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 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

(b) Calculate

(c) Calculate Ktot = ????????? J

(d) Calculate Ktrans = ???????? J

(e) Calculate Krel = ???????? J

Explanation / Answer

c) Ktotal =0.5 (m1v1 ^2. + m2v2 ^2)

= 0.5 (8 ×(121 +16) + 4×(9+100))= 0.5× 8× 137 + 0.5×4×109

=766 J

d) Ktrans = 0.5×Mtotal×Vcm^2=

0.5×12×(1.667^2 +10.667^2) = 699J

e)Krel= 766-699 = 67J

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