A beam of hydrogen molecules is directed toward a wall, at an angle 32∘ with the normal to the wall. Each molecule in the beam has a speed of 1.0 km/s and a mass of 3.3×1024g. The beam strikes the wall over an area of 2.0 Cm2, at a rate of 4.0×1023 molecules per second. What is the beam's pressure on the wall?
11 kPa
We need the pressure on that 2 cm2 patch on the wall. But by definitions,
Pressure P=[forcearea]per molecule×number of molecules.
=[rate of change of momentumarea]per molecules×N
[m→vfinal−m→vinitialarea×time]per molecules×N
=[2×(3.3×10−27 kg)×1000 m/s×cos32∘(2×10−4m2)×1s]×(4×1023)Pa
=11.2×103 Pa≈11 kPa.