A meter stick is motionless on an icy surface (frictionless). A hockey puck is o

Question

A meter stick is motionless on an icy surface (frictionless). A hockey puck is on a collision course towards the stick. The puck hits the stick at the 30 cm mark and is traveling perpendicular to the length of the stick.

After hitting the stick, the puck is deflected 30 degrees from its original trajectory and is traveling at half of its original speed.

Mass of a meter stick = 0.05 kg

Mass of hockey puck = 0.17 kg

Initial speed of the hockey puck = 9 m/s

a) Choosing an origin at the starting position of the meter stick’s center of mass, what is the angular momentum of the hockey puck before the collision.

b) What is the angular momentum of the hockey puck after the collision (use the same origin)?

c) What is the velocity (direction and speed) of the stick’s center of mass after the collision?

d) What is the angular velocity of the stick (assume it will rotate about its center of mass)?

please be specific and show all steps

Explanation / Answer

Here ,

a)

initial angular momentum of puck = m * v * r

initial angular momentum of puck = 0.17 * 9 * (1 - 0.30)

initial angular momentum of puck = 1.07 Kg.m^2/s

the initial angular momentum of puck is 1.07 Kg.m^2/s

b)

after the collision ,

final angular momentum of puck = m* v * (r) * sin(theta)

final angular momentum of puck = 0.17 * 9/2 * (1 - 0.30) * sin(30)

final angular momentum of puck = 0.28 Kg.m^2/s

c)

let the velocity of centre of mass is v

Using conservation of momentum

0.17 * 9 i = 0.17 * 4.5 *(cos(45) i + j * sin(45)) + 0.05 * v

v = 19.8 i - 10.8 j

v= sqrt(19.8^2 + 10.8^2) at 180 + arctan(10.8/19.8) degree with initial direction

v = 22.6 m/s at 208.6 degree

the final speed of rod is 22.6 m/s at 208.6 degree

d)

let the angular velocity is w

using conservation of angular momentum

0.5 * 0.05 * 1^2/12 * w = 1.07 - 0.28

w = 379 rad/s

the angular velocity of stick is 379 rad/s

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