• Support PF! Buy your school textbooks, materials and every day products Here!

Hooke's Law/Oscillation

  • #1

Homework Statement


Find the stiffness of the spring in a child's pogo stick if the child has a mass of 35kg and bounces once every 2.0 seconds.

T = 2.0 seconds m = 35kg

Homework Equations


T = 2π√(m/k)

The Attempt at a Solution


Using the above, I figured k = mπ2 which worked out to be 345.44

This problem didn't have an answer in the back of the book. I saw a similar equation for frequency so I used the frequency/period relationship to formulate the above equation. I figured I should ask for a check in case I assumed wrong.
 

Answers and Replies

  • #2
DEvens
Education Advisor
Gold Member
1,203
451
You have some minor issues with your k=m pi squared form. The units don't work because you did some cancellation and you were somewhat sloppy. What are the units for k? What are the units for m?

When you do problems like this be sure to keep your steps and show them. And in particular, be sure that you check that the units work.
 
  • #3
You have some minor issues with your k=m pi squared form. The units don't work because you did some cancellation and you were somewhat sloppy. What are the units for k? What are the units for m?

When you do problems like this be sure to keep your steps and show them. And in particular, be sure that you check that the units work.
The units do work.
T = 2π√(m/k)
substituting value of T as 2s,
2 = 2π√(m/k)
1 = π√(m/k)
√(k/m) = π
now, squaring on both the sides,
k/m = π^2
k =mπ^2
 
  • #4
DEvens
Education Advisor
Gold Member
1,203
451
Read my post again please. What are the units of k? What are the units of m? Just because 2 seconds divided by 2 gives you 1 *something* does not mean the units work when you discard that *something*.
 
  • #5
You have some minor issues with your k=m pi squared form. The units don't work because you did some cancellation and you were somewhat sloppy. What are the units for k? What are the units for m?

When you do problems like this be sure to keep your steps and show them. And in particular, be sure that you check that the units work.
I'll re-work it again and see if I can find a different way
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,723
5,031
I'll re-work it again and see if I can find a different way
Your method is ok. I think all DEvens is complaining about is that you did not keep track of units, so didn't state the units in the answer. But with the most obvious filling in of those omissions, I believe your answer is numerically correct.
 
  • #7
I actually found the answer to it. It states 350 N/m which I can see from rounding but it didn't say anything about estimating in the problem. Maybe an unfortunate mistake
 
Last edited:
  • #8
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
32,723
5,031
I actually found the answer to it. It states 350 N which I can see from rounding but it didn't say anything about estimating in the problem. Maybe an unfortunate mistake
In principle, you should infer the number of significant figures to quote in the answer from (the fewest of) those provided. The clue here is 2.0 seconds, not 2.00 or 2.
 
  • #9
In principle, you should infer the number of significant figures to quote in the answer from (the fewest of) those provided. The clue here is 2.0 seconds, not 2.00 or 2.
This would make sense since I always forget about significant figures.
 
  • #10
lightgrav
Homework Helper
1,248
30
the units of k is NOT Newtons! How IS Force related to the spring stiffness?
 
  • #11
the units of k is NOT Newtons! How IS Force related to the spring stiffness?
Oops that was supposed to be 350 N/m not N.
 
  • #12
lightgrav
Homework Helper
1,248
30
Every spring's stiffness is described by k N/m ... that's how we know it is a stiffness - way more important than the number!
 

Related Threads on Hooke's Law/Oscillation

  • Last Post
Replies
11
Views
8K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
963
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
Top