Question

Derive the expression for the initial velocity v of a ballistic pendulum in terms of the swept-out angle theta. Use the following equations of momentum and energy conservation...

When the projectile and the pendulum stick together, they have total mass m + M and we define their combined velocity to be V⃗ . The relationship from conservation of momentum is: mv = (m + M)V⃗

Conservation of energy requires the initial kinetic energy of the pendulum system to equal the potential energy at the top of the swing, which is mathematically given as: 0.5(m+M)V² = (m+M)gh, where h is the height of the combined pendulum bob + metal ball above their lowest point.

Finally, h can be represented as a function of θ in the following way: h = R(cos θ₀ − cos θ)

(solve for v in terms of θ)

Answer 1