Need help setting up the problem.

  • Thread starter qball1982
  • Start date
In summary, qball1982 is looking for help with a homework problem that has him stumped. He used the formulas K1+U1=K2+U2 and K1-Uel1=Uel2-Ug1 to calculate kinetic energy and potential energy, respectively. He also calculated the spring's displacement using x1=8-1=7 meters, x2=√(22+62) -1=5.32 meters, and -1 due to the springs unstretched length of 1 meter. Finally, he compared his results to a handy spreadsheet provided by tiny-tim
  • #1
qball1982
5
0
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.

Homework Statement


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.
 
Physics news on Phys.org
  • #2
welcome to pf!

hello qball1982! welcome to pf! :smile:

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

hint: try conservation of energy …

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

what do you get? :smile:​
 
  • #3
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
hi qball1982! :smile:

(just got up :zzz:)

yes that's the correct method :smile:

(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
Hello tiny-tim!

I suppose exact calculations would help. Sorry about that. :wink:

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. :smile:

Thanks again for all the help!
 
  • #6
yes that looks ok :smile:

just one thing, you could save time and make it look neater if instead of doing all this …
qball1982 said:
Uel1= 1/2(30N/m)(7m)2 = 735N/m
Uel2= 1/2(30N/m)(5.32m)2 = 425.25N/m

Ug1= (6kg)(9.8m/s2)(8m)=470.4
Ug2= (6kg)(9.8m/s2)(6m)= 352.8

you just work out Uel1 - Uel2 = 1/2(30N/m){(7m)2 - (5.32m)2} :wink:

(and the same for Ug)
 

FAQ: Need help setting up the problem.

1. What is the purpose of setting up a problem?

The purpose of setting up a problem is to clearly define and understand the question or issue at hand. It helps to identify what information or variables are needed to solve the problem and provides a structured approach for finding the solution.

2. How do I go about setting up a problem?

To set up a problem, start by identifying the question or issue that needs to be addressed. Then, break down the problem into smaller, more manageable parts. Next, gather all relevant information and variables needed to solve the problem. Finally, organize the information in a logical and structured manner.

3. What are some common mistakes to avoid when setting up a problem?

Some common mistakes to avoid when setting up a problem include not clearly defining the question or issue, not properly identifying the necessary variables, and not organizing the information in a logical manner. It's also important to check for any assumptions or biases that may affect the problem setup.

4. How does setting up a problem help with finding the solution?

Setting up a problem helps with finding the solution by providing a clear and organized approach to the problem. It allows for a systematic analysis of the information and variables involved, making it easier to identify patterns and potential solutions. It also helps to prevent errors or oversights that may occur when attempting to solve a problem without a structured approach.

5. Can setting up a problem be applied to all scientific disciplines?

Yes, setting up a problem can be applied to all scientific disciplines. The process of identifying and organizing information to solve a problem is a fundamental aspect of scientific inquiry. Whether conducting experiments, analyzing data, or developing theories, setting up a problem is an essential step in the scientific method.

Similar threads

Principle of work and energy to a collar and spring system, been stuck for hours
Replies
4
Views
6K
Normal force in a curvilnear motion
Replies
12
Views
3K
First post: work and energy problem
Replies
5
Views
1K
Conservation of Energy: Spring pushing a block up an incline
Replies
15
Views
3K
Elastic potential energy (spring) problem
Replies
3
Views
1K
Physics spring/crate hits another spring problem
Replies
3
Views
6K
Box and a Spring on on an inclined plane
Replies
11
Views
3K
Spring Potential Energy: Horizontal Spring Problem
Replies
6
Views
1K
Work Problem -- Wood Block Sliding into a Spring
Replies
7
Views
2K
Distance of box pushed up incline by spring
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top