A narrow stream of oxygen molecules, each of mass 5.3 × 10⁻²⁶ kg, hits a flat plate of area 2.0 cm²…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A narrow stream of oxygen molecules, each of mass kg, hits a flat plate of area . Every second, molecules strike it at m/s, at to the normal of the plate. Each one bounces off elastically, like a ball from a wall. Find the force on the plate and the pressure on it.
Need a reminder? The key ideaShow
A molecule bouncing off a wall gives it the momentum in each hit, and hits it times each second. For a gas:
where is the total translational kinetic energy.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. kg, m/s at to the normal, hits each second, .
Step 1. One hit. The normal part of the velocity is . It reverses, so the plate gets kg m/s.
Step 2. Force. Momentum given each second: N.
Step 3. Pressure. Pa kPa.
Answer: N and Pa.
Watch out. The part of the velocity along the plate does not change, so it gives the plate no push. Using instead of makes the force too large by a factor .
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