# How to find the k constant of a spring?

1. Apr 7, 2009

1. The problem statement, all variables and given/known data
We had a lab where we launch springs with an unknown k constant to a target 2.01m away and 0.22m high. We also know the angle at which we shot the spring.

We need to find the k constant of the spring, so my question is, does the kinetic energy matter?

2. Relevant equations

Will the equation be:

Eg + Ee = Eg + Ek (The spring had gravitational potential as it was launched a bit higher than the reference position (the table)

or

Eg + Ee = Eg

3. The attempt at a solution

If I did the Eg + Ee = Eg method, then my k constant turned out to be 2.752 N/m.

The spring's length at equilibrium is 0.04m; the spring is quite tiny.

Does this k constant seem to small? Also, using F= kx, the force contained in the spring when x = 0.035m, is 0.09632N

Are these values too small, which could possibly hint the method I tried is wrong?

2. Apr 7, 2009

### Astronuc

Staff Emeritus
One is launching the spring, as opposed to a projectile?

Neglecting friction and air resistance, the spring energy will go into the kinetic energy of the mass (spring?) being launched. Some of that kinetic energy changes the gravitational potential energy which is then recovered on the way down, and some kinetic energy stays constant, assuming the mass travels at constant horizontal velocity to the target.

See these - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html#tra8

Use the parameters of the trajectory to determine the initial velocity. The use the initial velocity to determine the kinetic energy, which must come from the stored energy in the spring.

3. Apr 7, 2009

How do I obtain the parameters required to determine the initial velocity?

The only values I have are:
- the angle
- the distance to the target, and the distance the target is above the ground
- the stretch (x) of the spring

The very first thing I need to do is get the K constant of the spring, so I can know how much force the spring launches with. However, to do this, I need the initial velocity of the spring, so I can use the formula: Eg + Ee = Eg + Ek

Am I supposed to cancel out the Ek somehow? Do i assume that the final velocity is 0, and use kinematics from there?

EDIT: The spring is indeed the projectile, and the mass of the spring is known.

Last edited: Apr 7, 2009
4. Apr 7, 2009

### LowlyPion

Consider the link that Astronuc provided as a handy calculator to determine the Vo from the measured parameters.

But I have to think this is not a great way to determine k.

But if you must, once you figure Vo, you might want to use the relationship that 1/2m*v2 = 1/2*k*x2 that relates the Kinetic energy of the launched spring to the potential energy of the compressed spring.

5. Apr 7, 2009

Yeah, that link is handy, but the thing is, I don't have the horizontal range, we only know the distance to the target (distance to the fence in link)

Also, we don't know the time.

6. Apr 7, 2009

Here is a diagram of the situation. The arrows show the known distances.

#### Attached Files:

• ###### diagramspring.jpg
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7. Apr 7, 2009

C'mon guys, there has to be a way. . .

8. Apr 7, 2009

Okay, so I made a scale diagram to find the range. I used the formula to get the velocity using this range.

To check if this range was accurate, I entered the velocity and angle and range, to see the value for y, which turned out to be 0, which was expected.

Then i entered the value for x as 2.01m (the distance to the target), and y turned out to be 0.09m (which is the distance above the target!)

Therefore, the velocity i obtained is correct.

Now I just have to do kinematics to find the highest height possible for y.

9. Apr 7, 2009