# Homework Help: Determining Spring Constant

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1. Dec 12, 2015

### arche1

1. The problem statement, all variables and given/known data
A pendulum, initially at equilibrium, is set into motion by a spring-loaded launcher (compressed a distance of 0.0150 m) which fires horizontally. If the mass of the pendulum bob is 0.340 kg and it rises to a maximum height 0.120 m (relative to equilibrium), what is the spring constant of the spring?

2. Relevant equations
Gravitational energy: E = mgh
Elastic energy: E = (0.5) (k) (x^2), where k is the spring constant and x is the displacement from equilibrium

3. The attempt at a solution
My initial examination of this problem was to state that the gravitational energy at the point where the pendulum is at it's maximum height (and it is instantaneously at rest) was equal to the elastic energy input into the system. Therefore, mgh = (0.5) (k) (x^2). This resulted in a value of k that is not equal to 3550 N / m (the accepted answer in the textbook). As well, as change in energy is work, and the work done by the spring onto the pendulum wasn't equal to it's elastic potential energy (as we don't know how long the spring was in contact with the pendulum), this answer makes even less sense. I am at a loss as to how to further analyze the question.

2. Dec 12, 2015

### Staff: Mentor

Hi arche1, Welcome to Physics Forums.

Can you provide some computational details for your attempt? You've assumed conservation of energy for the spring-bob interaction, which seems quite plausible given the limited number of parameters supplied by the problem statement. So what value did you find for the spring constant (show your work)?

3. Dec 12, 2015

### arche1

I'm sorry, but having put my data into a new calculator gives me the right answer, and as a result I have solved the question. Thank you very much for your time in helping me!

4. Dec 12, 2015

### Staff: Mentor

No problem. As long as you've solved your problem everything's good