Nitrogen gas molecules, which have mass 4.65×10−26 kg, are striking a vertical container wall at a horizontal velocity of positive 440 m/s. 5.00×1021 molecules strike the wall each second. Assume the collisions are perfectly elastic, so each particle rebounds off the wall in the opposite direction but at the same speed. (a) What is the change in momentum of each particle? (b) What is the average force of the particles on the wall?
If you could also explain this as you go that would be fantastic! Thank you :)
Sure! Let's break down the problem step by step.
(a) In order to find the change in momentum of each particle, we need to use the formula for momentum:
Momentum = mass × velocity
From the given information, we know that the mass of each nitrogen gas molecule is 4.65×10−26 kg and the velocity is 440 m/s. Plugging these values into the formula, we can calculate the momentum of each particle.
Momentum = (4.65×10−26 kg) × (440 m/s)
Calculating this expression, we find:
Momentum = 2.046 × 10−23 kg·m/s
So the change in momentum of each particle is 2.046 × 10−23 kg·m/s.
(b) To find the average force of the particles on the wall, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
Force = rate of change of momentum
We know from the problem that 5.00×1021 particles strike the wall each second. Therefore, the rate of change of momentum can be calculated by multiplying the change in momentum of each particle (which we calculated in part (a)) by the number of particles that strike the wall per second.
Rate of change of momentum = (2.046 × 10−23 kg·m/s) × (5.00×1021 particles/s)
Calculating this expression, we find:
Rate of change of momentum = 1.023 × 10−1 kg·m/s^2
Therefore, the average force of the particles on the wall is 1.023 × 10−1 N (Newton).
So, the change in momentum of each particle is 2.046 × 10−23 kg·m/s, and the average force of the particles on the wall is 1.023 × 10−1 N.
I hope that helps! Let me know if you have any further questions.
Δp= m•Δv =m•[v –(-v)] = 2mv =2• 4.65•10^-26•440 =4.1•10^-23 kg•m/s.
F•Δt = Δp,
Fₒ = Δp/ Δt =4.1•10^-23/1 =4.1•10^-23 N.
F=N• Fₒ = 5•10^21•4.1•10^-23=0.2 N