Incorrect. Tries 10 Previous Tries A puck of mass 86.0g and radius 3.67cm slides
ID: 1294732 • Letter: I
Question
Incorrect. Tries 10 Previous TriesA puck of mass 86.0g and radius 3.67cm slides along an air table at a speed of v = 1.52m/s, as shown in the figure below. It makes a glancing collision with a second puck of radius 5.41cm and mass 130g (initially at rest) such that their rims just touch. The pucks stick together and spin after the collision (b). What is the angular momentum of the system relative to the center of mass? 0.0233 kg*m^2/s sf-pic0862.png What is the angular velocity about the center of mass?
Explanation / Answer
Ans.:
The center of mass is located at a point along the line segment joining their centers and at such a distance that their moments of mass are equal: r1m1 = r2m2.
r1 + r2 = 3.67 + 5.41 = 9.08 cm, so that r2 = (9.08 cm - r1).
r1*86 g = r2*130 gm = (9.08cm - r1)*130 gm
216 gm*r1 = 1180 gm*cm, and
r1 = (1180 gm*cm)/(216 gm) = 5.463 cm for the mass m1.
This leaves 3.617 cm for the mass m2.
In the initial case, where the pucks have not yet come together, the only angular momentum is that of the moving smaller puck. With a speed of 1.52 m/s, or 152 cm/s, it has an angular momentum of r1 times this speed and times its mass, m1, when taken around the center of mass:
Am1 = (152 cm/s)*(5.463cm)(86gm)
Am1 = 71,412 (cm^2*gm/s)
= 7.1412[10^(-2)] (kg*m^2/s)....... This is the answer to part (a).
B.) The angular momentum will be the same after the collision as it was before it, but each mass will have only a part of this total angular momentum. The two masses will have the same angular speed around the center of mass after the collision: call this Va.
The angular speed equals the linear speed divided by the radius from the center or rotation, which is the center of mass in this case.
So after the collision:
m1*Va*r1^2 + m2*Va*r2^2 = 71,412(cm^2*gm/s)
[86 gm*(5.463 cm)^2] + [130 gm*(3.617 cm)^2]*Va = 71,412 (cm^2*gm/s)
[(2566.61 + 1700.7 )(g*cm^2)]*Va = 71,412 (cm^2*gm/s)
(4267.35 gm*cm^2) = 71,412 (cm^2*gm/s)
and thus
Va = [71,412 (cm^2*gm/s)]/(4267.35 gm*cm^2)
= 16.734 (radians)/s ....................Answer to (b) part.