In Example 18.7 (Section 18.3) we saw that Urms, > Vav. It is not difficult to show that this is always the case. (The only exception is when the particles have the same speed, in which case Urms = Vav.)
(a) For two particles with speeds UI and U2, show that Urms≥ Uav. Regardless of the numerical values of UI and U2. Then show that Urms > Uav. If U1≠ U2.
(b) Suppose that for a collection of N particles you know that Urms > Uav.
Another particle, with speed u, is added to the collection of particles. If the new rms and average
Speeds are denoted as Urms and Uav show that
(c) Use the expressions in part (b) to show that Urms > Uav regardless of the numerical alue of u. (d) Explain why your results for (a) and (c) together show that Urms > Uav for any collec1ion of particles if the particles do not all have the same speed.
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