Spring-Loaded Gun-spring constant

[gaimon]

Okay, so having a bit of trouble with this problem. There is a spring loaded gun pointing vertically in the air. If the spring in the gun is compressed a distance of 0.147 m, the gun can launch a 25.4g projectile from rest to a maximum height of 24.0 m above the starting point of the projectile. Neglecting all resistive forces, determine the spring constant.

What I've done so far is first assume the distance the projectile travels is irrelevant.
Then using Hooke's law: k=mg/x so k=25.4(9.8)/0.147.
I keep coming up with the answer 1693.3 N/m but am told that that is not correct.

What am I doing wrong?

 

[drpizza]

Newton's are kilograms*m/s^2; you're using a mass measured in grams.

However, you're assuming that the weight of the mass is compressing the spring that distance. There's a mysterious hand that pushed the mass down until some mechanism clicked and held it into place. Otherwise, when you pull the trigger, it's not going to go anywhere.

Do you have a formula for the elastic energy of the spring? The maximum height of the projectile is very important in this problem.

 

[kyle8921]

Your approach is correct, but the answer you are getting is incorrect. The spring constant should be in units of N/m, not just N. To convert your answer, you need to divide by the unit of distance (m) to get the correct units. So the correct spring constant would be 1693.3 N/m/0.147 m = 11522.4 N/m.

Another possible error could be in the use of Hooke's law. Are you sure that the mass of the projectile is 25.4 g and not 25.4 kg? If it is in kg, then the correct spring constant would be 169.33 N/m.

It is also important to check your calculations and make sure you are using the correct units throughout. Double check the values you are using for mass, distance, and acceleration due to gravity to ensure accuracy.