Conservation of Energy: Spring PE: Toy gun on spring

• DracoMalfoy
In summary, the toy gun points a styrofoam ball upward with a spring that has a constant k. The ball moves upward until it reaches a max height, and then the air resistance causes it to slow down.f

Homework Statement

A toy gun is pointed toward the sky. A Styrofoam ball of mass 10g is at rest against a spring compressed 2cm. The spring is released causing the ball to move upward through the air to a max height of 1m. The air exerts a frictional force of 0.35N on the ball. What is the spring constant(k) of the spring? (Answer: 2240N/m)

Homework Equations

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.5m⋅Vi^2+.5Kxi^2+mg⋅yi+Ff⋅Δd=.5m⋅Vf^2+.5Kxf^2+mg⋅yf

The Attempt at a Solution

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I revised the equation as:

.5⋅Kx^2+Ff⋅Δd=mg⋅yf

I took out velocity since it isn't offered in the problem.

m=10g=.01kg
x=2cm=.02m
Δd=1m
Ff=0.35N
K=?

I converted g to kg and cm to m. Then I tried to solve for k.

.5⋅K(.02)^2-.35⋅1=.01⋅9.8⋅1

.0002K-.35=0.98

.0002K=.63

K=.63/.0002

K= 3150

So... I don't know exactly what I did wrong here. I thought that I was on the right path.

Instead of just writing the equation, you should first think of the physics of the problem. Ask yourself the following questions:
2. What are the surroundings exerting forces on the system?
3. What is the total initial energy of the system? What are the different contributions to it?
4. What is the final energy of the system?
5. Is the initial energy equal to the final energy? If so, why? If not, why?
6. Can any external forces change the energy of the system?
7. What is the Work-Energy theorem?
8 How do you calculate the work done by the external forces?

Instead of just writing the equation, you should first think of the physics of the problem. Ask yourself the following questions:
2. What are the surroundings exerting forces on the system?
3. What is the total initial energy of the system? What are the different contributions to it?
4. What is the final energy of the system?
5. Is the initial energy equal to the final energy? If so, why? If not, why?
6. Can any external forces change the energy of the system?
7. What is the Work-Energy theorem?
8 How do you calculate the work done by the external forces?

Ive been thinking about it and trying to figure it out all day.

So let us figure out the meaning of each term in your relevant equation. Start with the first term, and state what it is. Also state how you revised the relevant equation and got what you wrote.

k is spring constant. x is the compression of the spring. ff is friction force. and then there's displacement. which equals mass multiplied by force due to gravity then that times the displacement again.
.5⋅Kx^2+Ff⋅Δd=mg⋅yf

.5K(.02)^2-.35(1)=(.01)(9.8)(.1)

.0002K-.35=0.098

.0002K=.448

K=.448/.0002

K=2240N/m

I put .98 in the part that I got wrong. I figured it out now thanks.