Maximizing Projectile Distance with Torsion Spring Catapult

[Berwin]

Homework Statement

Determine maximum distance an one ounce projectile can be launched with a torsion spring catapult.

Homework Equations

E = F * d = 1/2 * m * v₀²Note: Theta is the measurement of how far the lever arm is being pulled back.

Am I missing something?

 

[haruspex]

There does not appear to be enough information, in two ways.
There's no basis for figuring the distance through which the force acts. It doesn't say what the force is for smaller angles. It could be linear down to about 10 degrees, or it might suddenly drop to zero somewhere below 140.
But your equation E = F * d is only valid for constant forces, which this clearly is not. The more general form requires you to integrate F over the distance. If the force is a linear function of distance over the range of integration (which it looks to be from the table) then the result will be quadratic.

 

[Berwin]

If it helps at all, the torsion spring in this case is one you find in a mousetrap. We've attached a plastic spoon to the lever arm of the mousetrap, which together reach 0.17145 meters. Does this make a difference?

 

[haruspex]

We've attached a plastic spoon to the lever arm of the mousetrap, which together reach 0.17145 meters.

That's useful info. So as the arm moves through angle dθ, the force advances rdθ, where r = 0.17145 m. That allows you to calculate the energy imparted as the angle changes.
However, just realized I should have checked something. The F values in the table really are the force at the end of the arm, yes? They're not torque (Nm)?
That leaves the question of whether the table is complete. I.e., as the angle falls below 140^o, does the force suddenly vanish or does it continue to decline linearly?

 

[Berwin]

Yes, it's just the force at the end of the arm. The force suddenly vanishes. We only wanted to test the angles given above in the chart.

 

[haruspex]

Yes, it's just the force at the end of the arm. The force suddenly vanishes. We only wanted to test the angles given above in the chart.

Ok, so do you understand how to compute the total energy from that chart (combined with knowledge of the length of the arm)?