# Finding ideal energy transferred to a projectile.

Find the ideal energy transferred to a projectile in a spring launching device, the device is a catapult which involves a bungee cord being stretched and has the cord attached to a throwarm which is pivoting on a circular rod. i have calculated the elastic energy stored in the cord at the maximum stretch and in order to calculate ideal energy, i need to find the energy required to get the throwarm moving so i can subtract the two to find the ideal energy that should be transferred to the projectile. My teacher says that you need to use torque and lever energy knowledge to solve this problem. (Sorry for the bad english)

my catapult looks something like this
http://www.stormthecastle.com/catapult/backyard-ogre-catapult-index.htm
on the same page if you scroll down, it will show you how the catapult works i a video

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## Answers and Replies

LowlyPion
Homework Helper
Find the ideal energy transferred to a projectile in a spring launching device, the device is a catapult which involves a bungee cord being stretched and has the cord attached to a throwarm which is pivoting on a circular rod. i have calculated the elastic energy stored in the cord at the maximum stretch and in order to calculate ideal energy, i need to find the energy required to get the throwarm moving so i can subtract the two to find the ideal energy that should be transferred to the projectile. My teacher says that you need to use torque and lever energy knowledge to solve this problem. (Sorry for the bad english)

Welcome to PF.

Torque is the product of the moment arm from the pivot and the force applied. So you will need to take into account the distances from the pivot that the forces are acting.

Moreover, you need to determine the moment of inertia for the arm and the loaded weight to determine the acceleration that you will get as a result.

Welcome to PF.

Torque is the product of the moment arm from the pivot and the force applied. So you will need to take into account the distances from the pivot that the forces are acting.

Moreover, you need to determine the moment of inertia for the arm and the loaded weight to determine the acceleration that you will get as a result.

hey but that doesnt really tell me what to do i mean i know that torque is cross product of force and turn arm length but i need to know how to apply it in finding energy loss

LowlyPion
Homework Helper
hey but that doesnt really tell me what to do i mean i know that torque is cross product of force and turn arm length but i need to know how to apply it in finding energy loss

What is the moment of inertia of the arm? And the moment of inertia of the arm with the rock?

i believe its at the point when the rock enters projectile motion and the stopping point of the throw arm

still need an annswer please ppl

Moment of Inertia is the rotational equivalent of inertial mass. If you simplify the catapult into 2 parts: the moving arm (a rod) and the projectile (a point mass), and apply the moment of inertia formulas (let me know if you need them), you can calculate the total moment of inertia of the system.

Calculate the torque on the arm by noting that it's a spring launching device and so the force on the arm is $$k*x$$. So if you know the spring constant (k) for the spring loading mechanism and you know how far the spring is compressed or stretched you can find the force, and calculate the torque on the arm when the spring is released.
Torque = Moment of Inertia * angular acceleration, and angular acceleration is r x a where a is the linear acceleration.

That should be the general approach you need to take. Also, it's generally not considered polite to post multiple threads concerning a topic matter.

Good luck!
Arjun

Moment of Inertia is the rotational equivalent of inertial mass. If you simplify the catapult into 2 parts: the moving arm (a rod) and the projectile (a point mass), and apply the moment of inertia formulas (let me know if you need them), you can calculate the total moment of inertia of the system.

Calculate the torque on the arm by noting that it's a spring launching device and so the force on the arm is $$k*x$$. So if you know the spring constant (k) for the spring loading mechanism and you know how far the spring is compressed or stretched you can find the force, and calculate the torque on the arm when the spring is released.
Torque = Moment of Inertia * angular acceleration, and angular acceleration is r x a where a is the linear acceleration.

That should be the general approach you need to take. Also, it's generally not considered polite to post multiple threads concerning a topic matter.

Good luck!
Arjun

hey arjun i am sorry but i am still in grade 12 and we havent learnt the moment of inertia formulas, so i would appreciate it if you would tell me the formulas thanks and also i have no idea what angular acceleration and how to calculate linear acceleration in my device

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Moment of Inertia is the rotational equivalent of inertial mass. If you simplify the catapult into 2 parts: the moving arm (a rod) and the projectile (a point mass), and apply the moment of inertia formulas (let me know if you need them), you can calculate the total moment of inertia of the system.

Calculate the torque on the arm by noting that it's a spring launching device and so the force on the arm is $$k*x$$. So if you know the spring constant (k) for the spring loading mechanism and you know how far the spring is compressed or stretched you can find the force, and calculate the torque on the arm when the spring is released.
Torque = Moment of Inertia * angular acceleration, and angular acceleration is r x a where a is the linear acceleration.

That should be the general approach you need to take. Also, it's generally not considered polite to post multiple threads concerning a topic matter.

Good luck!
Arjun

hey arjun i am sorry but i am still in grade 12 and we havent learnt the moment of inertia formulas, so i would appreciate it if you would tell me the formulas thanks

Sure, no problem. Here's a list of moment of inertia formulas: http://en.wikipedia.org/wiki/List_of_moments_of_inertia

But more importantly, you really need to take a moment to learn rotational mechanics to really understand what's going on in this problem. From the description of the problem, you need to find the energy given to the projectile, which is the energy stored in the spring - the energy required to rotate the arm. energy stored in spring = 1/2*k*x^2, energy required to rotate arm = 1/2*I*w^2, where I is the moment of inertia of the rod (find the formula on the link earlier), and w is the angular velocity. Try and figure out the angular velocity on your own! It's good practice.

Good luck!
Arjun

HINT: Rotational mechanics is VERY similar to normal mechanics (i.e. linear). For example, Torques operate the same as forces, angles as displacements, etc.. As such, try to create equivalent expressions for energy from the definition of work in linear coordinates (i.e. W=F*delta x).

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Sure, no problem. Here's a list of moment of inertia formulas: http://en.wikipedia.org/wiki/List_of_moments_of_inertia

But more importantly, you really need to take a moment to learn rotational mechanics to really understand what's going on in this problem. From the description of the problem, you need to find the energy given to the projectile, which is the energy stored in the spring - the energy required to rotate the arm. energy stored in spring = 1/2*k*x^2, energy required to rotate arm = 1/2*I*w^2, where I is the moment of inertia of the rod (find the formula on the link earlier), and w is the angular velocity. Try and figure out the angular velocity on your own! It's good practice.

Good luck!
Arjun

HINT: Rotational mechanics is VERY similar to normal mechanics (i.e. linear). For example, Torques operate the same as forces, angles as displacements, etc.. As such, try to create equivalent expressions for energy from the definition of work in linear coordinates (i.e. W=F*delta x).
hey Arjun i figured it out and finally have calculated my ideal energy given to the projectile. Thanks a lot for your help i dont think that i could have figured it out without your advice.
Thanks again
Abhi

Glad to hear I helped! You are very welcome.

Arjun

hi i have to do this same lab and its been a while since i was introduced to practice problems involving this... i was just wondering how i can figure out the elastic energy?? my catapult is the exact same as the one mentioned by Abhi...http://www.stormthecastle.com/catapu...pult-index.htm
can someone help please...