- #1

danielsmith123123

- 26

- 4

- Homework Statement
- A spring with a spring constant of 185 N/m hangs vertically from a surface, as shown in the image below. A mass of 200 g is then hung from the spring and the spring stretches to a new length as shown at right. How much (Δx) has this spring been stretched from its equilibrium length?

- Relevant Equations
- F_spring = -kx

WD_ spring = (1/2)kx^2

Finding x by force formula

- only force acting is gravity

ma/-k = x

(0.2)(-9.8)/185 = x

0.010594594 = x

Finding x by wd formula

WD_ spring = (1/2)kx^2

F x = (1/2)kx^2

2(mg)/k = x

[2(0.2)(-9.8)]/ 185 = x

0.021189189 = x

how come the work done and force formulas produce different values for x. I noticed without the 1/2 in the WD formula, I would get the same answer but isn't this the standard?

- only force acting is gravity

ma/-k = x

(0.2)(-9.8)/185 = x

0.010594594 = x

Finding x by wd formula

WD_ spring = (1/2)kx^2

F x = (1/2)kx^2

2(mg)/k = x

[2(0.2)(-9.8)]/ 185 = x

0.021189189 = x

how come the work done and force formulas produce different values for x. I noticed without the 1/2 in the WD formula, I would get the same answer but isn't this the standard?