A thin metal rod of mass 1.1 kg and length 0.9 m is at rest in outer space, near

Question

A thin metal rod of mass 1.1 kg and length 0.9 m is at rest in outer space, near a space station (see figure below). A tiny meteorite with mass 0.09 kg traveling at a high speed of 175 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 ?i = 26° and ?f = 82°.

(a) Afterward, what is the velocity of the center of the rod? (Express your answer in vector form.)

(b) Afterward, what is the angular velocity ? of the rod? (Express your answer in vector form.)

(c) What is the increase in internal energy of the objects?

Explanation / Answer

a)

m = mass of  meteorite = 0.09 kg

M = mass of rod = 1.1 kg

vi = initial velocity of the meteorite = (175 Cos26) i + (175 Sin26) j = 157.3 i + 76.7 j

vf = final velocity of the meteorite = - (60 Cos82) i + (60 Sin82) j = - 8.4 i + 59.4 j

Vi = initial velocity of the rod = 0

Vf = final velocity of the rod = ?

Using conservation of momentum

m vi + MVi = m vf + M Vf

(0.09) (157.3 i + 76.7 j ) + (1.1) (0) = (0.09) (- 8.4 i + 59.4 j ) + (1.1) Vf

(14.2 i + 6.9 j) - (- 0.8 i + 5.4 j) = (1.1) Vf

15 i + 1.5 j =  (1.1) Vf

Vf = 13.6 i + 1.4 j

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