By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the
relationships and . Consider an object consisting of two balls connected by a
spring, whose stiffness is 400 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 0.3 m, and the two balls at the ends of the spring have the following masses and
velocities:
1: 5 kg, (8, 14, 0) m/s
2: 3 kg, (− 5, 9, 0) m/s
(a) For this system, calculate .
(b) Calculate .
(c) Calculate Ktot.
(d) Calculate Ktrans.
(e) Calculate Krel.
(f) 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).
Section 9.4