00:01
Okay, we have a box being moved up a ramp and the box has a mass of 20 kilos.
00:14
The initial velocity it's given is one meter per second up the slope.
00:20
The angle of theta is 18 degrees.
00:26
And the coefficients of friction are 0 .38 for static friction and 0 .1 for kinetic friction or sliding friction as they call it here.
00:47
Okay, so first what we need to decide is that this is our coordinate system.
00:55
So x is up the slope and y is normal to the slope.
01:00
And we'll say x equals zero is where this box starts.
01:06
So for part a we want to look at how for how much time does the box slide up the range.
01:15
So for how long is it's sliding up.
01:20
Okay, we can use a kinematic equation here.
01:24
So this is motion in the x direction.
01:26
So velocity x final equals velocity x initial, or we've just called that v -not, plus the acceleration times time.
01:37
We know that the final velocity we want is zero.
01:39
That's when the box stops moving.
01:42
So then the time at which it reaches the highest point on the ramp is going to be equal to the initial velocity over the acceleration, or rather the negative of the initial velocity over the acceleration.
02:09
So now we've got to figure out the acceleration.
02:11
So we'll draw our slope a little more pronounced here.
02:16
Let's pretend our block is right here.
02:19
We look at the forces.
02:20
Well, we just look at the accelerations.
02:26
So we just look at gravity here.
02:28
This is the acceleration that we want, right? this is what is slowing it down, is this acceleration of gravity.
02:36
So if we make this little triangle here so that the legs of the triangle correspond to x and y.
02:56
Okay, so we want the component in the x direction.
02:59
So the acceleration in the x is then equal to g and we know that this angle here is theta sine theta.
03:10
We know that angle is theta because this angle here is going to be um, 90 subtract theta and this angle here is going to be 90 subtract 90 subtract theta so this is angle of state.
03:35
Okay so then the time is equal to minus v not over the acceleration and i should put a negative here because it's pointing in the negative x direction minus g sine theta.
03:51
Okay so we plug all that in and we get 0 .3 3 seconds.
04:05
Okay, that is how long it takes for the box to get up the ramp.
04:12
Now we want to see how far up it went.
04:16
Okay, well, we can just use another kinematic equation here.
04:19
Or we could use energy, but this feels like they want you to use a kinematic equation, so we'll just do that.
04:28
So x -final equals x initial, plus the initial velocity in the x times time plus one -half times the acceleration in the x times time squared.
04:41
Well, we know x -not is zero.
04:46
So that will tell us what we want to know here.
04:53
So solving for x -final.
04:57
Oh, i guess that's what we're solving for.
04:58
So x -final is then equal to the initial velocity times time plus one -half times the acceleration in the x, which is negative g sine theta time squared.
05:19
Okay, that will be our final distance in the x direction.
05:26
And this is equal to 1 point, or sorry, 0 .165 meters.
05:38
0 .165 meters.
05:40
Okay.
05:40
Now, when the box is going up the ramp, or when it stops going up the ramp, does it remain stopped or does it start sliding down again? okay, so this one is a little trickier.
05:56
Let's get a new page here.
05:59
So for this, what we want to look at is the...
06:03
We want to look at the forces.
06:04
So let's look at the forces here.
06:09
So here it is at the highest point...