# Projectile motion via a spring (well, actually, rubber bands )

In summary, the problem is that the physics-savvy student forgot most of what they learned from physics in their second semester back at college - even basic things like how to build a catapult to shoot a tennis ball. However, with the help of some basic formulas, they can still figure out how far the ball will travel and how fast it will go.

Okay, here's the deal. 2nd day back at college and I pretty much have forgot most everything Physics related already :uhh:

Had a very easy assignment today in one of my engineering classes to take two dowels and a bunch of rubber bands and build something that could launch/throw a tennis ball from atop a terrace towards a point on the ground below (goal to get as close as possible, if not a bulls-eye). So, you say, that's elementary stuff, what's the problem? Here you go:

I have:
-the mass of the ball
-the distance it traveled in 4 different trials
-the times it traveled
-the actual distance from the terrace to the target (x)
-the height of the terrace (y)

I need to write and use equations to:
1) predict where the ball will land (assuming we hadn't actually launched it)
2) determine the effective spring constant for the system (in this case, two strings of rubber bands)

3) in addition to, I guess, finding the initial velocity using what info. I have

So, while this is, in essence, so easy it hurts, I'm brain dead right now and just need to know how to get/do #1,2,3 based on what I already have (ball mass,travel/height distances, and times).

Thanks!

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Anyone? All I need is k, v, and distance... ...except I'm too stupid to remember how to get those 3 things...

Do you know any formulas connecting the things you are given: strength of the rubber bands, initial velocity, and initial position, and final position?

Well, here's what I do have:

Equations on our sheet:
v=v0+at
y=y0+v0*sin(theta)*t+(1/2)at^2 where a is gravity
x=x0+v0*cos(theta)*t+(1/2)at^2 "a" is zero, ignoring deceleration due to wind resistance

KE=(1/2)mv^2
PE=mgh

f=ma

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

Don't know the strength of the rubber bands, which I guess is why we're supposed to find the "spring constant" or k of our rubber bands. Similarly, that's also why I need to find the initial velocity, from what I do have. Initial position is, I guess, the launching point at 10'3" height off the ground (y-value) and horizontally at 50'3" from the target (though it really only traveled horizontally 2'11", 7'6", 16'1", and 38'2" from the launching point when we shot it).

Using those numbers, plus the ball mass of 5oz./0.14kg, and a launch angle of 30deg., the main lines in my instructions with that all says "Develop the equations of motion describing the tennis ball's flight and use them to predict where the tennis ball will land. Determine the effective spring constant for your system."

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Do you HAVE these rubber bands? any known weights?
It would be a lot easier to measure their elasticity
BEFORE tying fastening them into a device!

lightgrav said:
Do you HAVE these rubber bands? any known weights?
It would be a lot easier to measure their elasticity
BEFORE tying fastening them into a device!

That's true, but it was never meant to be that complicated. Apparently we're just supposed to take the distance and mass results we have and, coupled with the given equations, answer those two main questions (i.e., the "spring" constant of the system and the expected shoot distance).

you mean wasn't expected to be that straightforward!

Working backwards from measured range and launch angle
can get you the initial speed pretty easily (recall, max at 45).
But to get the rubber band's "k" , you need measured stretch distance,
or its mechanical advantage and time duration in launcher, or...

lightgrav said:
you mean wasn't expected to be that straightforward!

Working backwards from measured range and launch angle
can get you the initial speed pretty easily (recall, max at 45).
But to get the rubber band's "k" , you need measured stretch distance,
or its mechanical advantage and time duration in launcher, or...

Oh, forgot, I do have that--stretched it 2ft back from 0, to shoot.

And the flight times weren't recorded, but I can make them up fairly accurately if need be.

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lightgrav said:
you mean wasn't expected to be that straightforward!

Working backwards from measured range and launch angle
can get you the initial speed pretty easily (recall, max at 45).
But to get the rubber band's "k" , you need measured stretch distance,
or its mechanical advantage and time duration in launcher, or...

So what formulas should I use? I always get confused with projectiles, because of there being both x and y components of velocity, etc., so what to use?

If someone could just guide me a little with the right formulas, I could probably take it from there...until then, I'll keep trying it incorrectly

Here's how far my stupidness has gotten me...
http://img388.imageshack.us/img388/3677/egrproblem5dq.jpg [Broken]

...ponder and point out what is wrong.

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And the flight times weren't recorded, but I can make them up fairly accurately if need be.

You're going to FUDGE data??

Tide said:
You're going to FUDGE data??

No, not exactly, I said that wrong. I meant I specifically hadn't recorded them down, but someone else did, I just have to get them from them. Until then, I'm just going to plug in "good guesses" if you catch my drift, and finalize it all when I get the real ones.

Anything look blatantly wrong on my sheet so far? Can't believe I forgot so much so quickly...

## 1. What is projectile motion via a spring?

Projectile motion via a spring is a type of motion in which an object is launched into the air by the force of a spring. The object follows a parabolic path due to the combination of its initial velocity and the force of gravity.

## 2. How does a spring launch an object into projectile motion?

A spring stores potential energy when it is stretched or compressed. When released, this potential energy is converted into kinetic energy, causing the spring to push or pull on the object and launch it into the air.

## 3. What factors affect the trajectory of an object launched by a spring?

The trajectory of an object launched by a spring is affected by the initial velocity, the angle at which the object is launched, the force of gravity, and air resistance. The stiffness and length of the spring also play a role in the trajectory.

## 4. Can projectile motion via a spring be used in practical applications?

Yes, projectile motion via a spring has many practical applications such as in launching projectiles in a catapult or in the design of roller coasters. It is also used in sports equipment like a slingshot or a bow and arrow.

## 5. How can the motion of an object launched by a spring be calculated?

The motion of an object launched by a spring can be calculated using the principles of projectile motion, taking into account the initial velocity, angle of launch, and other factors mentioned. This can be done using mathematical equations or through computer simulations.