- #1
Kibbel
- 27
- 0
Homework Statement
m1 = 5 kg, v1 = < 11, -4, 12 > m/s
m2 = 7 kg, v2 = < -14, 6, -6 > m/s
m3 = 5 kg, v3 = < -27, 35, 24 > m/s
What is the total kinetic energy of this system?
Homework Equations
Momentum(total) = Mass(total)*Velocty(of Center of Mass)
Ktranslation = (Mass(total)*(Velocity of Ceneter of mass)^2)/2
The Attempt at a Solution
I followed this as close to the textbook as possible and still two ways i did it i got it wrong.
I started off by finding the momentum of the entire system by doing m1v1+m2v2+m3v3. Then i divided that by the total mass (m1+m2+m3). this gave me the velocity of the center of mass.
One i had that i plugged that directly into the equaltion to find the total kinetic energy of the system. v << c, and there is no Kinetic vibrational or rotational energy, so its just translational.
so i plugged that into the K translational formula, but neither solutions i got worked out.
I know my velocity of center of mass is correct at <-10.47, 11.59, 8.118>
So i did the dot product multiplication of that to itsself, and got 309.85. squared that to get 96007.6, then mutiplied by 17/2, to get 816060 Joules, which is not accurate.
(17/2)(<-10.47,11.59,8.118>)^2 = 816060 Joules.
other solution i tried was finding the magnitude of Velocity of center of mass, and squaring that and multiplying it by 17/2. which ends up working out exactly the same.
can someone tell me what I am doing wrong? I've followed every rule and haven't ommitted everything and I've done the problem several times so i know I am not making a small mistake