# How do you find the spring constant of a bungee cord without using a mass?

I have a bungee cord which is approximately 60 cm long. I want to find out it's spring constant, but I have no masses to do so. Is there a way I can find the spring constant?

P.S thanx for any answers/suggestions in advance.

### 1 Answer

- 1 decade agoFavorite Answer
well i don't know if you have studied waves yet but i just thought of a way

measure the string's resting distance then stretch it out and measure the new distance. subtract these two distances and you have the value for d in hooke's law F=kd

now jiggle one end of the string and measure the time it takes for a wave to travel from end to end (make sure the string is stretched out at the new distance when you create the wave).

now there is another equation which has been proved by some random person hundreds of years ago which states v = sqrt(T/D).

v = speed of a wave in a stretched string

T = tension on the string

D = linear mass density of the string (mass divided by total length)

you have just measured the speed of the wave v, and hopefully you can weigh the string with a scale and use a ruler to determine D. when you have these two variables you can solve for the tension T.

because the string is stretched a distance d, hooke's law says tension = force = spring constant * distance

so

v^2 = T/D

v^2 = kd / (M/L)

k = v^2 * (M/L) / d

k = v^2 * M / (L * d)

where k = spring constant, v = speed of wave, M = mass, L = length, d = stretched distance