MasteringPhysics: HW08 - Google Chrome https://session.masteringphysics.com/myct

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MasteringPhysics: HW08 - Google Chrome https://session.masteringphysics.com/myct/item KHW08 Exercise 8.31: Asteroid Collision Constants Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at vA1 40.0 m/s with respect to an inertial frame in which asteroid B was at rest, is deflected 30.0° from its original direction, while asteroid B travels at 45.0o to the original direction of A as shown in (Figure 1)

Explanation / Answer

using momentum conservation

in X-direction

Pxi = Pxf

mA = mB = m

m*Vaxi + m*Vbxi = m*Vaf*cos 30 deg + m*Vbf*cos 45 deg

Vaxi + Vbxi = Vaf*cos 30 deg + Vbf*cos 45 deg

Vbxi = 0

40 + 0 = Vaf*0.866 + Vbf*0.707

in y-direction

Pyi = Pyf

mA = mB = m

m*Vayi + m*Vbyi = m*Vaf*sin 30 deg - m*Vbf*sin 45 deg

Vayi + Vbyi = Vaf*sin 30 deg - Vbf*sin 45 deg

Vbyi = Vayi = 0

0 + 0 = [Vaf*0.5 - Vbf*0.707]

Vaf = Vbf*(0.707/0.5) = 1.414*Vbf

using bolded equation

40 + 0 = Vaf*0.866 + Vbf*0.707

40 = Vbf*1.414*0.866 + Vbf*0.707

Vbf = 40/(1.414*0.866 + 0.707) m/sec = 20.71 m/sec (Speed of Asteroid B)

Vaf = 1.414*Vbf = 1.414*20.71 m/sec = 29.28 m/sec (Speed of Asteroid A)

Part C

Fraction of KE will be

F = dKE/KEi

dKE = KEf - KEi

KEi = 0.5*m*Vai^2

KEf = 0.5*m*Vaf^2 + 0.5*m*Vbf^2

F = [(0.5*m*Vaf^2 + 0.5*m*Vbf^2) - 0.5*m*Vai^2]/(0.5*m*Vai^2)

F = [Vaf^2 + Vbf^2 - Vai^2]/Vai^2

F = (29.28^2 + 20.71^2 - 40^2)/40^2

F = -0.1961 = 19.61%

(Please Check in which you need fraction, try both 0.1961 OR 19.61%)

Please Upvote.

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