By calculating numerical quantities for a multiparticle system, one can get a co

Question

By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships

and

Ktot = Ktrans + Krel.

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 0.40 m, and the two balls at the ends of the spring have the following masses and velocities:
• 1: 8 kg,

‹ 4, 13, 0 › m/s

• 2: 4 kg,

‹ 4, 8, 0 › m/s

(a) For this system, calculate

=

(16,136,0)

=

(1612,13612,0)

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

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

PART C

Ktot = 0,5(m1v12+m2v22)

v1 = (42+132)1/2 = 13,6015 m/s

v2 = (42 + 82)1/2 = 8,9443 m/s

Ktot = 0,5(8*185+4*80) = 900 J

PART D

Ktrans = 0,5 (m1+m2)*vCM2 = 0,5*12*130,22 = 781,3 J

PART E

Krel = Ktot - Ktrans = 900 - 781,3 = 118,7 J

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