Question

A surface is bombarded by particles, each of mass small 'm', which have velocity

normal to the surface. On average, n particles strike unit area of the surface each second
and rebound elastically. What is the pressure on the surface?

A. nmv
B. 2nmv
C. nmv²
D. 1/2nmv²​

Answer 1

B. 2nmv

Step-by-step explanation:

Pressure is force over area.

P = F / A

Force is mass times acceleration.

F = ma

Acceleration is change in velocity over change in time.

a = Δv / Δt

Therefore:

F = m Δv / Δt

P = m Δv / (A Δt)

The total mass is nm.

The change in velocity is Δv = v − (-v) = 2v.

A = 1 and Δt = 1.

Plugging in:

P = (nm) (2v) / (1 × 1)

P = 2nmv