00:01
So we've got a few questions here about an atwoods machine.
00:04
A standard atwoods machine looks like this, where you've got two blocks that are accelerating around a pulley system, and one block is usually heavier than the other.
00:14
And it doesn't say anything about these blocks on this particular thing, but let's just say that m1 is heavier.
00:21
So if this is our system, a whole set of blocks here, there's two forces acting on the system.
00:30
There's the force of gravity on m2.
00:32
Which is m2g, and the force of gravity on m1, which is m1g.
00:38
So if we want to say net force is equal to mass times acceleration, it would be the difference in these forces.
00:46
So one of these directions is going to be positive.
00:49
Let's make this positive, and one of these is going to be negative.
00:52
And my number line sort of goes like this, from positive to negative.
00:57
So there's like a clockwise, there's like a clockwise rotation of this pulley.
01:04
Kind of counterclockwise.
01:05
I said that backwards.
01:07
Counterclockwise and clockwise.
01:09
And one of those directions is positive.
01:11
One is negative.
01:12
So if this is my positive direction, my net force is going to be m1g minus in the negative direction m2g, and that's equal to math times acceleration.
01:24
Since we're looking at both blocks together, it would be m1 plus m2 and then times a.
01:31
Okay, so in this question, i want to know how do you determine the acceleration due to gravity.
01:37
So one way to do this would be to actually solve for g.
01:42
If you factor it out a g, you have m1 minus m2 equals m1 plus m2 times a, and then divide by that m1 minus m2, m1 plus m2 times a over m1 minus m2.
02:04
So this would be our formula for g.
02:07
And so if you're doing an experiment, you would want to make some measurements.
02:09
For example, you could vary m1 and m2.
02:13
You could, you know, like, let's say you had, i don't know, two kilograms, two kilograms, and four kilograms or something.
02:23
Those were your two masses.
02:25
On the next trial, you could do three and three, or you could do four and two, or you could do five and one.
02:31
It's probably good to keep the system mass a constant.
02:36
So, you know, keep this numerator constant, but vary where the masses are located, very different trials.
02:42
And you'll find, you know, some values for the masses, and you can measure the acceleration.
02:49
How would you measure the acceleration? you might use a motion detector, or you might use kinematic equations and measure the displacements, time, and initial velocity.
03:00
Make that zero if it starts from rest.
03:04
Okay, and in that case, you could find the acceleration using the equation delta x equals vit plus one half a t squared.
03:14
And vi would be zero to two times delta x divided by t squared would be the acceleration.
03:21
So those are some thoughts on how you could find the acceleration due to gravity.
03:25
There's not one correct answer, but i think you want to talk about this equation that we've got here.
03:30
And talk about what you would measure in your system.
03:34
You'd want to measure position, displacement, and time, that is...