A spring of negligible mass has force constant k = 1800 N/m. Part A How far must

Question

A spring of negligible mass has force constant k = 1800 N/m.

Part A

How far must the spring be compressed for an amount 3.40 J of potential energy to be stored in it?

Express your answer using two significant figures.

Part B

You place the spring vertically with one end on the floor. You then drop a book of mass 1.40 kg onto it from a height of 0.900 m above the top of the spring. Find the maximum distance the spring will be compressed.

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

Please explain all the steps!! I need to be able to figure out similar problems and am very confused about how to do part B... (I think the correct equation to use is mg(h+x)=0.5kx2 but am not quite sure.)

Explanation / Answer

Here, k = 1800 N/m

part A)

potential energy stored = 3.40 J

U = 0.5 * k * x^2

3.4 = 0.5 * 1800 * x^2

solving for x

x = 1.415 m

part B)

h = 0.90 m

let the maximum compression is x

Using energy conservation

0.5 * k * x^2 = m * g * (h + x)

0.5 * 1800 * x^2 = 1.4 * 9.8 * (0.90 + x)

solving for x

x = 0.125 m

the compression in the spring will be 0.125 m

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