Question

A ballistic pendulum is a device used to measure the speed of a projectile of mass m (at point A). The projectile is launched horizontally into a target of mass M which is suspended like a pendulum (point b). When the projectile strikes the target it imbeds. The maximum height reached by the pendulum and projectile together is then measured (point c).

. -find the equation describing the collision from point a-->b. (conservation of momentum)

- find equation describing the upswing point B-->C ( conservation of mechanical energy)

-find equation relating the maximum hight h to the maximum angle (theda) of the upswing.

-combine previous three equations above to derive muzzle velocity as a function of things that are measurable in a lab.

Answer 1

let the mass of the projectile be m and the speed with which it strikes be u.so,

applying law of conservation of momentum,

initial momentum = final momentum.

or m*u = (M+m)*v

or v=m*u/(M+m)

for the second part, we now apply law of conservation of energy to get the results,

or (m+M)*gh=0.5(M+m)*v^2

or gh=0.5v^2

or h=v^2/(2g)

where v = m*u/(M+m)

let the angle it makes with the vertical(theta) be x.so,

Lcos(x) = L-h

=> x = theta = arccos(1-(h/l))

where h has been derived from the previous part.

So basically use the above three equations along with the facility in your lab to get the result.