Kinetic energy at height 2.5?

Question

1.     Some bored physics students find a long bungee cord and decide to use it as a slingshot to launch a 1.6 kg ball straight up into the air. They find that it takes 25.6 N to stretch the bungee cord 0.8 meters. When they launch the ball, they are able to stretch the bungee cord 1.8 meters. How much kinetic energy does the ball have when it reaches a height of 2.5 meters above the top of their slingshot?

Answer 1

You need to start by finding the energy stored in the bungee cord, which is given by the equation:

PE = 0.5kx² where PE is the potential energy stored in the bungee, k is the spring constant (or bungee constant in this case), and x is the displacement of the bungee

But to use that formula, you will need to determine the spring constant by using Hooke's Law:

F = kx , where F is the force on the spring, k is the spring constant, and x is the displacement of the spring.

Once you calculate the potential energy in the bungee at the beginning, you know the total energy in the system because in the beginning, there is no kinetic energy, so the total energy is only potential energy.

Then, you can use the formula:

TE = PE + KE where TE is the total energy, PE is the potential energy due to gravity, and KE is the kinetic energy.

PE = mgh where m is the mass, g is the gravitational acceleration constant, and h is the height

You can use all of these formulas to calculate the KE of the ball at a height of 2.5 meters.