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 750 g. What kind of spring do you need to launch the mug at least 2 stories high (8 m) - as measured from the relaxed spring position - using the maximum compression?

Answer 1

To reach height of 8 cm the value of k should be less than or equal to 18750 N/m .

Step-by-step explanation:

We need to find what kind of spring do you need to launch the mug at least 2 stories high (8 m) i.e what is the minimum spring constant should be .

Also , the maximum compression is 8 cm .

Therefore , by conservation of energy .

`(kx^2)/(2)=mgh\\\\h\geq (kx^2)/(2mg)\\\\k\leq ((2mg)h)/(x^2)`

Putting all values in above equation .

We get :

`k\leq ((2* 0.750* 10)* 8)/(0.08^2)\\\\k\leq 18750\ N/m`

Therefore , to reach height of 8 cm the value of k should be less than or equal to 18750 N/m .