The change in momentum of the particle upon hitting the
wall is expressed as:
Change in momentum = Δp = 2 m v cosθ
where m = 3.3E-24 g = 3.3E-27 kg, v = 1.0 km/s = 1000 m/s,
θ = 55°
Dividing both sides by Δt:
Δp / Δt = 2 (Δm / Δt) v cosθ
By definition, the force applied to a particle is equal
to the change in momentum per second of the particle (by Newton's Second Law).
Therefore:
Force on wall = Δp / Δt = 2 (Δm / Δt) v cosθ
We can get or calculate the value of (Δm / Δt) from the given data. That is:
Δm / Δt = m * particles per second = (3.3E-27 kg/particle)
(1023 particle/s)
Δm / Δt = 3.3759 E-24 kg/s
Therefore the force is:
Total force on wall = 2 (3.3759 E-24 kg/s) (1000 m/s)
cos(55)
Total Force on wall = 1.494E-22 N
Pressure = Total Force / Area = 1.494E-22 N / 2.0E-4 m^2
Pressure = 7.47E-19 Pascals
Therefore the pressure is 7.47*10^-19 Pa.
