Answer to Question #175226 in Mechanics | Relativity for Sadie

Question

Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, (Figure 1). He falls for 15 m

m before the bungee cord begins to stretch. Chris's mass is 80.0 kg

kg and the cord stop his fall (momentarily) after he has fallen a distance of 59.0 N/m

N/m m from the bridge.

Calculate Chris's gravitational potential energy when the cord just begins to stretch (position b), relative to: the bridge (position a)., the stopping point (position c).

Answer 1

Explanations & Calculations

Refer to the sketch attached

• His gravitational potential energy relative to the bridge is

$\qquad\qquad \begin{aligned} \small E_{p_1}&=\small mgH=80kg\times 9.8\times (-15m)\\ &=\small \bold{-11760\,J} \end{aligned}$

• And that relative to the end point is

$\qquad\qquad \begin{aligned} \small E_{p_1}&=\small mgx..................................(1) \end{aligned}$

• Then it's about calculating the distance $\small x$ which is the stretched length of the cord.
• To find this, apply conservation of mechanical energy of the jumper & the cord between the bridge and the endpoint but neglect the effect of the cord as no evidence of its mass is given.

$\qquad\qquad \begin{aligned} \small E_p+E_k&=\small E_{p_1}+E_{k_1}\\ \small 0&=\small -mg(15+x)+\frac{1}{2}kx^2\\ &=\small -80\times9.8(15+x)+\frac{1}{2}\times59x^2\\ &=\small 29.5x^2-784x-11760\\ \\ \small x &=\begin{cases} \small 37.27m\\ \small -10.70m:<0\therefore \text{neglected} \end{cases} \end{aligned}$

• Then from the equation (1),

$\qquad\qquad \begin{aligned} \small E_{p_1} &=\small 80kg\times 9.8\times (+37.27m)\\ &=\small \bold{+29219.7\,J} \end{aligned}$