By calculating numerical quantities for a multiparticle system, one can get a co
ID: 1381278 • Letter: B
Question
By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships . Consider an object consisting of two balls connected by a spring, whose stiffness is 480 N/m. The object has been thrown through the air and is rotating and vibrating as it moves. At a particular instant the spring is stretched 0.36 m, and the two balls at the ends of the spring have the following masses and velocities: For this system, calculate Calculate Calculate Ktot = 758 Calculate Ktrans = 600 Calculate Krel = 28.7 Here is a way to check your result for Krel. The velocity of a particle relative to the center of mass is calculated by subtracting from the particle's velocity. To take a simple example, if you're riding in a car that's moving with vCM,x = 20 m/s/ and You throw a ball with vrel/x = 35 m/s, relative to the car, a bystander on the ground sees the ball moving with vx = 55 m/s. So and therefore we have . Calculate for each mass and calculate the corresponding Krel. Compare with the result you obtained in part (e).Explanation / Answer
given that ::
m1 : 8 kg < 6, 11, 0 > m/s
m2 : 4 kg < -4, 7, 0 > m/s
vCM = ( 8/3 , 29/3 , 0 ) m/s
using equation : v = vCM + vrel { eq. 1 }
m1 has a relative velocity of :
vrel = v - vCM { eq. 2 }
< 6 - 8/3, 11 - 29/3 > which simplify that < 10/3, 4/3 >
relative kinetic energy of :
Krel 1 = (1/2) m1 (vrel)2 { eq. 3 }
(1/2) (8 kg) [ (3.33)2 + (1.33)2 ] = 51.43 J
m2 has a relative velocity of :
< -4 - 8/3, 7 - 29/3 > which simplify that < -20/3, -8/3 >
relative kinetic energy of :
Krel 2 = (1/2) m2 (vrel)2
(1/2) (4 kg) [ (6.66)2 + 2.66)2 ] = 28.30 J
total relative kinetic kinergy of :
Krel = K1 + K2 { eq. 4 }
inserting the values in above eq,
Krel = 51.43 J + (- 28.30 J) = 109.73 J
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