# Catapult/Seesaw Calculations, part 2?

• Milchstrabe
In summary, the conversation is about a seesaw style catapult and its components. The speaker has a release point, a hacky sack that weighs 50 grams, and a beam that weighs 381 grams with a length of 50 cm. They have calculated the necessary velocity to launch the hacky sack and want to know how high they need to drop a 1 kg weight in order to achieve this velocity. They also mention issues such as torque, kinetic energy, and friction. However, there are too many unknown factors to come up with a simple solution and it may require a computer simulation or building a prototype to find a satisfactory solution.
Milchstrabe
I have a seesaw style catapult.

the arms are at a 4 to 1 ratio. I have all the masses and everything, the hacky is 50 grams, and The beam is 381 grams with a length of 50 cm (1 arm is 40 other is 10).

My velocity to launch the hacky 2.5 meters away from the release point and have it land .76 m high is 6.4 m/s at a 64 degree angle off the floor.

If i want to drop a 1 kg weight, how high would i need to drop it in order to achieve this velocity?

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any ideas? Anyone?

IS this purely a matter of torques? Torque of gravity on the board, torque of hacky sack on the board, torque required to get the hacky sack to a certain velocity? Then countering all those torques?

Would Torque for velocity be KE = 1/2 (m) v^2 so then W = torque (theta-sweep angle) ?

How are you going to ask, in less than 3 hours, if anyone has solved your problem?

I have been working on this for more than a week, and i still have no solution. Also no one seems to be able to help. I'm running out of time and I'm just trying to understand how the kinetic energy of the mass falling is converted into the kinetic energy of the hacky sack with a beam with the fulcrum at a 1 to 4 ratio on the beam.

Milchstrabe said:
I have been working on this for more than a week, and i still have no solution. Also no one seems to be able to help. I'm running out of time and I'm just trying to understand how the kinetic energy of the mass falling is converted into the kinetic energy of the hacky sack with a beam with the fulcrum at a 1 to 4 ratio on the beam.

There are too many unknowns in your problem. Is the kg mass going to bounce? Is the arm it lands on going to hit the floor? At what angle will the beam be postioned when the 1 kg hits it? Is friction in the fulcrum an issue? Will the beam bend like a springboard? Those come to mind real quick. I expect there are more issues, but those are enough to preclude a simple solution.

I can answer all those questions i just need someone who will know how to solve it.

Milchstrabe said:
I can answer all those questions i just need someone who will know how to solve it.

Qualitative answers will not do. You will have to quantify them. How much energy will be lost when the 1 kg hits the beam? How much more will be lost when the beam hits the floor? How high is the fulcrum? It sounds like you have determined only one possible path for you hacky. There may very well be no solution that will give that path. The physics may yield a result that cannot be solved analytically. It may require a computer simulation to get even an approximate solution

An oversimplified solution:

If the beam starts out horizontal, the system will have angular momentum due to the dropping kg. Say it hits with speed v and sticks to the board (no bounce) exactly at the end, L/5 from the fulcrum and assume the board is rigid. Angular momentum will be conserved, and the initial angular momentum will be mvr. After that, the angular mometum will be in three parts: as long as the hacky is in contact with the board, its speed will be a multiple of the speed of the 1kg. The speed of the center of mass of the board will be a multiple of the speed of the 1kg. Figure out those speeds from the geometry and calculate the angular momentum of each of the three objects based on their speeds, masses, and distances from the fulcrum. From that you will find the speed of the hacky going straight up.

Now you have to figure out the modifications to make this work the way you want. How far from the end of the board will the 1kg really hit? How can you make sure it sticks? What angle does the board have to be at to give the hacky the right launch angle? What is the angle of the board going to do to the angular momentum calculations? If you came within 30 to 40% of the intitial velocity needed, you have probably done well. Then you would have to build a prototype and tweak it. That's what engineers do.

## 1. How do you calculate the force of a catapult/seesaw?

To calculate the force of a catapult/seesaw, you will need to know the mass of the object being launched or balanced on the seesaw, as well as the distance the object is being launched or the length of the seesaw lever arm. Using the formula F = m x a, where F is force, m is mass, and a is acceleration, you can calculate the force needed to launch the object or balance the seesaw.

## 2. What is the difference between a catapult and a seesaw?

A catapult is a type of lever that uses stored energy to launch an object, while a seesaw is a type of lever that uses the weight distribution of two objects to balance. Additionally, a catapult typically has a shorter lever arm and is used for launching objects over a longer distance, while a seesaw has a longer lever arm and is used for balancing objects at a shorter distance.

## 3. How do you determine the angle of launch for a catapult?

The angle of launch for a catapult can be determined by finding the point where the horizontal distance traveled is equal to the vertical distance traveled. This is also known as the point of maximum range. The angle at this point will be the optimal angle for launch, as it will result in the longest distance traveled by the object.

## 4. What factors affect the accuracy of a catapult/seesaw?

The accuracy of a catapult/seesaw can be affected by several factors, including the accuracy of the measurements used in the calculations, the stability and strength of the materials used to construct the catapult/seesaw, and the consistency of the force used to launch or balance the object.

## 5. How can you increase the force of a catapult/seesaw?

The force of a catapult/seesaw can be increased by increasing the mass of the object being launched or balanced, increasing the length of the lever arm, or by using a more powerful force to launch or balance the object. Additionally, optimizing the design and construction of the catapult/seesaw can also increase its force and efficiency.

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