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An unstable particle with a mass equal to 3.34 ✕ 10−27 kg is initially at rest....

An unstable particle with a mass equal to 3.34 ✕ 10−27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.976c and −0.862c, respectively. Find the masses of the fragments. (Hint: Conserve both mass–energy and momentum.)

m(0.976c) = kg
m(-0.862c) =kg

Solutions

Expert Solution

Given: The mass of particle, m = 3.34 *10-27 Kg ; velocity v1 of fragment 1 = 0.976c ; velocity v2 of fragment 2 = -0.862c ; speed of light = 3 *108 m/s

Required to find: The masses of the fragments.

Solution:

From the Conservation of Mass, since the total mass of the particle is constant,

----(1), where m1 and m2 are the masses of the fragments.

From the Conservation of Momentum,

Since the initial velocity of the particle is zero, the LHS of the above equation becomes zero.

[Cancelling 'c' on both sides and rearranging]

----(2)

Putting the value of equation (2) into (1),

Therefore the value of m1,

Answer: The mass of the fragments are m(0.976c) = 1.566414*10-27 Kg and m(-0.862c) = 1.773586*10-27 Kg.

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genius_generous answered 2 years ago
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