A proton collides head on with a helium atom at rest. Their combined velocity after the collision is 8 x 10^5 ms^-1. Calculate the initial velocity of the proton.
*** HELP PO PLEASE!!
To calculate the initial velocity of the proton, we need to use the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the initial velocity of the proton as Vp and the mass of the proton as Mp. The helium atom is at rest, so its initial velocity is 0. The combined mass of the helium atom is Mh.
Using the conservation of momentum, we can write the equation:
Momentum before collision = Momentum after collision
(Mp * Vp) + (Mh * 0) = (Mp + Mh) * (8 x 10^5 ms^-1)
Since the mass of the helium atom is negligible compared to the mass of the proton, we can simplify the equation to:
Mp * Vp = (Mp + Mh) * (8 x 10^5 ms^-1)
Now we can substitute the known values. The mass of the proton, Mp, is approximately 1.67 x 10^-27 kg. The mass of the helium atom, Mh, is approximately 6.64 x 10^-27 kg.
1.67 x 10^-27 kg * Vp = (1.67 x 10^-27 kg + 6.64 x 10^-27 kg) * (8 x 10^5 ms^-1)
We can simplify further:
1.67 x 10^-27 kg * Vp = 8 x 10^5 ms^-1 * 8.31 x 10^-27 kg
Cross-multiplying and solving for Vp:
Vp = (8 x 10^5 ms^-1 * 8.31 x 10^-27 kg) / (1.67 x 10^-27 kg)
Vp ≈ 4 x 10^5 ms^-1
Therefore, the initial velocity of the proton is approximately 4 x 10^5 ms^-1.