A proton of mass m undergoes a head on collision with a stationary atom of mass 13m. If the initial speed of the proton is 485 m/s, find the speed of the proton after the collision.
485 m = m u + 13 m v
now you have to know if the collision is elastic or if they proton sticks to the atom
If they stick
then u = v
if elastic
then (1/2) m(485^2) = (1/2) m u^2 + (1/2)(13 m) v^2
Given:
M1 = m, V1 = 485 m/s.
M2 = 13m, V2 = 0.
V3 = Velocity of proton(M1) after collision.
Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V4.
m*485 + 13m*0 = m*V3 + 13m*V4,
485m + 0 = m*V3 + 13m*V4,
Divide both sides by m:
485 = V3 + 13V4,
V3 = (V1(M1-M2) + 2M2*V2)/(M1+M2).
V3 = (485(m-13m) + 26m*0)/14m = -5820m /14m = -416 m/s.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum before and after a collision remains constant if no external forces are involved.
The momentum of an object is given by its mass multiplied by its velocity:
Momentum = mass × velocity
Initially, only the proton is in motion, so the total initial momentum is:
Initial momentum = mass of the proton × initial velocity of the proton
After the collision, both the proton and the atom will be in motion. Let's assume the final velocity of the proton is v_p and the final velocity of the atom is v_a.
The total final momentum is:
Final momentum = (mass of the proton × final velocity of the proton) + (mass of the atom × final velocity of the atom)
Using the principle of conservation of momentum, we can set the initial momentum equal to the final momentum:
Initial momentum = Final momentum
Or,
mass of the proton × initial velocity of the proton = mass of the proton × final velocity of the proton + mass of the atom × final velocity of the atom
Now, let's plug in the given values. The mass of the proton is 'm', the initial velocity of the proton is 485 m/s, and the mass of the atom is 13m.
m × 485 = m × v_p + 13m × v_a
Simplifying this equation, we get:
485 = v_p + 13v_a
Now, we need some additional information to find the final velocity of the proton or the atom. The problem statement does not provide any information about the collision itself, such as whether it is elastic or inelastic.
In an elastic collision, both kinetic energy and momentum are conserved. The formulae for an elastic collision are more complex and require knowing the masses of the particles involved. If the collision is elastic, we would need additional information about the masses and any potential energy loss to calculate the final velocities.
In an inelastic collision, momentum is conserved but kinetic energy is not. In this case, the final velocity of the proton or the atom depends on the given masses and their initial velocities, but cannot be determined without more information.
Therefore, without further information about the type of collision, we cannot determine the final velocity of the proton or the atom.