Physics question:?

Question

I need an equation for this:
There is a ballistic pendulum. The ball is in the cannon-like thing that is spring loaded. it is launched and it shoots into a pendulum where it gets stuck and makes the pendulum move to the right a certain number of degrees. I need an equation to describe this, so I can plug in numbers and get the original velocity of the ball when it's launched.

Help is MUCH appreciated!

I forgot to mention, since this is an inelastic collision, would kinetic energy be conserved? so would kinetic energy = potential energy before and after?

Answer 1

This can be approached by using conservation of momentum and energy. The momentum of the ball is .mb*vb. After it hits the pendulum, the momentum of the ball mass and the pendulum mass is, (mb + mp)*vp,

The velocity of the pendulum at impact is then

vp = vb*mb/(mb+mp)

The kinetic energy of the ball-pendulum system is 0.5*(mb + mp)*vp^2 immediately after impact.

KEp = 0.5*(mb + mp)*[vb*mb/(mb+mp)]^2

The pendulum will then rise to a height h such that the potential energy at that point equals the initial kinetic energy, or

0.5*(mb + mp)*[vb*mb/(mb+mp)]^2 = (mb+mp)*g*h.

h = .5*[vb*mb/(mb+mp)]^2/g

To find the angle, the pendulum moves in a circular arc. Geometrically, the angle of swing is given by

ø = arccos((R-h)/R,

or

cosø = (1 - h/R),

where R is the radius of the circle = length of the pendulum. Therefore the formula for the angle is

cosø = 1 - .5*[vb*mb/(mb+mp)]^2/g*R];

Solve for vb = √[2*(1 - cosø)*g*R] * [(mb+mp)/mb]

Answer 2

mass of projectile times velocity of projectile equals new total mass (projectile + mass it stuck to) times velocity. Use the angle to find the velocity. Use the angle to find how high the ball climbed to find potential energy (mass*gravity*height). And then set mgh = (1/2)mV^2. I don't know exactly what information your given but I hope that helps.

Answer 3

I'll give you a start. All you really need to know is what forces are involved. Gravity and momentum.