Calculating Height of a Pebbled Launched by a Catapult

[Jtappan]

Homework Statement

You shoot a 57 g pebble straight up with a catapult whose spring constant is 310 N/m. The catapult is initially stretched by 0.30 m. How high above the starting point does the pebble fly? Ignore air resistance.
_____ m

Homework Equations

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The Attempt at a Solution

I am totally lost...this incorporates gravity and the spring...and ah...my head hurts...any one help?

 

[Anadyne]

There's more than one way to solve this problem. Do you want to use the force of the spring to figure out its acceleration?

Or to use conservation of energy?

Can you think of any equations that might help you?

 

[ogb p]

I can provide a response to this problem. First, we need to understand the basic principles of projectile motion and the concept of potential and kinetic energy.

The pebble launched by the catapult will experience a vertical motion due to the force of gravity acting on it. The initial potential energy stored in the stretched spring of the catapult is converted into kinetic energy as the pebble is launched. At the highest point of its trajectory, all of the initial potential energy will be converted into kinetic energy.

To calculate the height of the pebble, we can use the equation for potential energy: PE = mgh, where m is the mass of the pebble, g is the acceleration due to gravity (9.8 m/s^2), and h is the height above the starting point.

We also need to consider the work done by the spring in launching the pebble. The work done by the spring is equal to the change in potential energy, which can be calculated using the spring constant (k) and the displacement of the spring (x): W = 1/2 kx^2.

Setting these two equations equal to each other, we can solve for h:

PE = W
mgh = 1/2 kx^2
h = (1/2 kx^2) / mg

Substituting the given values, we get:

h = (1/2 * 310 N/m * 0.30 m^2) / (0.057 kg * 9.8 m/s^2)
h = 0.29 m

Therefore, the pebble will fly approximately 0.29 meters above the starting point. It is important to note that this calculation is an ideal scenario and does not account for air resistance, which would affect the actual height reached by the pebble.