00:01
Hi there.
00:01
So for this problem, we are told that spring has a spring constant that is equal to 100 newton's per meter and there is a mass that is equal to 100 grams that is drop from a height that is equal to 20 centimeters.
00:37
And for this problem, what we need to calculate is how much will the spring compress? in that quantity, we're going to call it x.
00:51
Now the situation that we are going to have in here, just i'm going to draw the initial situation.
00:59
So we have a mass and an uncompressed, uncompressed, something like this.
01:12
This in here corresponds to the height age.
01:19
And then when the ball compresses the stream, we're going to obtain something like this.
01:30
So as you can see, there's going to be a distance x that the spring moves when the ball drops.
01:42
So what we need to obtain in here is this distance x.
01:48
Now, we need to obtain here.
01:50
We are going to set that the zero of potential is in here.
01:59
So what we are going to have is that the initial potential energy, that in this case is gravitational potential energy, is going to be the mass times the acceleration, times the total height that in this case is going to be all of this, that is h plus x.
02:21
So we're going to have that.
02:24
And the final potential energy is going to be 1 over 2 times the spring constant times the distance adds to the square, which corresponds to the potential energy for a spring.
02:42
So we know from the conservation of energy that the initial energy should be equal to the final energy.
02:52
So in this case, we're going to have that the mass.
02:55
Times acceleration due to gravity times the distance adds plus h is equal to 1 over 2 times the spring constant times the distance adds to the square.
03:17
So if we start solving this, we're going to have m times acceleration due to gravity times x plus n times acceleration due to gravity times h plus n times acceleration due gravity times h.
03:29
Is equal to 1 over 2 times the sprems constant times x.
03:36
So if we pass all of this to the left side, we are going to be left with an equation of the following 4.
03:46
1 over 2 times the sprems constant times x to the square, and the others are going to be negative.
04:00
So we have the mass times acceleration due to gravity.
04:07
We're going to put this better to the last position.
04:11
So let me put mass times acceleration due to gravity times x minus the mass acceleration to gravity times h...