What are the energy conservation principles at play in a catapult launch?

In summary: The potential energy of the lever arm is the difference in energy between the lever arm and the mass it is lifting. In this case, the mass is the rock. So, the potential energy of the lever arm is (0.045 kg)*(0.18 meters) - (0.205 kg)*(0.15 meters) = 0.14 kg.
  • #1
GopherTv
7
1
TL;DR Summary
Im trying to calculate the velocity of a projectile on a catapult at different levels of stretch in the spring.
1653014662125.png

This is the catapult.
At equalibrium the spring is 0.09 meters in length.

1653014707384.png

When its fully stretched out its 0.225 meters long and I place a rock (0.205 kg) close to where my finger is on the catapult.

The catapult starts with this much energy because 1/2 * k * x^2
1653014854257.png

90.54 is the spring constant which I got already, 0.225 is the length of the spring and i subtract 0.09 to get the stretch from equalibrium for x.
1653014931235.png

i then subtract this because the rock slides off the lever arm before it can fully extend, 0.165 is just a random number i picked for the length of the spring when the rock slides off
.
1653015009665.png


We have this:
1653015036746.png


This energy goes to 4 things, rotational energy of the lever arm, rotational energy of the rock (since its moving in a circular motion), the gravitational potential energy gained in the rock from it's center of mass now being heigher in the air, and the same for the lever arm, it also gains potential energy.

omega for both the arm and rock will be the same since the angular velocity is same.
subscript 1 is for the lever arm; 2 is for the rock
1653015406204.png

the rotational inertia for the lever arm will be 1/3*m*r^2
and for the rock it will be mr^2
1653015336867.png
 
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  • #2
1653015576698.png

I plugged in some numbers, the mass of the lever arm was 0.045 kg and its length was 0.18 meters

The mass of the rock I am launching was 0.205 kg and its distance from the pivot was 0.15 meters
 
  • #3
I didn't exactly ask a question when posting, but i wanted to know if my math makes sence. i hope it does
 
  • #4
Your equation makes sense but it needs a modification and a clarification.
In the last equation of post #1 you use three symbols for two masses, ##m##, ##m_1## and ##m_2##. Fix that.
In that same equation you have ##h_1## and ##h_2##. One of these is the potential energy of the lever arm. How do you figure what ##h## you use for that?
 

Related to What are the energy conservation principles at play in a catapult launch?

1. How does a catapult conserve energy?

A catapult conserves energy by using the stored potential energy from the tension in its elastic materials, such as ropes or springs, to launch a projectile. This allows for the conversion of potential energy into kinetic energy, resulting in a more efficient use of energy compared to other methods of launching.

2. What are some ways to increase the energy conservation of a catapult?

There are a few ways to increase the energy conservation of a catapult. One way is to use more elastic materials with higher potential energy, such as stronger ropes or thicker springs. Another way is to optimize the design of the catapult, such as adjusting the angle or length of the throwing arm, to maximize the transfer of energy from potential to kinetic.

3. Can a catapult be used for renewable energy?

Yes, a catapult can be used for renewable energy by utilizing the stored potential energy in the elastic materials to power machinery or generate electricity. This can be achieved by attaching a generator to the catapult and using the kinetic energy of the launching motion to produce electricity.

4. How does friction affect the energy conservation of a catapult?

Friction can have a negative impact on the energy conservation of a catapult by reducing the efficiency of the transfer of energy from potential to kinetic. This can be minimized by using smoother and more slippery materials for the launching mechanism, as well as reducing the weight of the projectile to decrease the amount of friction during launch.

5. Are there any safety concerns when using a catapult for energy conservation?

Yes, there are safety concerns when using a catapult for energy conservation. The high tension and force involved in launching a projectile can be dangerous, so proper precautions should be taken to ensure the safety of those operating the catapult. This includes proper training, wearing protective gear, and following safety guidelines for handling and launching projectiles.

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