00:01
Okay, we have a 4 kilogram block that is at rest on a surface that has been inclined 30 degrees above the horizontal.
00:23
Okay, something like this.
00:45
Okay, let's call this block m1.
00:50
And then we're told there's also another one.
00:57
M2, i've got a pulley, string connects the two.
01:09
Okay, and we're giving the friction coefficients between the surface.
01:15
So, let's see, this is theta.
01:21
So i have m1 equals 4 kilograms, m2 equals 0 .8 kilograms, static coefficient is 0 .33, kinetic coefficient is 0 .26.
01:44
And theta is 30 degrees.
01:49
Okay, does the block move? and if so, what is the acceleration? okay, we've got an incline system, so i'm just going to, we're going to guess a direction of acceleration.
02:06
So i'm guessing, and we could be wrong, we'll see.
02:09
I'm going to guess the m1 goes up the slope, and m2 goes down.
02:13
So i assign positive directions in the, same direction as the acceleration and then we draw the forces acting on each.
02:24
So on m2, tension up, weight down on m1, weight down, normal force, normal to the slope, tension up the slope, and friction down the slope.
02:47
Next we write down the force sum for each block so for m1 forces in the x equals m1a so tension minus friction minus we take our weight and decompose it into x and y components so it would be m1g sine theta equals m1a and for m1 the sum of the forces in the y equals 0.
03:28
It doesn't accelerate normal to the slope at all.
03:31
So we have the normal force minus m1 g cosine theta equals 0.
03:47
Okay.
03:48
Come over to block 2.
03:51
This one's pretty straightforward.
03:53
Some of the forces in the x, in the y rather, equals m2a.
03:59
So tension is negative in our coordinate system the weight is positive and we've guessed acceleration is positive down okay so we have a couple of different equations there's probably a few different ways you could do this the way that i did it is i'm gonna take tension here and solve for it so tension is equal to m to g minus m2a and then i'm going to solve the other tension equation down here and i'll set the two equal so tension equals m1a plus friction plus m1g sine theta what's friction it's the coefficient of friction times the normal force and i'm not going to put me use of s or k i'm just going to put the coefficient so we can just plug in whichever coefficient we want later...