# Shank with attached spring

1. Mar 25, 2013

### doombanana

1. The problem statement, all variables and given/known data

The shank of a 5-lb vertical plunger is .25 inches above a button when resting in equilibrium against the spring of stiffness k = 10 lb/in. The upper end of the spring is welded to the plunger, and the lower end is welded to the base plate. If the plunger is lifted 1.5 inches above its equilibrium position and released from rest, calculate its velocity as it strikes the button A. Friction is negligible.

2. Relevant equations
$E_1=E_2$
$PE_{spring} = \frac{1}{2}k(x_1-x_0)^2$
$PE_{gravity} = mgh$
$KE = \frac{1}{2}mv^2$

3. The attempt at a solution
let y=0 at the equilibrium position .25 inches above the button.

1.5in = .125 ft
10 lb/in = 120 lb/ft
.25 in = .0208 ft

It is released from rest, so KE1=0.

My energy balance ends up being:

$PE_{spring,1} + PE_{gravity,1} = PE_{spring,2} + PE_{gravity,2} + KE_2$

Plugging in numbers gives:
$\frac{1}{2}(1.2)(.125)^2 + (5)(.125) = \frac{1}{2}(1.2)(-.0208)^2 - (5)(.0208) + \frac{1}{2}(\frac{5}{32.2})v^2$

I get 4.27 ft/s.

The correct answer should be 3.43 ft/s. I'm just not sure where I went wrong

2. Mar 25, 2013

### TSny

Did you find the value of $x_0$?

Did you mean to let k = 120 lb/ft here?

3. Mar 25, 2013

### doombanana

Ah, that's what it was. I forgot that the spring is compressed at the equilibrium point.

Thank you again!