What is the effective spring constant and velocity of a bungee jumper?

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In summary, a man with a mass of 80.0 kg jumps off a bridge with a lightweight rubber rope attached to his feet. He falls 50.0 m before turning around and coming back up, reaching a distance of 30.0 m beyond the equilibrium point of the rubber band. To find the effective spring constant of the rope, we can use the formula k = F/x, where F is the force of the man's weight and x is the distance of 30.0 m. This gives us a value of 26.1 N/m. To determine the speed of the man when passing the equilibrium point on his way up, we would need more information such as the length of the rope and the time it
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toad22
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A man of mass 80,0 kg jumps out from a bridge, with a lightweight rubber rope attached to his feet. He falls 50.0 m before turning around and coming back up, which is 30,0 m further than the equilibrium point of the rubber band (without man), which we take to be like a spring when stretched (but not when squeezed; no spring force on the man until he has passed the equilibrium point.)
a) What is the effective spring constant of the rope?
b) How fast is the man going when passing the equilibrium point on his way up again?

I tried finding the spring constant like this, but I'm not sure if it's right..:
m = 80,0 kg
x = 30,0 m
F = mg
= 80,0 kg * 9,81 m/s^2
= 784 N
F = kx
k = F/x
= 784 N/30 m
= 26,1

I have no idea where to even start at problem b)..
 
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  • #2
The force at the bottom is more than 784 N - the man is slowed down and then accelerated upwards there.
What about the energy?
 

1. How does the bungee jumper problem relate to science?

The bungee jumper problem is a physics problem that involves the study of forces, energy, and motion. It can also be applied to other fields of science such as engineering and biomechanics.

2. What is the bungee jumper problem?

The bungee jumper problem is a mathematical and physical problem that involves calculating the length of a bungee cord needed for a person to safely jump off a platform and reach a desired distance without hitting the ground or the water.

3. What factors affect the bungee jumper problem?

The factors that affect the bungee jumper problem include the weight of the jumper, the elasticity of the bungee cord, the height of the jump, and the location of the jump.

4. How is the bungee cord length calculated in the bungee jumper problem?

The length of the bungee cord is calculated using the equation L = (mg)/(k), where L is the length of the bungee cord, m is the mass of the jumper, g is the acceleration due to gravity, and k is the spring constant of the bungee cord.

5. What safety measures should be taken in the bungee jumper problem?

In the bungee jumper problem, it is important to ensure that the bungee cord is strong enough to withstand the weight of the jumper and that it is properly attached to the jumper and the platform. It is also important to have a backup system in case the bungee cord fails. Safety checks and inspections should be done regularly to ensure the safety of the jumper.

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