00:01
Here's an interesting problem to consider.
00:03
Let's say a person is interested in moving a box.
00:09
He can either a push down on the box from this side a downward angle or he can be on this other side and pull on it say with a rope with an upward angle.
00:30
All right.
00:31
The question is is a or b better.
00:40
The answer is both are equal.
00:49
What's important one is to consider, of course, how the box moves.
00:54
The box is going to move to the right.
00:56
That's just true.
00:58
Okay? now mark that by displacement.
01:00
If i put these vectors together, we have our, in case number a, you have our displacement vector d and we have our force vector.
01:16
Oops, oops, oops, oops.
01:18
Not that one, but this one for pushing downward.
01:24
And it makes an angle theta.
01:26
Well, if we're interested in say the work, our work equation says that work is equal to force times displacement times cosine the angle between them.
01:38
Well, in this case, angle, theta, d, and f, well, that's just going to, to be f, d, coast, theta equals work and once in a situation a.
01:54
Well, let's revisit this, but again, we'll look for the case that instead of pushing downward, he's instead pushing upward.
02:03
And i'll call this force one.
02:06
Well, if i write this out again, oh, and that's going to be at the same angle theta.
02:10
And i'll put a little one there.
02:12
Well, that's going to come out to f1, displacement, cost, theta, 1, and that's work, and we'll call this for case b.
02:22
Well, it's the same force, so this one doesn't even matter, and it's the same theta, so this doesn't matter.
02:27
So the work done by pushing downward is equal to the work done by pushing upward.
02:33
It's the exact same, so it doesn't matter whether the person pushes down or rather the person pushes upward when you're pushing a box across the floor, and this displacement is the exact same.
02:45
Now let's actually put some numbers.
02:47
Let's say the crate has a mass of 50 kilograms and the coefficient of kinetic friction between the box and the ground is 0 .75.
03:07
Let's find out what force is necessary to move it at a steady speed...