By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships
p with arrowsys = Mtotv with arrowCM
and
Ktot = Ktrans + Krel.
Consider an object consisting of two balls connected by a spring, whose stiffness is460 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 0.37 m, and the two balls at the ends of the spring have the following masses and velocities:
• 1: 8 kg, ‹ 4, 11, 0 › m/s
• 2: 4 kg, ‹ −3, 10, 0 › m/s
(a) For this system, calculate
p with arrowsys = ??????? kg · m/s
(b) Calculate v with arrowCM ????????? = m/s
(c) Calculate Ktot ?????????= J
(d) Calculate Ktrans ????????? = J
(e) Calculate Krel ????????? = J
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 v with arrowCM 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 v with arrow = v with arrowCM + v with arrowrel,and therefore we have v with arrowrel = v with arrow − v with arrowCM. Calculate v with arrowrel = v with arrow − v with arrowCM for each mass and calculate the correspondingKrel. Compare with the result you obtained in part (e).
