A particle of mass m = 1 0 − 6 kg moves inside a sphere of radius R with velocity v = 100 m / s , elastically striking its walls. The particle velocity forms an angle α = 3 0 ∘ with the radius drawn t

Question

A particle of mass m = 1 0 − 6 kg moves inside a sphere of radius R with velocity v = 100 m / s , elastically striking its walls. The particle velocity forms an angle α = 3 0 ∘ with the radius drawn to the impact point. What is the average force acting per unit area of a sphere (in SI units) if there are N = 100 such particles per unit volume? The particles do not collide with each other.

TestHub · Accepted Answer

Each particle travels a chord 2 R cos α between hits: hit rate 2 R c o s α v ​ , momentum transfer per hit 2 m v cos α ⇒ force per particle R m v 2 ​ . Total force = N × 3 4 ​ π R 3 × R m v 2 ​ ; pressure = 4 π R 2 F ​ = 3 N m v 2 ​ . P = 3 100 × 1 0 − 6 × 1 0 4 ​ = 0.33 N/m 2

Physics - Center of Mass Question with Solution | TestHub

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