A lump of uranium has a mass of 2.0 kg,and begins at rest.Half of the lump's mass is going to be totally converted into kinetic energy of the other half.After this is done,how fast is the remaining half going?
A)0.60c
B)0.80c
C)0.87c
D)1.0c

Question

Quizplus · Accepted Answer

According to the law of conservation of energy, the initial potential energy of the lump will be converted into kinetic energy. Therefore, we can say:

Initial potential energy = Final kinetic energy

Let the initial mass of the lump be m, and the final mass be m/2 (half of the mass is converted).

Initial potential energy = (m)c^2

Final kinetic energy = (m/2)(v^2/c^2)

Where v is the velocity of the remaining half.

Equating the above expressions, we get:

(m)c^2 = (m/2)(v^2/c^2)

Simplifying, we get:

v^2 = (2c^2)/3

v = sqrt((2c^2)/3) = 0.87c

Therefore, the remaining half of the uranium lump will be moving at a velocity of 0.87 times the speed of light, which is the best choice C.

A Lump of Uranium Has a Mass of 2