## dainel40 2 years ago The first figure gives spring force Fx versus position x for the spring–block arrangement of the second figure. The scale is set by Fs = 190 N. We release the block at x = 16.0 cm. How much work does the spring do on the block when the block moves from xi =+8.0 cm to (a)x=+6.0 cm, (b)x=-6.0 cm, (c)x=-8.0 cm, and (d)x=-10.0 cm?

1. dainel40

2. dainel40

3. azolotor

Hooke's Law is $F = k \delta x$ where k is the spring constant and delta x is the displacement of the spring. Work is defined as $W =Fdcos(\theta)$ where theta is the angle between the two vectors when they are drawn tail to tail. So, first we calculate the force generated by the displacement of the spring and then from there since the force is parallel to the distance the block is traveling we get $W=Fd$ so once the force is found you can calculate the work at each displacement.

4. dainel40

yes but I'm stuck I can calculate the force but I dont know what to do after. Work is force*distance

5. azolotor

They give you the distances so if you have the force you can calculate the work just plug into the above formula

6. dainel40

but wouldnt I have to subtract from my original distance x=16?

7. azolotor

If I am reading this correctly no because they are asking for the distance from x(i). If I misread this then yes you just need to determine the actual displacement that's all.

8. dainel40

okay thanks!

9. dainel40

yea that didn't work just by pluging it in

10. dainel40

and I tried subtracting the distance and I got it wrong too

11. azolotor

let met take a look

12. dainel40

thanks

13. azolotor

First of all make sure you are putting the right sign on everything. Also you can extrapolate from the graph since it is a line you can easily find the equation for it and find the values at the respective x values to calculate the work. Also, make sure you convert to SI units

14. dainel40

Could u do step A as an examples then I will follow ur steps for the rest

15. azolotor

Sure hold on

16. azolotor

The graph has a slope of -1 and you can pick the point 0,0 for ease since it passes through the origin so y=-x. It wants it at +8cm so that is y=-8 so 8 newtons in the negative direction of force is exerted. It went a distance of 0.08 m so 0.08m *8N =64 Joules