Can anyone show me how to properly solve these A ballistic pendulum (like the on
ID: 1414848 • Letter: C
Question
Can anyone show me how to properly solve these A ballistic pendulum (like the one we studied in lab) can be used to measure the initial velocity of a projectile. One such pendulum has a 2.50 kg mass held by a massless rod of length 55.0 cm. A 150 g projectile is fired from a launcher, and is caught by the pendulum mass, which then deflects by 65.* What is the kinetic energy of the pendulum/projectile immediately after the impact? (This will require a bit of trigonometry.) What is the initial velocity of the projectile? What % of the kinetic energy is lost in the collision?Explanation / Answer
part a:
let the position when the rod is completely vertical, the height at which the mass stays is our reference point for zero potential energy.
as there is no friction involved, total mechanical energy is conserved from the motion from right after the impact till the deflection of angle theta.
let right after impact , speed of the mass and projectile is v m/s
then total initial mechanical energy=kinetic energy=0.5*(2.5+0.15)*v^2
=1.325*v^2
when it travels an angle of theta=65 degrees,
height reached by the pendulum=L-L*cos(theta)=0.31756 m
then total final mechanical energy=potential energy at this point (as kinetic energy=0)
=mass*g*height
=(2.5+0.15)*9.8*0.31756=8.247 J
comparing both the energy values,
initial kinetic energy of the system was 8.247 J
1.325*v^2=8.247
==>v=2.498 m/s
part b:
just before the collision and after the collision, momentum is conserved.
hence if speed of the projectile before collision is v0,
then initial momentum=final momentum
==>0.15*v0+2.5*0=(2.5+0.15)*2.498
==>v0=44.131 m/s
part c:
kinetic energy lost in the collision=initial kinetic energy of the projectile-final kinetic energy of the projectile+mass system
=0.5*0.15*v0^2-0.5*(2.5+0.15)*v^2
=137.397 J
initial kinetic energy=0.5*0.15*44.131^2=146.06588 J
then % of kinetic energy lost=137.397/146.06588=94.065%