00:01
So we have a block attached to a spring resting on a frictionless surface, and the block has a mass of 1 .3 kilograms.
00:10
The spring constant of the spring is 770 newtons per meter.
00:15
And part a, i know the question really asks for part b and c, but we'll do part a just for, i guess, posterity sake, anybody else looking at this problem.
00:25
So we're told the spring is initially compressed by a distance of 5 .2 centimeters.
00:30
Meters.
00:31
And so we want to know what's the potential energy stored in the spring? what is delta use? so this is going to be one -half k -delta -x squared.
00:40
And so this will be one -half times 770 newtons per meter times 0 .052 meters squared.
00:50
And this comes out to about 1 .04 joules of energy being stored in this spring.
00:57
Next up, we want to find the speed of the block, it passes through this equilibrium point.
01:03
So the spring is compressed and then released.
01:06
And so we'll have our change in kinetic energy is equal to the negative change of potential energy.
01:11
Technically, the potential energy would be the negative of this value because of, you know, the way hooksaw works and everything.
01:19
So what we have is our changing kinetic energy is going to be basically, with this starts from rest, it's just one half nb squared.
01:27
And this is equal to 1 .04 joules.
01:32
And so v squared, if we saw for it, is going to be like 2 .08 joules divided by 1 .3 kilograms.
01:42
And so naturally, v is the square root of this...