Question

A spring of negligible mass has a force constant k = 1600 N/m. You place the spring vertically with one end on the floor. You then drop a 1.20 kg book onto it from a height of 0.8 m above the top of the spring. Find the maximum distance the spring will compress.


The answer is 12cm but I can't get it. I'm using the equation mg(0.8+x)=0.5kx^2.
What's wrong with my equation? Or is the answer wrong?

Answer 1

I agree with your equation. X = 0.12 m is close to the correct answer. There may be an issue with significant figures.

Answer 2

I couldn't get x=0.12m. May I know how you did it?

Answer 3

twertw

Answer 4

The energy stored in a spring is 0.5*k*∆x², where ∆x is the amount of compression from relaxed state. Thus 0.5*1600*∆x² = 3.20, solve for ∆x

The energy of the ball that transfers to the spring is the change in potential energy of the ball. That is m*g*∆h, where ∆h is the difference in height from drop point to max deflection of the spring. ∆h = 0.8 + ∆x; then

(0.8 + ∆x)*m*g = 0.5*k*∆x²

solve for ∆x

~can't really this the answer?~