Question

A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. After many oscillations, he finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.

Answer 1

To calculate the spring stiffness constant, we can use Hooke's Law and the equation F = -mg. The spring constant is approximately -254.8 N/m. The unstretched length of the bungee cord cannot be calculated based on the given information.

Step-by-step explanation:

The spring stiffness constant, also known as the force constant or spring constant, can be calculated using Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring.

F = kx

Where F is the force, k is the spring constant, and x is the displacement. From the given information, we can use the equation:

F = -mg

Where m is the mass and g is the acceleration due to gravity. Rearranging the equation gives:

kx = -mg

Now we can solve for the spring constant:

k = -mg/x

Using the values given, the mass (m) is 65.0 kg, the acceleration due to gravity (g) is 9.8 m/s^2, and the displacement (x) is 25.0 m. Substituting these values into the equation, we get:

k = -(65.0 kg)(9.8 m/s^2)/(25.0 m)

Simplifying the equation, we find that the spring constant is approximately -254.8 N/m.

The unstretched length of the bungee cord can be calculated by subtracting the total stretched length from the length of the bridge. In this case, the total stretched length is 25.0 m and the length of the bridge is not provided. Therefore, it is not possible to calculate the unstretched length of the bungee cord based on the given information.

Answer 2

Step-by-step explanation:

It is given that,

Mass of a bungee jumper is 65 kg

The time period of the oscillation is 38 s, hitting a low point eight more times.It means its time period is

`T=(38)/(8)\\\\T=4.75\ s`

After many oscillations, he finally comes to rest 25.0 m below the level of the bridge.

For an oscillating object, the time period is given by :

`T=2\pi \sqrt{(m)/(k)}`

k = spring stiffness constant

So,

`k=(4\pi ^2m)/(T^2)\\\\k=(4\pi ^2* 65)/((4.75)^2)\\\\k=113.43\ N/m`

When the cord is in air,

mg=kx

x = the extension in the cord

`x=(mg)/(k)\\\\x=(65* 9.8)/(113.6)\\\\x=5.6\ m`

So, the unstretched length of the bungee cord is equal to 25 m - 5.6 m = 19.4 m