Question

A spring is used to launch a coffee mug. The 20cm long spring can be compressed by a maximum of 8cm. The mug has a mass of 500 g. What kind of spring do you need to launch the mug at least 2 stories high (5 m) - as measured from the relaxed spring position - using the maximum compression?

Answer 1

7664.06249 N/m

Step-by-step explanation:

m = Mass of mug = 0.5 kg

x = Compression of spring = 0.08 m

h = Height of fall = 5 m

g = Acceleration due to gravity = 9.81 m/s²

The kinetic energy of the spring and potential energy of the fall are conserved

`(1)/(2)kx^2=mgh\\\Rightarrow k=(2mgh)/(x^2)\\\Rightarrow k=(2* 0.5* 9.81* 5)/(0.08^2)\\\Rightarrow k=7664.06249\ N/m`

The spring constant of the spring is 7664.06249 N/m