- #1
MikeyDoubleDEE
- 4
- 2
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 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.
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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