- #1
MechaMZ
- 128
- 0
Homework Statement
A 2 kg disk traveling at 3 m/s strikes a 1 kg stick of length 4 m that is lying flat on nearly frictionless ice .Assume the collision is elastic and the disk does not deviate from its original line of motion. Find the translational speed of the disk, the translational speed of the stick, and the angular speed of the stick after collision. The moment of inertia of the stick about center of mass is 1.33 kg m2
Attempt:
conservation. of linear momentum
mdvdi = mdvdf + msvs
(2 kg) (3 m/s)=(2 kg) vdf + (1 kg)vs
6 kg m/s-(2 kg) vdf = (1 kg)vs----------------------(1)
conservation. of angular momentum
-rmdvdi = -rmdvdf + I*omega
-12kgm2/s=(- 4kg m) vdf + (1.33 kg m2)*omega----------------------(2)
-9rad/s+(3rad/m) vdf = omega
elastic collision
1/2 mdvdi2 = 1/2mdvdf2 +1/2 I*omega2 + 1/2msvs2
18 m2 /s2 =2mdvdf2 +(1.33 m2 )*omega2 + vs2--------------------------(3)
solve .(1), (2), (3) >>> vdf =2.3 m/s, omega = -2rad/s , vs =1.3 m/s
For my solution above, I have no idea why the rmdvdi and rmdvdf are negative, but I*omega is positive. I tried to figure it with right hand rule, but i still find three of them should be in the same direction.