Design Project Help: Building a Pumpkin Throwing Machine with a 300ft Range

In summary, the conversation is about designing and building a scale model that can throw a 10 lbf pumpkin 300 feet. The design chosen is an Onager-style machine, which uses ropes to act as a spring. The main challenge is how to calculate the work done by the ropes, as they are being rotated instead of stretched. The student suggests measuring the force required to rotate the arm 360 degrees and adjusting the formula for work accordingly. However, they are unsure if this is the correct approach. They also mention the need to calculate the total work required for the machine to function. Possible solutions include testing different rope materials or gauges to find the best option.
  • #1
BishopUser
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Homework Statement


I need to design, and build a scale model of something that can throw a 10 lbf pumpkin 300 feet.

No variables right now are for certain other than that I know I need a 98.3 ft/s launch velocity at 45 degrees. Right now I've pretty much just been playing with symbols trying to get an equation that gives values that seem right

For the design my group has chosen http://members.lycos.nl/onager/OnagerPic.jpg

Homework Equations


[tex]W_{sp} = \frac{1}{2}k(x_i^2-x_f^2)[/tex]
[tex]W_{net}=\Delta KE[/tex]

The Attempt at a Solution



The kinematic analysis isn't hard; I won't list the steps, but I know that for a distance of 300ft and 45 degree launch angle that it will require an initial velocity of 98.3 ft/s. Different parts of the arm will be moving at different speeds, but in the end the entire arm/projectile should be moving at the same angular velocity W = (98.3 ft/s)/(6 ft/rad) W = 16.4 rad/s (for an arm length of 5 ft and end part of 1 ft).

A kinetic analysis is what has got me stuck. The machine gets its energy from the ropes that the arm run through. The ropes act like a spring but I can't think of how to measure an experimental K value. In a normal spring you can just stretch it out, measure how much force, the distance from its neutral position and do K = F/x. In this design the spring isn't pulled it is rotated. I have never dealt with anything like this before.

What I was thinking was measure how much force it takes to rotate the arm 360 degrees; However that force is dependent on how far away from the center you hold the arm, but the amount of torque would be constant. So if you spun the arm around 360 degrees and measured that it took 300 lbf to hold the arm at the very end (say the arm is 5 feet) then the K value may be considered as

K = (5ft)*(300lbf)/(360 degrees) or
K = 4.16 ft*lbf/degree

Then I thought adjusting the formula from
Wsp = .5*k*x^2 to
Wsp = .5*k*(theta)^2

I know right away that this assumption is wrong because of how the units work out (also such a large number).
Wsp = .5*(4.16ft*lbf/degree)*(360degrees)^2.
Wsp = 269,568 ft*lbf*degreeI know that this type of rope setup was common in ancient balista/catapult design. I've found many sources on how to build them, but nothing on how to theoretically calculate the work that they output. Any advice/sources on how to calculate this would be helpful.Aside from needing to know how to calculate the work that the spring/rope does, I need to calculate the total amount of work that is required. I think I have this right. I know that Wnet = change in kinetic energy. I know the change in kinetic energy of the projectile, but I'm skeptical on whether I know how to calculate the change in kinetic energy of the arm. This is what I have done

Total change in kinetic energy = .5*m*v^2 + .5*M*V^2 where m/v is in regards to the arm and M/V is in regards to the projectile.

Ke = .5*(w/g)*[(angular velocity)*(.5*length of arm)]^2 + .5*(W/g)*[(angular velocity)*(total length)]^2

I know this is probably confusing to read but basically it is just Ke = 1/2 mv^2 + 1/2 mv^2. Where the first term is mass of the arm * velocity at the centroid, and the second term is mass of projectile * velocity at the end. That equation should give me the total work that needs to be done by the spring (excluding work done by gravity/friction for now). Is calculating the total change in kinetic energy this way correct?
 
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  • #2
I think you might be making the spring constant too hard. While rotating it is not exactly the same as simple linear stretch, for your purposes, it is entirely possible that F=-kN where n is the number of loops. But that will take building it and testing. Can you just buy a short length of rope and measure vert. stretch with people of various wts hanging from it? If the rope is too stout, maybe you could find one of the same material and use a smaller gauge. Just blue sky ideas here.
 
  • #3


As a scientist, my first advice would be to make sure you have a clear understanding of the physics principles involved in your design project. It appears that your group has chosen a trebuchet design, which uses the potential energy stored in a counterweight to launch a projectile. In this case, the ropes and arm are acting as a lever to transfer the energy from the counterweight to the projectile.

To calculate the work done by the ropes, you can use the equation W = F*d, where F is the force applied by the ropes and d is the distance over which the force is applied. In this case, the force applied by the ropes is equal to the tension in the ropes, which can be calculated using the principle of torque. Since the arm is rotating at a constant angular velocity, the torque applied by the ropes must be equal to the torque applied by the counterweight. You can use this information, along with the length of the arm and the angle of rotation, to calculate the tension in the ropes.

In terms of calculating the total work required, you are correct in using the equation Wnet = ΔKE. However, you need to take into account the rotational kinetic energy of the arm in addition to the linear kinetic energy of the projectile. This can be calculated using the equation KE = ½*I*ω^2, where I is the moment of inertia of the arm and ω is the angular velocity. You can find the moment of inertia of a uniform rod using the equation I = ½*m*L^2, where m is the mass of the arm and L is the length. Adding the rotational kinetic energy to the linear kinetic energy of the projectile will give you the total change in kinetic energy and thus the total work required.

I would also recommend consulting with your physics teacher or a professional engineer for further guidance on your design project. They can provide valuable insight and assistance in calculating the necessary variables and ensuring the accuracy of your calculations. Good luck with your project!
 

What is the first step in a design project?

The first step in a design project is to clearly define the goals and objectives of the project. This involves understanding the problem or need that the design project aims to address, as well as establishing a timeline and budget for the project.

How do you come up with design ideas?

Design ideas can come from a variety of sources, such as brainstorming sessions, research, or inspiration from other designs. It is important to consider the target audience and the goals of the project when coming up with design ideas.

What is the role of research in a design project?

Research is a crucial aspect of a design project as it helps to inform and guide the design process. This can include researching the target audience, competitors, current design trends, and potential solutions to the problem at hand.

What is the importance of prototyping in a design project?

Prototyping allows designers to test and refine their ideas before finalizing the design. It can help identify any potential issues or areas for improvement, and allows for feedback from stakeholders and users before moving on to the final design.

How do you ensure the success of a design project?

To ensure the success of a design project, it is important to have clear communication and collaboration among all team members involved. Regular check-ins and feedback sessions can help address any issues or concerns and keep the project on track. It is also important to regularly review and evaluate the project's progress against the established goals and objectives.

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