Question

A bungee jumper jumps off a bridge and bounces up and down several times.She finally comes to rest 30 m below the bridge from which she just jumped.If her mass is 50 kg and the spring constant of the bungee cord is 10 N/m,how much energy was lost due to air resistance while she was bouncing?(Recall that g = 9.8 m/s2)A. 9200 NB. 7330 Nc. 10,200 ND. 8605 N

Answer 1

The energy lost due to air resistance is calculated by the difference between the initial potential energy and the sum of final elastic and gravitational potential energies. The bridge height cancels out, resulting in a calculation of energy lost which is not matching with any of the provided options.

Step-by-step explanation:

To calculate the energy lost due to air resistance during a bungee jump, we can compare the gravitational potential energy at the start of the jump to the elastic potential energy of the cord when the jumper comes to rest, as well as her final gravitational potential energy. Initially, the energy is purely gravitational potential, given by Ep(gravitational) = mgh, where m is the mass of the jumper, g is the acceleration due to gravity, and h is the height of the bridge.

When the jumper comes to rest, the cord's elastic potential energy (Ep(elastic)) can be calculated using the formula Ep(elastic) = 0.5kx², where k is the spring constant and x is the extension of the spring. Additionally, the jumper has gravitational potential energy due to being 30 m below the bridge, which can be calculated as Ep(gravitational rest) = mg(bridge height - 30 m). The energy lost to air resistance is the difference between the initial gravitational potential energy and the sum of the final potential energies, both elastic and gravitational.

Calculations:

Initial gravitational potential energy: Ep(gravitational) = 50 kg * 9.8 m/s² * bridge height.

Final gravitational potential energy at rest: Ep(gravitational rest) = 50 kg * 9.8 m/s² * (bridge height - 30 m).

Elastic potential energy when at rest: Ep(elastic) = 0.5 * 10 N/m * x².

Energy lost to air resistance = Ep(gravitational) - (Ep(elastic) + Ep(gravitational rest)).

Without knowing the bridge height, we assume it is enough so that the bungee cord is fully extended and then calculate the energy lost:

Energy lost to air resistance: = (50 * 9.8 * bridge height) - (0.5 * 10 * (302)) - (50 * 9.8 * (bridge height - 30 m)).

Please note that this will result in the bridge height cancelling out, and simplifying the equation will enable us to find the energy lost to air resistance:

Energy lost to air resistance = - (0.5 * 10 * 302) + (50 * 9.8 * 30).

Carrying out the calculation:

Energy lost to air resistance = -150 + 14700 = 14550 J.

The correct answer is not among the provided options.

Answer 2

Given data

*The given height is h = 30 m

*The given mass is m = 50 kg

*The spring constant of bungee cord is k = 10 N/m

*The value of the acceleration due to the gravity is g = 9.8 m/s^2

The net change in potential energy is calculated as

`\begin{gathered} \Delta U_p=mgh \\ =(50)(9.8)(30) \\ =14700\text{ J} \end{gathered}`

The spring stretch is calculated by using the relation as

`\begin{gathered} F=mg \\ kx=mg \\ x=(mg)/(k) \\ =((50)(9.8))/(10) \\ =49\text{ m} \end{gathered}`

The energy stored in spring is calculated as

`\begin{gathered} U_s=(1)/(2)kx^2 \\ =(1)/(2)(10)(49)^2 \\ =12005 \end{gathered}`

The energy was lost due to air resistance while she was bouncing is calculated as

`\begin{gathered} \Delta E=\Delta U_p-U_s_{}_{} \\ =14700-12005 \\ =2695\text{ J} \end{gathered}`

Hence, the energy was lost due to air resistance while she was bouncing is 2695 J