By calculating numerical quantities for a multiparticle system, one can get a co
ID: 1498374 • Letter: B
Question
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 is 540 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: 7 kg, ‹ 5, 11, 0 › m/s • 2: 3 kg, ‹ 6, 9, 0 › m/s (a) For this system, calculate p with arrowsys = 17,104,0 Correct: Your answer is correct. kg · m/s (b) Calculate v with arrowCM = 1.7,10.4,0 Correct: Your answer is correct. m/s (c) Calculate Ktot = J (d) Calculate Ktrans = Incorrect: Your answer is incorrect. 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 corresponding Krel. Compare with the result you obtained in part (e).
Explanation / Answer
Part C)
Ktot = [1/2]*[m1v12 + m2v22]
Ktot = 0.5*[7*(25+121) + 3*(36+81)]
Ktot = 686.5 J
Part D)
Ktrans = [1/2]*Mtot*Vcm2
Ktrans = 0.5*(7+3)*(1.72+10.42)
Ktrans = 555.25 J
Part E)
Krel = Ktot - Ktrans
Krel = 686.5 J - 555.25 J
Krel = 131.25 J
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