A uranium nucleus (initially m U = 235 u) sits at rest in empty space. Suddenly
ID: 1294476 • Letter: A
Question
A uranium nucleus (initially mU = 235 u) sits at rest in empty space. Suddenly it undergoes fission, splitting into an iridium nucleus (mU = 192 u) traveling to the right with velocity vSc.(Asume that no othe particles are created or ejected in the fission.) Fill in the following blanks:
(Assume that the masses given above are exact. Express the following answers EITHER as decimal values to 3 significant figures OR as exact rational numbers. Ignore friction and air resistance)
a. vSc equals _____________ times vIr.
b. The kinetic energies of the outgoing particles are KIr and KSc.KSc. equals __________ times KIr.
c. What is the velocity of the center-of-mass of the two outgoing nuclei? vcm = ________
Explanation / Answer
(a)
Conservation of momentum:
0 = mSc * vSc + mIr*vIr
==> mSc*vSc = -mIr*vIr
==> vSc/vIr = -mIr/mSc
vSc/vIr = -192/235
vSc = -192/235 times vIr
(b)
KE is proportional to mv2.
KEIr/KESc = mIr/mSc * (vIr/vSc)2
KEIr/KESc = 192/235 * (235/192)2
KEIr/KESc = 235/192
KESc = 192/235 times KEIr
(c)
By Conservation of momentum: vcm = 0
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