Answer:
To reach height of 8 cm the value of k should be less than or equal to 18750 N/m .
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 .
[tex]\dfrac{kx^2}{2}=mgh\\\\h\geq \dfrac{kx^2}{2mg}\\\\k\leq \dfrac{(2mg)h}{x^2}[/tex]
Putting all values in above equation .
We get :
[tex]k\leq \dfrac{(2\times 0.750\times 10)\times 8}{0.08^2}\\\\k\leq 18750\ N/m[/tex]
Therefore , to reach height of 8 cm the value of k should be less than or equal to 18750 N/m .
