Finding ideal energy transferred to a projectile.

In summary, the conversation discusses finding the ideal energy transferred to a projectile in a spring launching device, specifically in a catapult with a bungee cord and throwarm pivoting on a circular rod. The approach involves calculating the elastic energy stored in the cord at maximum stretch and then finding the energy required to get the throwarm moving. To do this, one must use knowledge of torque and lever energy and determine the moment of inertia and torque on the arm. The formulas for moment of inertia and torque are needed for this calculation.
  • #1
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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  • #2
helloabhihere said:
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.
 
  • #3
LowlyPion said:
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 doesn't 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
 
  • #4
helloabhihere said:
hey but that doesn't 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?
 
  • #5
i believe its at the point when the rock enters projectile motion and the stopping point of the throw arm
 
  • #6
still need an annswer please ppl
 
  • #7
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 [tex]k*x[/tex]. 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
 
  • #8
NruJaC said:
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 [tex]k*x[/tex]. 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 haven't learned 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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  • #9
NruJaC said:
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 [tex]k*x[/tex]. 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 haven't learned the moment of inertia formulas, so i would appreciate it if you would tell me the formulas thanks
 
  • #10
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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  • #12
NruJaC said:
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 don't think that i could have figured it out without your advice.
Thanks again
Abhi
 
  • #13
Glad to hear I helped! You are very welcome.

Arjun
 
  • #14
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...
 

1. What is the definition of ideal energy transferred to a projectile?

Ideal energy transferred to a projectile refers to the amount of energy that is transferred from a source to a projectile, such as a bullet or a projectile fired from a slingshot, without any loss or dissipation of energy due to factors like air resistance or friction.

2. How is the ideal energy transferred to a projectile calculated?

The ideal energy transferred to a projectile is calculated using the equation E = 1/2 * m * v^2, where E is the energy, m is the mass of the projectile, and v is the velocity of the projectile.

3. What factors affect the ideal energy transferred to a projectile?

The ideal energy transferred to a projectile is affected by the mass and velocity of the projectile, as well as external factors such as air resistance and gravity. The type of material used for the projectile and the angle at which it is launched can also impact the ideal energy transferred.

4. Why is it important to consider the ideal energy transferred to a projectile?

The ideal energy transferred to a projectile is important because it determines the effectiveness and accuracy of the projectile. A higher energy transfer means the projectile will travel faster and with greater force, making it more likely to reach its target. It also helps in determining the range and trajectory of the projectile.

5. How can the ideal energy transferred to a projectile be optimized?

The ideal energy transferred to a projectile can be optimized by using a lighter and more aerodynamic projectile, increasing the velocity of the launch, and minimizing external factors that can affect the energy transfer, such as air resistance and friction. Additionally, using the appropriate materials and launch angle can also help optimize the ideal energy transferred to a projectile.

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