Trampolines and Energy

Energy types and transformations occurring

               

Somehow, someone managed to transport a trampoline to the festival to demonstrate the law of conservation of energy!

Conservation of Energy

The law of conservation of energy states that ΔE=ΔK+ΔU, ΔK being the change in kinetic energy and ΔU being the change in potential energy, both spring and gravitational.

ΔK=1/2mv²
ΔU_g=mgh
ΔU_s=1/2kx²

Trampoline Transformations

In the case of trampolines, energy is changed from gravitational potential energy to kinetic energy to spring potential energy on the downward section of motion. Although there is kinetic energy in the process, the change in kinetic energy is 0 because the person begins and ends with velocity=0 m/s. 

                                    So, mgh=1/2kx²
If we want to determine the spring constant of the trampoline as a whole (Not of each spring and surface separately), we can observe how high a 60 kg person goes, and how far the trampoline surface depresses.

Say the person goes 2m high and the trampoline depresses 0.5m, then:

                    k = 2mgh = 2(60kg)(9.8m/s²)(2m) = 9408N/m
                              x²                    (0.5m)²