91影视

The given data can be listed below,

• The length of the bungee cord is $l=30\text{鈥尘}$,
• The height of the platform is $y_1=45\text{鈥尘}$,
• The maximum height the cord will fall is $y_2=41\text{鈥尘}$,
• The mass of the person is $m=95\text{鈥塳驳}$,
• The force on the bungee cord is$F=380\text{鈥塏}$

The energy an item or body possesses as a result of its motion is known as kinetic energy. Every atom that is engaged in some sort of motion possesses it.

The stretched amount of cord is given by,

$\begin{array}{c}d=41\text{鈥尘}鈭�30\text{鈥尘}\\ =11.0\text{鈥尘}\end{array}$

The cord is initially at equilibrium so the initial gravitational potential energy which can be given by,

$\begin{array}{c}{U}_{grav,1}=mg{y}_1\\ =0\end{array}$

The elastic potential energy is given by,

$U_{el,2}=\frac{1}{2}k{x}^2$

Here, kis the force constant and x is the stretched distance of cord.

Substitute all the values in the above,

$\begin{array}{c}{U}_{el,2}=\frac{1}{2}k{\left(11\text{鈥尘}\right)}^2\\ =60.5k\end{array}$

The kinetic energy of the person is zero as it will eventually come at rest.

So, from the law of conservation of energy the force constant is given by,

$\begin{array}{c}{K}_1+U_{grav,1}+U_{el}=K_2+U_{grav,2}+U_{el}\\ 0+0+0=0鈭�mg{y}_2+60.5k\\ k=\frac{mg{y}_2}{60.5}\end{array}$

Here, m is the mass of the person, g is the acceleration due to gravity, and $y_2$is the maximum fallen distance.

Substitute all the values in the above,

$\begin{array}{c}k=\frac{鈭�\left(95\text{鈥塳驳}\right)\left(9.8{\text{鈥尘/s}}^2\right)(鈭�41\text{鈥尘})}{60.5}\\ =630.9\text{鈥塏/尘}\end{array}$

The restoring force is given by,

$F=kx$

The stretched length of the cord is calculated by substitute all the values in the above,

$\begin{array}{c}380.0\text{鈥塏}=630.9x\\ x=0.602\text{鈥尘}\end{array}$

Thus, the stretched length of the bungee cord is .

$0.602\text{鈥尘}$