Springlauncher And Projectile Motion

In summary: KE=PE1/2mv^2=1/2kx^2Find v^2 and set it equal to the x and y components of the range formulaIn summary, the purpose of this conversation was to discuss the construction of a spring launcher for a grade 12 physics course. The launcher is used to shoot a spring into a bucket, and the k value of the spring is 28.57. The height of the bucket is 40 cm and the angle of the launcher can be adjusted. The distance between the launcher and the bucket will be determined on the day of the experiment. The relevant equations for this problem are Fa=kx, PE=1/2kx^2, and KE=
  • #1
springlauncher
6
0
For my grade 12 physics course I have to make a spring launcher. The purpose is to aim and shoot a spring with the use of a spring launcher into a bucket. I have a spring with the k value of 28.57. I found out the k value using k=f/x. The height of the bucket is 40 cm. We can set the angle on the spring launcher. The distance of the spring launcher to the bucket will be decided on the day of the experiment. Using an equation (that I have no idea wat it is:confused: ) We have to figure out x (how far back we have to pull the spring).

So basically the distance of the springlauncher to the bucket, the angle, and x are unknown. However, on the day of the experiment, we will be given the distance to the bucket from the springlauncher.

Any help will be greatly appreciated.:smile:

basically the only equation i know of now is Fa=kx

THANK Uo:)
 
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  • #2
^ I think you mean F=kx

unless a is some subscript your class uses.

think about the potential energy stored in the springs ;)

out of curiosity is your class calculus based?
 
  • #3
Hey CPL.Luke,
yes a is a subscript our class uses. I think it stands for applied force. And no it isn't calculus based. I am so confuseeed. what about the potential energy stored in the springs. I am not sure what equation to used.
 
  • #4
hmm, you learned about energy correct? and more specifically conseration of energy.

the relevant formulas are

PE=1/2kx^2

KE= 1/2mv^2

v=at
x=vt
x=1/2at^2

you need to think abuot how the energy gets transferred around in the problem, if the spring launcher is compressed than, then it stores energy, and when the spring is released it will release its energy into the ball that its launching in the form of kinetic energy.

now think about what formulas to use.
 
  • #5
Shouldn't you consider also gravitational potential energy?
 
  • #6
Haywire said:
Shouldn't you consider also gravitational potential energy?
Certainly if the spring is oriented at other than horizontal. However the change in GPE over the displacement of the spring maybe negligible at small angles above horizontal, but then one would need to consider friction.
 
  • #7
Astronuc said:
Certainly if the spring is oriented at other than horizontal. However the change in GPE over the displacement of the spring maybe negligible at small angles above horizontal, but then one would need to consider friction.

Internal friction in the spring? Isn't it really neglegible?
 
  • #8
Haywire said:
Internal friction in the spring? Isn't it really neglegible?
Internal friction in the spring is likely negligible. I was thing of whatever guide channel or tube might be used to direct the mass at the end of the spring, although one may not need one.
 
  • #9
The only other equation we learned in the course that can be applied to this is the one for elastic potential energy. The equation is E=1/2kx^2. By the way there is no mass at the end of the spring. The entire spring must be launched into the bucket.
 
  • #10
By the way there is no mass at the end of the spring. The entire spring must be launched into the bucket.

So basically there's some device that you put your spring in, compress your spring by a certain distance, release, and watch the spring go?

springlauncher said:
The only other equation we learned in the course that can be applied to this is the one for elastic potential energy. The equation is E=1/2kx^2.

Well, yes, the only other equation that can be applied to the compression of the spring. But when you stop squishing it, it is supposed to fly away, no? And become a projectile... which has a velocity and all sorts of fun...
 
  • #11
mbrmbrg said:
So basically there's some device that you put your spring in, compress your spring by a certain distance, release, and watch the spring go?



Well, yes, the only other equation that can be applied to the compression of the spring. But when you stop squishing it, it is supposed to fly away, no? And become a projectile... which has a velocity and all sorts of fun...

Yes you hook the spring onto a device and then you pull it back a certain distance (x) and then let it go in order to launch it into the bucket. The purpose of the experiment is to find out how far back we have to pull the spriing (which is the unknown x) in order for it to travel the distance that we are given. Also, we must determine what angle we have to have it so the spring goes into the bucket.
 
  • #12
Physics isn't exactly my strongest subject so this may take me a while :S
So basically I need to come up with a formula to figure out x (the distance I have to pull the spring back) and the angle at which I have to position the spring launcher in order for it to land in the bucket.

I know that the total energy in the spring is equal to the kinetic energy and the potential energy in the spring : Etotal= Ek + Ep

As CPL.Luke has already mentioned:

PE=1/2kx^2

KE= 1/2mv^2



I DONT KNOW WHERE TO GO FROM THERE :S
 
  • #13
If there is no difference in height between the launcher and the bucket, I would start by looking at the range formula. You'll be given the required range the day of, so you'll need to manipulate initial velocity (which will be derived from the energy equations) and angle.
 
  • #14
R=vi^2sin2theta/g

I now have this equation as well.
 
  • #15
springlauncher said:
Physics isn't exactly my strongest subject so this may take me a while :S
So basically I need to come up with a formula to figure out x (the distance I have to pull the spring back) and the angle at which I have to position the spring launcher in order for it to land in the bucket.

I know that the total energy in the spring is equal to the kinetic energy and the potential energy in the spring : Etotal= Ek + Ep

As CPL.Luke has already mentioned:

PE=1/2kx^2

KE= 1/2mv^2



I DONT KNOW WHERE TO GO FROM THERE :S

I would use the kinematic equations to obtain the velocity with which the spring must be lanuched in order for it to hit the bucket. (i.e. consider the projectile motion of the spring). Then you can use the conservation of energy equation, namely that the energy of the spring whilst compressed must equal the kinetic energy of the spring just after it is released, in order to calculate the distance the spring needs to be pulled back, by substituting the velocity obtained into this equation.

I would suggest you start by modelling the spring as a projectile and obtain the intial velocity.

Edit: If this equation is correct
R=vi^2sin2theta/g
(I've not checked it) then use this to calculate vi and then substitute into the energy equation.
 
Last edited:
  • #16
springlauncher said:
R=vi^2sin2theta/g

I now have this equation as well.

Note that this equation is maximized when the firing angle is ...? (assuming, of course, no air resistance. I believe the maximizing angle is about five degrees larger when air resistance is not negligable.)

Now all you need is to solve for initial velocity (which would depend, of course, on how far back you pull your spring).
 

1. What is Springlauncher and Projectile Motion?

Springlauncher and Projectile Motion is a scientific concept that involves the study of the motion of objects that are launched into the air, typically using a spring mechanism. It is a combination of two principles: the force of a spring and the laws of projectile motion.

2. How does a Springlauncher work?

A Springlauncher works by utilizing the elastic potential energy stored in a spring to propel an object into the air. When the spring is compressed and then released, the potential energy is converted into kinetic energy, causing the object to launch into the air.

3. What factors affect the trajectory of a projectile launched by a Springlauncher?

The trajectory of a projectile launched by a Springlauncher is affected by several factors, including the initial velocity, angle of launch, air resistance, and gravity. These factors all play a role in determining the path and distance of the projectile.

4. How do you calculate the range of a projectile launched by a Springlauncher?

The range of a projectile launched by a Springlauncher can be calculated using the equation R = v2sin(2θ)/g, where R is the range, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity. This formula assumes no air resistance and a flat surface.

5. What real-world applications does Springlauncher and Projectile Motion have?

Springlauncher and Projectile Motion have numerous real-world applications, including in sports such as baseball and golf, where the motion of the ball can be analyzed using these principles. It is also used in engineering and physics to design and test the trajectory of objects, such as missiles or rockets, launched into the air.

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