- #1

MikeyDoubleDEE

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Hello All.

I am mentoring a high school student in my area with his class project for school. He has chosen he wants to launch an object (in our case, a softball) into a 5' diameter area. The idea is to build basically an oversized slingshot using an extension spring as the source of energy.

We arbitrarily picked a distance of 50yds (45.7 m) with a launch angle of 30°. Using projectile motion fundamentals we came up with the following:

d=(Vi²/g)*sin2Θ

Plugging in:

d = 45.7m

Vi = ?

Θ = 30°

g = 9.81m/s²Solving for Vi, I got

So now we migrate into spring fundamentals. I initially thought to use an engineer's best friend F=ma but quickly realized that the acceleration is not constant in the context of springs and that calculus would need to be leveraged for a diminishing a value. So scratch that.

Settling on the law of conservation of energy, I sought to find the Kinetic Energy of the mass (Softball = .195kg) at my

K=1/2(mv²)

Plugging in:

m = .195kg

v = 22m/s

Solving for K, I got

This is where I start to doubt myself:

I found this equation in my old College Physics textbook

Vmax=√(k/m) * A

(A standing for displacement, and k standing for spring constant)

Plugging in:

Vmax = 22m/s

m = .195kg

A = .61m (24" is what we arbitrarily selected as a starting point for our spring selection)

Solving for the spring constant

Is this the correct approach? I don't want to start buying hardware to build our prototype unless I can get some feedback from the physics community that our approach to solving this design problem is valid. Thank you so much for your time!

Disclaimer: I realize that this approach does not take into account gravity during the acceleration of the mass "uphill" at 30 deg. Also, this assumes a frictionless slingshot. And we decided to ignore wind resistance in the projectile motion portion of this problem.

I am mentoring a high school student in my area with his class project for school. He has chosen he wants to launch an object (in our case, a softball) into a 5' diameter area. The idea is to build basically an oversized slingshot using an extension spring as the source of energy.

We arbitrarily picked a distance of 50yds (45.7 m) with a launch angle of 30°. Using projectile motion fundamentals we came up with the following:

d=(Vi²/g)*sin2Θ

Plugging in:

d = 45.7m

Vi = ?

Θ = 30°

g = 9.81m/s²Solving for Vi, I got

**22m/s**(Which will serve as the*final*Velocity in my forthcoming spring calcs)So now we migrate into spring fundamentals. I initially thought to use an engineer's best friend F=ma but quickly realized that the acceleration is not constant in the context of springs and that calculus would need to be leveraged for a diminishing a value. So scratch that.

Settling on the law of conservation of energy, I sought to find the Kinetic Energy of the mass (Softball = .195kg) at my

*final*Velocity of 22m/s.K=1/2(mv²)

Plugging in:

m = .195kg

v = 22m/s

Solving for K, I got

**47.19 Joules**This is where I start to doubt myself:

I found this equation in my old College Physics textbook

Vmax=√(k/m) * A

(A standing for displacement, and k standing for spring constant)

Plugging in:

Vmax = 22m/s

m = .195kg

A = .61m (24" is what we arbitrarily selected as a starting point for our spring selection)

Solving for the spring constant

**k**, I got**2507 N/m (14.315 lbs/in :**My mind thinks in pounds and inches, not Newtons and meters**)**Is this the correct approach? I don't want to start buying hardware to build our prototype unless I can get some feedback from the physics community that our approach to solving this design problem is valid. Thank you so much for your time!

Disclaimer: I realize that this approach does not take into account gravity during the acceleration of the mass "uphill" at 30 deg. Also, this assumes a frictionless slingshot. And we decided to ignore wind resistance in the projectile motion portion of this problem.

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