4. 3/5 points | Previous Answers MI4 9.1.015 My Notes Ask Your Teacher By calcul

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4. 3/5 points | Previous Answers MI4 9.1.015 My Notes Ask Your Teacher By calculating numerical quantities for a multiparticle system, one can get a concrete sense of the meaning of the relationships psys = MtodeM and Ktot-Ktrans + Krei. Consider an object consisting of two balls connected by a spring, whose stiffness is 500 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: +1: 8 kg, m/s 2: 5 kg, m/s (a) For this system, calculate psys = (a) For this system, calculate Psys(23, 136, 0 (23, 136, 0 kg·m/s (b) Calculate UCM = (1.77, 10.5, 0 m/s (c) Calculate Ktot-809 (d) Calculate Ktrans (e) Calculate Krel149.9 = 732 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 UcM 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 u = UCM + u rel, and therefore we have UrelUcM. Calculate Urel UCM for each mass and calculate the corresponding Krel. Compare with the result you obtained in part (e)

Explanation / Answer

A) The momentum of the system = m1v1+m2v2 = <23,136,0> kg m/s

B) velocity of the center of mass = momentum of the system / mass of the system = <1.77,10.5,0> m/s

C) The total kinetic energy:

KE = KE1+KE2 = 0.5m1v1^2 + 0.5m2v2^2 = 0.5*8*(6^2+12^2) + 0.5*5*(5^2+8^2) = 942.5 J

D) K tanslation = 732 J

E) Krel = Ktot - Ktrans = 942.5 - 732 = 210.5 J

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