Problem 11.51 A thin metal rod of mass 1.7 kg and length 0.5 m is at rest in out
ID: 1730722 • Letter: P
Question
Problem 11.51 A thin metal rod of mass 1.7 kg and length 0.5 m is at rest in outer space, near a space station (see figure below). A tiny meteorite with mass 0.06 kg traveling at a high speed of 190 m/s strikes the rod a distance 0.2 m from the center and bounces off with speed 60 m/s as shown in the diagram. The magnitudes of the initial and final angles to the x axis of the small mass's velocity are 26 and ep 82°. Vf ep Vi (a) Afterward, what is the velocity of the center of the rod? (Express your answer in vector form.) m/s (b) Afterward, what is the angular velocity ? of the rod? (Express your answer in vector form.) rad/s (c) What is the increase in internal energy of the objects?Explanation / Answer
a )
x - direction,
Vcm, x = m vi cos26 + m vf cos82 / M
= 0.06 X 190 X cos26 + 0.06 X 60 X cos82 / 1.7
Vcm, x = 6.321 m/s
Vcm, y = m vi sin26 + m vf sin82 / M
= 0.06 X 190 X cos26 - 0.06 X 60 X cos82 / 1.7
Vcm, y = 0.842 m/s
Vcm = 6.321 i + 0.842 j
= 7.163 m/s
b )
w = 0.06 X 0.2 X ( 190 X cos26 + 60 X cos82 ) / ( 1.7 X 0.52 / 12 )
= 60.69 rad/sec
direction of w is z - axis
c )
difference in KE = 0.5 ( m vi2 - mvf2 - M L2 w2 / 12 - m Vcm2 )
= 0.5 X ( 0.06 X 1902 - 0.06 X 602 - ( 1.7 X 0.52 / 12 ) X 60.692 - 1.7 X 7.1632 )
= 0.5 X ( 2166 - 216 - 130.44 - 87.224 )
difference in KE = 866.168 J