What Is the Minimum Spring Constant Needed for George's Safe Bungee Jump?

[killa0587]

1. George is going to bungee jump from a bridge that is 40.5 m over the river below. The bungee cord has an unstretched length of 27.5 m. To be safe, the bungee cord should stop George's fall when he is at least 2.00 m above the river. Ignoring air resistance, if George has a mass of 75.0 kg, what is the minimum spring constant of the bungee cord?
_______N/m

Homework Equations

Fx=-kx

The Attempt at a Solution

134

 

[kkrizka]

Your attempt at a solution should include more than yoru final answer.

Anyways, try drawing a diagram to see what the numbers in the question mean.

 

[Moetasim]

.5 N/mI would first clarify the units being used for the spring constant. The standard unit for spring constant is Newtons per meter (N/m), so it is important to include this unit in the answer. Additionally, I would check to make sure the calculation is correct by showing the steps taken to arrive at the answer.

To calculate the spring constant, we can use the equation Fx=-kx, where Fx is the force exerted by the bungee cord, k is the spring constant, and x is the displacement from the unstretched length. In this scenario, we know the displacement (2.00 m), the weight of George (75.0 kg), and the unstretched length of the bungee cord (27.5 m).

First, we need to calculate the force exerted by the bungee cord on George when he is at a displacement of 2.00 m. This can be done using Newton's second law, F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, the acceleration is due to gravity and can be calculated using the formula a=g, where g is the acceleration due to gravity (9.8 m/s^2).

F=ma
F=(75.0 kg)(9.8 m/s^2)
F=735 N

Next, we can plug in this value for force (735 N) and the displacement (2.00 m) into the equation Fx=-kx to solve for the spring constant.

735 N = -k(2.00 m)
k = -(735 N)/(2.00 m)
k = -367.5 N/m

We can see that the units for the spring constant are indeed N/m. However, the negative sign in front of the value indicates that the force and displacement are in opposite directions, which is not the case in this scenario. Therefore, the correct answer for the minimum spring constant of the bungee cord is 367.5 N/m.