Question

to compress spring 1 by 0.20m takes 150j of work. stretching spring by 2 by 0.30 m requires 210j of work . which spring is stiffer?

Answer 1

work to stretch the a spring is found by the equation 1/2kx^2 where k is the spring constant and x is the distance stretched or compressed. so just fill in the numbers to solve and see which spring has a higher k=spring constant. so for spring 1 we have 1/2kx^2=150j which gives 1/2k(.20m^2)=150j and solving for k we get k=7500, for spring 2 we have 1/2kx^2=210j which gives the equation 1/2k(.30m^2)=210j which gives k=4666.67 so spring 1 has a much spring higher spring constant so spring 1 is stiffer which means it takes more force to stretch or compress.

Answer 2

The spring constant of Spring 1 is greater than that of spring 2, hence the spring 1 will be stiffer than spring 2

The higher the spring constant, the stiffer the spring is.

The formula for calculating the work done by a spring is expressed as;

$W = \frac{1}{2} kx^2$

k is the spring constant

x is the distance

For the spring with workdone of 150Joules

$150 = \frac{1}{2}0.2^2k\\150 = 0.02k\\k = \frac{150}{0.02}\\k= 7500$

Similarly for the spring with workdone of 210 Joules and distance of 0.3m

$210= \frac{1}{2}0.3^2k\\210 = 0.02k\\k = \frac{150}{0.045}\\k= 3,333.33$

Since the spring constant of Spring 1 is greater than that of spring 2, hence the spring 1 will be stiffer than spring 2

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