A projectile of mass m moves to the right with a speed vi. The projectile strike
ID: 1402696 • Letter: A
Question
A projectile of mass m moves to the right with a speed vi. The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O. We wish to find the fractional change of kinetic energy in the system due to the collision. (Use any variable or symbol stated above as necessary.) (a) What is the appropriate analysis model to describe the projectile and the rod? O isolated system non-isolated system (b) What is the magnitude of the angular momentum of the system before the collision about an axis through O? total (c) What is the moment of inertia of the system about an axis through O after the projectile sticks to the rod? total = (d) If the angular speed of the system after the collision is , what is the magnitude of the angular momentum of the system after the collision? total =Explanation / Answer
a) Isolated system
b) Ltotal = m*Vi*(d/2)
c) Itotal = M*d^2/12 + m*(d/2)^2
= M*d^2/12 + m*d^2/4
= (M*d^2 + 3*m*d^2)/12
d) Lotal = Itotal*w
= (M*d^2 + 3*m*d^2)*w/12
e) Li = Lf
m*Vi*(d/2) = (M*d^2 + 3*m*d^2)*w/12
w = m*Vi*(d/2)/((M*d^2 + 3*m*d^2)/12 )
= 6*m*vi*d/(M*d^2 + 3*m*d^2)
f) K = 0.5*m*vi^2
g) Ktotal = 0.5*Itotal*w^2
= 0.5*((M*d^2 + 3*m*d^2)/12)*(6*m*vi*d/(M*d^2 + 3*m*d^2) )^2
= 1.5*m^2*vi^2*d^2/(M*d^2 + 3*m*d^2)
h) delta K = 0.5*m*vi^2 - 1.5*m^2*vi^2*d^2/(M*d^2 + 3*m*d^2)