How to Calculate the Max Launch Speed of a Catapult Using Elastic Bands?

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To calculate the maximum launch speed of a catapult using elastic bands, the energy stored in the bands (8 joules) can be equated to the kinetic energy at launch. The formula for kinetic energy (KE = 0.5 * m * v^2) can be rearranged to find the launch speed (v). The acceleration during launch can be determined using the force (16 Newtons) and mass of the projectile, while the maximum height and range depend on the launch angle and initial speed. The design will include a mechanism to adjust launch angles, enhancing its functionality. Understanding these principles will aid in the successful construction and performance evaluation of the catapult.
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Ok, so for a summative project, my group has to build a catapult which must use elastic bands to propel an object. I have the energy, force, and maximum stretch distance of the elastic band. The values are 8 joules, 16 Newtons, and 0.5 meters. The catapult is not built yet, so I can't give any specs about it.

Now from this, is it possible to calculate the max launch speed, acceleration during launch, max height, and max range?

Any help would be greatly appreciated.
 
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Can you show how that catapult will look like?

ehild
 


The design won't be much different than this http://www.redstoneprojects.com/trebuchetstore/catapult_2.jpg"

The main difference is that my group's catapult has to launch at different angles, so we're adding a mechanism to do that.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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