# Homework Help: Need help setting up the problem.

1. Apr 7, 2012

### qball1982

Hello,
I was looking to get some help with setting up this problem so I may solve it. For some reason I just don't see what to do to work towards a solution.
1. The problem statement, all variables and given/known data
A 6kg collar is allowed to slide over a frictionless pole whose height above the ground obeys the parabolic equation y=8-(1/2)x^2. Attached to the collar is a k=30N/m spring. The spring is 1 m when unstretched and connected in a way that the spring will always start at the origin. If the collar started from rest at (0,8), how fast will it be traveling at x=2? Hint: Don't forget gravity!

Any help to point me in the right direction would be fantastic. Thank you.

2. Apr 7, 2012

### tiny-tim

welcome to pf!

hello qball1982! welcome to pf!

(try using the X2 button just above the Reply box )

hint: try conservation of energy …

kinetic energy + gravitational potential energy + elastic potential energy = constant …

what do you get?

3. Apr 7, 2012

### qball1982

Excellent! Thank you tiny-tim!

I worked this out using the formula: K1+U1=K2+U2
where U= mgy+1/2kx2

Crunching the numbers I get :
0+1205.4=K2+778.05
427.35=K2
427.35=1/2(6)v2

then finally: v=11.935m/s

Does this seem like the right path?

4. Apr 8, 2012

### tiny-tim

hi qball1982!

(just got up :zzz:)

yes that's the correct method

(but we need to see your detailed calculations if you want us to check the actual figures … for example, did you use √(x2 + y2) in the spring PE?)

5. Apr 8, 2012

### qball1982

Hello tiny-tim!

I suppose exact calculations would help. Sorry about that.

Spring displacement calculations:
x1 = 8-1 = 7 meters
x2 = √(22+62) -1 = 5.32 meters
And of course the -1 in each is due to the springs unstretched length of 1 meter.

Spring Uel Calculations:
Uel1= 1/2(30N/m)(7m)2 = 735N/m
Uel2= 1/2(30N/m)(5.32m)2 = 425.25N/m

Gravitational Potential Energy Calculations:
Ug1= (6kg)(9.8m/s2)(8m)=470.4
Ug2= (6kg)(9.8m/s2)(6m)= 352.8

To solve:
K1+Uel1[/SUB+Ug1=K2+Uel2+Ug2

0+ 735+ 470.4 =K2+ 425.25 + 352.8
1205.2 = K2 + 778.05
427.15 =K2
427.15 = 1/2(m)(v2)
427.15 = 3(v2)
142.38 = (v2)
v=√(142.38)
v = 11.93 m/s

I think it looks right but I am also wrong quite a bit too.

Thanks again for all the help!

6. Apr 8, 2012

### tiny-tim

yes that looks ok

just one thing, you could save time and make it look neater if instead of doing all this …
you just work out Uel1 - Uel2 = 1/2(30N/m){(7m)2 - (5.32m)2}

(and the same for Ug)