1)The projectile launcher which we used in lab consisted of a ball and spring, s

Question

1)The projectile launcher which we used in lab consisted of a ball and spring, similar to what is depicted above.
In order to compress this spring a distance of 3 cm, the spring must be pushed with a force of 72.1 N.
What is the spring constant of this spring?

The projectile has a mass of 85 g.
What is the velocity of the projectile once the compressed spring is released?
(Assume that all of the potential energy in the spring is converted into kinetic energy of the projectile.)

2) A 74.4-kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 12.2 m, and falls a total of 32.8 m. Calculate the spring stiffness constant k of the bungee cord, assuming Hooke's law applies.

Calculate the maximum acceleration experienced by the jumper.

Explanation / Answer

Part A)

For the spring constant of the spring, apply F = kx

72.1 = k(.03)

k = 2403 N/m

Part B)

Apply .5kx^2 = .5mv^2

(.5)(2403)(.03)^2 = (.5)(.085)(v^2)

v = 5.04 m/s

Part C)

The Bungee Jumper

Application of the COnservation of Energy.

The PE in the initial Jump will be converted to Elastic PE

PE = mgh

EPE = .5kx^2

(74.4)(9.8)(32.8) = (.5)(k)(32.8 - 12.2)^2

k = 112.7 N/m

For the acceleration

The Spring Force is F = kx

The weight = W = mg

The formula is W - kx = ma

(74.4)(9.8) - (112.7)(20.6) = (74.4)(a)

a = -21.4 m/s^2 (The negative is sign convention detailing the direction of the vector of the acceleration. Your answer key may not want the negative, so you can ignore it if needed)

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