A proton (mass=1.67*10^-27 kg) moves with a velocity of 6.00*10^6 m/sec. Upon colliding with a stationary particle of unknown mass, the proton rebounds upon its own path with a velocity of 4.00*10^6 m/sec. The collision sends the unknown particle forward with a velocety of 2.00*10^6 m/sec. What is the mass of the unknown particle.
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To find the mass of the unknown particle, we can use the principle of conservation of momentum. According to this principle, the total momentum before a collision is equal to the total momentum after the collision.
Before the collision, let's denote the mass of the unknown particle as 'm'.
The momentum of the proton before the collision is given by:
p1 = mass_proton * velocity_proton
The momentum of the unknown particle before the collision is:
p2 = mass_unknown * 0 (since it is stationary)
After the collision, the proton rebounds with a velocity of 4.00*10^6 m/s in the opposite direction. Therefore, the momentum of the proton after the collision is:
p3 = mass_proton * (-4.00*10^6 m/s)
The unknown particle moves forward with a velocity of 2.00*10^6 m/s. Therefore, the momentum of the unknown particle after the collision is:
p4 = mass_unknown * (2.00*10^6 m/s)
Using the conservation of momentum, we can write the equation:
p1 + p2 = p3 + p4
Substituting the momentum expressions:
mass_proton * velocity_proton + 0 = mass_proton * (-4.00*10^6 m/s) + mass_unknown * (2.00*10^6 m/s)
Simplifying the equation:
(mass_proton * velocity_proton + mass_proton * 4.00*10^6 m/s) = mass_unknown * 2.00*10^6 m/s
Now we can solve for the mass_unknown:
mass_unknown = (mass_proton * velocity_proton + mass_proton * 4.00*10^6 m/s) / (2.00*10^6 m/s)
Substituting the given values:
mass_unknown = (1.67*10^-27 kg * 6.00*10^6 m/s + 1.67*10^-27 kg * 4.00*10^6 m/s) / (2.00*10^6 m/s)
Calculating the expression:
mass_unknown = (10.02*10^-21 kg m/s + 6.68*10^-21 kg m/s) / (2.00*10^6 m/s)
mass_unknown = 16.70*10^-21 kg / (2.00*10^6 m/s)
Final result:
mass_unknown = 8.35*10^-15 kg
Therefore, the mass of the unknown particle is approximately 8.35*10^-15 kg.