you measure it.

What a machine can do is reduce the amount of force you need in order to do a job.

But you'll pay for that, because in return, you'll have to move your force through a

longer distance.

I'm picturing a situation where you have two boards that are nailed together, and

you need to separate them. You only have to move them one inch apart and the

nails will let go. So you reach into your tool box and take out your pry-bar. It's

nothing but a flat metal bar, with one end tapered down to a skinny edge, and

the last couple inches of that same end are bent a little bit. You jam the skinny

edge in between the two boards and you get ready to pry. (The high-school kid

who's helping out on the job for the summer is watching. He's noticed that you've

got a first-class lever in you hand, but he's not going to say anything because he

knows that all the guys will laugh at him, and they'll be using that to yank his

chain for the rest of the summer, so he keeps his observations to himself.)

Now you pry down about a foot and a half on your end of the pry bar, and at

the other end, the little bent end of the bar separates the two boards by about

one inch, the nails let go, and the boards separate.

What happened here ? Lets you and I step over to the side of the yard for a

minute and talk about it. And call the kid over to join us, because he's the one

here who can explain it best.

Your pry-bar is a first-class lever. The little bend in it, two inches from one end,

is the pivot of the lever. You cranked your end about a foot and a half, and the

short end separated the boards about an inch. At the same time, the force that

separated the two boards was 18 times stronger than the force you had to

put into it. The kid knows that scientifically, "work" is (force) multiplied by (distance),

and the work at your end was exactly the same as the work at the short end.

Did the first class lever make the job "easier" ? I don't know. You had to crank

your end through all that extra distance, and the work at both ends came out

the same. What was the point of using the machine ?

It's absolutely true that you could have done the job without the machine, and

exerted your force through a much shorter distance. All you had to do was grab

one of the boards with your finger-tips, and pull it an inch away from the other

board with a force of 600 pounds.

The foreman over there with the crane-claws for hands and the 3/4" winch-line

for muscles might have done it that way, but you couldn't. Using the pry-bar,

you traded distance for more force.

In the language pf Physics, the work was the same at both ends. But I'd say

the first-class lever definitely made the job "easier" for you.