The average speed of a nitrogen molecule in air is about 6.70×102 m/s, and its mass is 4.68×10-26 kg. (a) If it takes 3.00×10-13 s for a nitrogen molecule to hit a wall and rebound with the same speed but
moving in the opposite direction, what is the average acceleration of the molecule during this time
interval?
(b) What average force does the molecule exert on the wall?
(c) What is the total force exerted
on the wall if it is struck by 1015 such molecules all at once?

a)   a = 3.06 10¹⁵ m / s , b)    F= 1.43  10⁻¹⁰ N, c)    F_total = 14.32 10⁻²⁶ N

Explanation:

This exercise will average solve using the moment relationship.

a ) let's use the relationship between momentum and momentum

          I = ∫ F dt = Δp

          F t = m - m v₀

          F = m (v_{f} -v₀o) / t

 in the exercise indicates that the speed module is the same, but in the opposite direction

          F = m (-2v) / t

if we use Newton's second law

          F = m a

we substitute

            - 2 mv / t = m a

            a = - 2 v / t

let's calculate

            a = - 2 4.59 10²/3 10⁻¹³

            a = 3.06 10¹⁵ m / s

b)      F= m a

        F= 4.68 10⁻²⁶ 3.06 10¹⁵

        F= 1.43  10⁻¹⁰ N

c) if we hit the wall for 1015 each exerts a force F

            F_total = n F

            F_total = n m a

            F_total = 10¹⁵  4.68 10⁻²⁶ 3.06 10¹⁵

            F_total = 14.32 10⁻²⁶ N

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