00:02
Hi there.
00:04
So for this problem, we have the mass that is given for this grade and that is 110 kilograms.
00:14
And it is being pulling across a floor.
00:17
And this with a constant force that is also given that is 350 newtoms.
00:23
Now for the first 15 meters, the floor is frictionless and for the remaining and 15 meters, the coefficient of friction is given.
00:31
And that coefficient of friction is 0 .3.
00:35
So the question is, what is the final speed of the crate? so we need to separate this into two exceptions.
00:41
One section that is frictionless, and the other exception that it has some coefficient of friction.
00:47
So let's just draw something like this.
00:51
Okay, so both of this measure 15 meters, and it starts, in here at this point in the in the frictionless section of this this is the mass that is being pulled now it is being pulled horizontally with the force f which magnitude is given and then what we need to do is to determine the speed at the moment that it stores the friction part of this and then obtain the final speed at the end of the friction part of this problem.
01:44
So with that said, let's calculate first the speed at this moment.
01:50
So remember that the crate is starting from rest.
01:54
So in here, the initial speed is equal to zero.
02:00
Now, we know that the only force that is acting on this is the force f, but remember that the sum of forces equals to the mass, times the acceleration.
02:12
So from this we can obtain the acceleration.
02:15
So the acceleration is just the force that is being applied divided by the mass of this.
02:19
So that will be 350 and this divided by the mass that is 110.
02:31
Then using our calculator we obtain a value of 3 .18 meters per second square.
02:45
Now with that, we can use kinematics to obtain the final speed at this moment.
02:53
So, for that we use the fact that the final speed square is equal to the initial speed square and this plus the 2 times the acceleration times the distance cover, which in this case is 15 meters.
03:07
So we know that the initial speed is zero.
03:09
So the final speed is just a square root of two times the acceleration times the distance of 3.
03:15
So that will be the square root of 2 times 3 .18 and this times the distance covered that is 15.
03:28
Then we take the square root of all of this.
03:30
Using our calculator, we obtain a value of 9 .77 meters per second.
03:42
So that is the speed just before it starts the friction part of this.
03:47
Now, we're going to set that that is the initial speed for this point, so that will be the initial speed is 9 .77.
03:57
And now the credits are going to move from here to this point to the final position at this point right here.
04:06
So for that, we now need to consider the friction because the force is just again being used through...