A projectile of mass m moves to the right with a speed vi (see figure below). 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. The moment of inertia of a rod is I = Md² and the moment of inertia of a particle is I = mr². 12 a. What is w, the angular speed of the system after the collision. Answer: W= mdvi Md²+1md² 12 energy before the collision? Answer: KE¡ = 1½ m(v;)². b. What is the kinetic C. What is the kinetic energy after the collision?

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A projectile of mass m moves to the right with a speed vi (see figure below). 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. The moment of inertia of a rod is I = Md² and the
moment of inertia of a particle is I = mr².
12
a. What is w, the angular speed of the system after the collision.
mdvi
Md²+1md²
12
b.
What is the kinetic energy before the collision? Answer: KE¡ = m(v¡)².
c. What is the kinetic energy after the collision?
(0₁)²
Answer: W=
1
m²d²
Answer: KE₁ = = =+M₁2² +² md²
12
4
m
O d
M
O
3
Transcribed Image Text:A projectile of mass m moves to the right with a speed vi (see figure below). 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. The moment of inertia of a rod is I = Md² and the moment of inertia of a particle is I = mr². 12 a. What is w, the angular speed of the system after the collision. mdvi Md²+1md² 12 b. What is the kinetic energy before the collision? Answer: KE¡ = m(v¡)². c. What is the kinetic energy after the collision? (0₁)² Answer: W= 1 m²d² Answer: KE₁ = = =+M₁2² +² md² 12 4 m O d M O 3
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