Spring-based Slingshot energy transfer

[MendicantBias]

Homework Statement

I am working on an AP physics project, and the assignment is to launch a golf ball accurately at close (10 - 15m) and long (50-60m) range. My group and I have decided on a spring based slingshot that will consist of a T shaped launcher with two springs (one on each side of the T) connected to a pouch. My question is about how to experimentally obtain a value e (efficiency).

Homework Equations

I know that Fs = -kx, so for two springs: Fs = -2kx

Integrate this to get the stored energy: Us = kx^2

I have researched some and found that an e is added to account for the efficiency at transferring this stored energy into kinetic energy, so: Us = ekx^2

And Kinetic energy: K = (1/2)mv^2

The Attempt at a Solution

Set k = Us
(1/2)mv^2 = ekx^2
mv^2 = 2ekx^2
v^2 = (2ekx^2)/m

v = ((2ekx^2)/m)^(1/2) meters per second

rearrange this to solve for e:

ekx^2 = (1/2)mv^2

e = (mv^2)/(2kx^2)

e is then the ratio of the actual kinetic energy of the golf ball to the stored energy in the spring for a given draw-length x.

My question is not so much about the math as it is how to find e accurately. I'm not sure what sensors can measure velocities upwards of 20m/s. Can e be accurately determined from one or two measurements at a low velocity?

Your input is greatly appreciated.

 

[anathema]

Dear student,

Thank you for your detailed explanation and question. It sounds like you have a solid understanding of the physics principles involved in your project. To accurately determine the efficiency value (e), you will need to conduct several experiments and measurements. Here are a few suggestions:

1. Use a high-speed camera: To accurately measure the velocity of the golf ball, you will need to use a high-speed camera that can capture footage at a high frame rate. This will allow you to track the motion of the golf ball and calculate its velocity. You can then use this velocity value in your equation to determine e.

2. Measure the distance traveled: Instead of directly measuring the velocity, you can also measure the distance traveled by the golf ball. This can be done using a measuring tape or a laser distance measuring device. By knowing the distance traveled and the time it took for the ball to reach that distance, you can calculate the velocity and then determine e.

3. Use multiple measurements: To increase the accuracy of your results, it is always best to conduct multiple experiments and take multiple measurements. This will help you to identify any outliers or errors in your data and improve the overall accuracy of your results.

4. Consider other factors: Keep in mind that there are other factors that can affect the efficiency of your slingshot, such as air resistance and the weight of the golf ball. You may need to account for these factors in your experiments and calculations to get a more accurate value for e.

I hope this helps and good luck with your project! Don't hesitate to reach out if you have any further questions.

 

[Moetasim]

The concept of using a spring-based slingshot to transfer energy to a golf ball is a great idea for your project. In terms of finding the efficiency (e) of this system, there are a few things to consider.

First, it is important to make sure that your measurements for velocity and draw-length are as accurate as possible. This means using high-quality sensors and making multiple measurements to reduce errors.

Secondly, it may be helpful to have a control group where you measure the velocity of the golf ball without the slingshot and compare it to the velocity with the slingshot. This will give you a baseline to compare your results to and help determine the efficiency of the slingshot.

Additionally, you may want to consider using video analysis software to track the motion of the golf ball and calculate its velocity. This can be more accurate than using sensors and can also allow you to track the motion at different points along the trajectory, giving you a more complete picture of the energy transfer.

It is also important to keep in mind that there will always be some energy lost due to friction and other factors, so your efficiency value may not be 100%. However, by making accurate measurements and using multiple methods to calculate velocity, you can get a good estimate of the efficiency of your spring-based slingshot system.

Good luck with your project!