- #1

purpleperson1717

- 12

- 1

- Homework Statement:
- A 4kg box is attached to a bungee cord of spring constant 20N/m and dropped off a 52m platform. It is in free fall for 3s, until the bungee catches. Will the box hit the ground?

- Relevant Equations:
- Conservation of energy

This is more of a check that I solved this assignment correctly. I got to an answer but I’m not sure it’s correct.

First, I decided that I needed to solve for the maximum stretch of the bungee. To do that I think I needed the length of the bungee (which is also the initial compression).

So next, I used d=v1t + 1/2at^2 to find the length of the bungee (this is the part I’m not so sure about). I used a=9.8m/s^2, t=3 and v1=0 and got d=44.1m. So I think this was the magnitude of the initial compression of the bungee.

Finally I used conservation of energy: mgh1 + 1/2kx1^2=1/2kx2^2

I used m=4, g=9.8, h1=44.1+x2, k=20, x1=44.1. After using the quadratic formula I got x2=48.02. I added that max stretch to 44.1 and got 92.12m, which is way more than 52 (the height of the platform). So my answer is that yes the box will hit the ground. But I’m not really sure that I did this right because 92.12 is not at all close to 52 so I would really appreciate some help.

First, I decided that I needed to solve for the maximum stretch of the bungee. To do that I think I needed the length of the bungee (which is also the initial compression).

So next, I used d=v1t + 1/2at^2 to find the length of the bungee (this is the part I’m not so sure about). I used a=9.8m/s^2, t=3 and v1=0 and got d=44.1m. So I think this was the magnitude of the initial compression of the bungee.

Finally I used conservation of energy: mgh1 + 1/2kx1^2=1/2kx2^2

I used m=4, g=9.8, h1=44.1+x2, k=20, x1=44.1. After using the quadratic formula I got x2=48.02. I added that max stretch to 44.1 and got 92.12m, which is way more than 52 (the height of the platform). So my answer is that yes the box will hit the ground. But I’m not really sure that I did this right because 92.12 is not at all close to 52 so I would really appreciate some help.