Question

A spring is used to launch a coffee mug. The 20 cm long spring can be compressed by a maximum of 8 cm. The mug has a mass of 300 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? N/m

Answer 1

Answer:k=4593.75

Step-by-step explanation:

Given

length of spring =20 cm

maximum compression in spring is x=8 cm

mass of mug m=300 gm

maximum height to which cup is needed to raise is h=5 m

By conserving Energy i.e. Elastic Potential Energy will be converted in to Potential energy of cup

`(kx^2)/(2)=mgh`

where
`k=spring\ constant`

`(k\cdot (0.08)^2)/(2)=0.3* 9.8* 5`

`k=(0.3* 9.8* 5* 2)/(64* 10^(-4))`

`k=4593.75 N/m`

so we should use a spring with spring constant k=4593.75 N/m