Elastisity: Hooke's Law Finding Spring Compression

Prophet029

1) A 28.86 kg child bounces on a pogo stick. The pogo stick has a spring constant 18016 N/m. When the child makes a nice big bounce, she finds that at the bottom of the bounce she is accelerating upwards at 4.802 m/s2. How much is the spring compressed?

Given:
Mass of Child: 28.86kg
Spring constant 18016N/m
Acceleration after spring was compressed: 4.802 m/s^2

Find:
x=?

2) Relevant Equations

Hooke's Law: F=-kx
Newton's second Law: F=ma

3) Attempt at solution:

All I set up was that F=(Mass of Child + Mass of Pogo stick)a.
Then set that equal to -kx. But as you can see there are two unknowns.

If I'm neglecting any other principle that would help solve this problem. I'd be most gracious if you could tell me. Thanks
1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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cepheid

Staff Emeritus
Gold Member
What two unknowns?

You know how much acceleration is produced by the upward restoring force, and what mass is being accelerated. Therefore, you know the upward restoring force. You also know the spring constant. Therefore, know the displacement from the equilibrium spring length.

Prophet029

What two unknowns?

You know how much acceleration is produced by the upward restoring force, and what mass is being accelerated. Therefore, you know the upward restoring force. You also know the spring constant. Therefore, know the displacement from the equilibrium spring length.
If I follow what you are saying. You want me to find the upward resulting force from the spring compression using the given mass of 28.86kg and multiply that my the acceleration given 4.802 m/s^2 and set that equal to the spring constant times the distance x.

F=(mass given)(acceleration given)
F=28.86kg*4.802m/s^2
F=138.58572N

138.58572N=-18016N/m*-deltax
deltax=0.007692369m

I did this, but the answer to my solution was wrong. Did I miss understand you? Am I missing something?

Ok I solved it

Prophet029

F=(mass given)(acceleration given)
F=28.86kg*4.802m/s^2
F=138.58572N

138.58572N=-18016N/m*-deltax
deltax=0.007692369m
For those who are solving any problem like such in the future.

The original equation I used was correct but you have to factor in that you also have the force of gravity that acted on the spring as well. So the Total net force is:

Fnet=((mass given)*(acceleration given)) + ((mass given)*(gravity acceleration) which equals
kx form hooke's law F=-kx

equation form:
Fnet=([(mass given)*(acceleration given)] + [(mass given)*(gravity acceleration)])

Fnet=-kx (since compression in this case find positive values so neglect the negative)

([(mass given)*(acceleration given)] + [(mass given)*(gravity acceleration)])=kx

and solve for x

Last edited:

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