00:01
Problem 7 .65.
00:03
We have a package handling system where we have a box that's being placed in front of a compressed spring, and the spring is then released, and it pushes the box on a surface that has a coefficient of friction of 0 .3.
00:22
I've told some information about all this.
00:24
The initial compression of the spring is 0 .28 meters, and what we'd like to know is what is the speed of the box as it leaves the spring, and what is the maximum speed that the box obtains? so we know that the box starts from rest.
00:48
And so initial energy must all be potential.
00:56
Okay, x squared.
01:04
And then work done on it by friction, and then the normal force is just its weight.
01:14
It seems x, not because this moves a distance of the .28 meters before it clears the spring, and that's the moment where we're wanting to find the speed for.
01:40
And then this is equal to the kinetic energy at that moment.
01:50
And so you solve this for v squared, put in the numbers, and you find you find that its speed is 0 .747 meters per second.
02:16
Now let's have a variable x that's the distance that's the distance along which the box has traveled and we want to maximize the speed as a function of that...