The average speed of a nitrogen molecule in air is about6.70 x 10 2 m/s, and its
ID: 1667698 • Letter: T
Question
The average speed of a nitrogen molecule in air is about6.70 x 102 m/s, and its mass is about4.68 x 10-26 kg. (a) If it takes 2.10 x10-13 s for a nitrogen molecule to hit a wall andrebound with the same speed but moving in an opposite direction(assumed to be the negative direction), what is the averageacceleration of the molecule during this time interval?
m/s2
(b) What average force does the molecule exert on the wall inNewtons?
The average speed of a nitrogen molecule in air is about6.70 x 102 m/s, and its mass is about
4.68 x 10-26 kg. (a) If it takes 2.10 x10-13 s for a nitrogen molecule to hit a wall andrebound with the same speed but moving in an opposite direction(assumed to be the negative direction), what is the averageacceleration of the molecule during this time interval?
m/s2
(b) What average force does the molecule exert on the wall inNewtons?
Explanation / Answer
a.) So impulse (j) is the change in momentum and isrepresented as p (m*vf - m*vi) or asforce times time (F*t). Since you are told that the moleculerebounds to the same speed it started at (just moving in theopposite direction), you can solve for impulse j = p = pf-pi = (-6.70 x102 m/s* 4.68 x 10-26 kg) - (6.70 x102 m/s* 4.68 x 10-26 kg) = -6.2712 x10-23 Using the other definition ofimpulse (j=F*t), you can solve for force by dividing impulse bytime F = j/t = (-6.2712 x 10-23/ 2.10 x 10-13 s) = -2.98629 x10-10 N Acceleration can then easily be solved forusing Newton's law of F=ma a=F/m = (-2.98629 x 10-10 N/ 4.68 x10-26 kg) = -6.38095 x 1015m/s2 b.) The force found by dividing impulse by time will be youraverage force. When you multiply force and time, you are basicallytaking the integral of a constant force with respect to time. Whenyou divide by time, all that you are left with is the constantforce F = j/t = (-6.2712 x 10-23/ 2.10 x 10-13 s) = -2.98629 x10-10 N
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