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 before the bungee cord begins to stretch. Chris's mass is 80 kg and we assume the cord obeys Hooke's law, F=−kx, with 54 N/m.

b) What is your acceleration at the bottom of the jump?

Answer 1

Explanations & Calculations

• I didn't jump off the bridge so my acceleration is meaningless however Chris experiences a one and it can be calculated as follows.
• To find the distance he fell along with the rope undergoing extension, you can consider the conservation of mechanical energy of the rope - Chris system in between the starting and ending points.

$\qquad\qquad \begin{aligned} \small mg(15+x)&=\small \frac{1}{2}kx^2\\ \small x&=\small 39.94\,m \end{aligned}$

• Then apply Newton's second law formula on Chris against the falling direction to calculate the acceleration.

$\qquad\qquad \begin{aligned} \small \uparrow\\ \small -mg+kx&=\small ma\\ \small a_{x=39.94}&=\small \frac{k(39.94)-mg}{m} \end{aligned}$

• Now you can substitute the values into it and try getting the answer in $\small ms^{-2}$