A spring of negligible mass has force constant k = 1600N/m . 1. How far in meter

Question

A spring of negligible mass has force constant k = 1600N/m .

1. How far in meters must the spring be compressed for an amount 3.40J of potential energy to be stored in it? Express your answer using two significant figures.

6.5 x 10^-2 ---> correct

2. You place the spring vertically with one end on the floor. You then drop a book of mass 1.50kg onto it from a height of 0.500m above the top of the spring. Find the maximum distance in meters the spring will be compressed. Take the free fall acceleration to be 9.80m/s2 . Express your answer using two significant figures

Explanation / Answer

a) P.E = 0.5 kx^2 = 3.1 J

x^2 = 3.4/ (0.5*1600)

x = 0.065 m

b) D be the total distance traveled by the book ,
P.E lost by the book = mgD = 1.5*9.8D = 14.7 D J
P.E gained by the spring = 0.5kx^2 = 800 x^2 J
800 x^2 = 14.7 D [D =( 0.5 + x) ]
800 x^2 = 14.7*( 0.5 + x)
solve for x

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