The average speed of a nitrogen molecule in air is about 686 m/s, and its mass is 4.85×10-26 kg. If it takes 3.78×10-13 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in the opposite direction.
a)what is the magnitude of the average acceleration of the molecule during this time interval?
b)What average force does the molecule exert on the wall?
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To solve this problem, we can use the following equations:
a) Average acceleration (a) can be calculated using the equation:
a = (change in velocity) / (time interval)
b) Average force (F) can be calculated using Newton's second law:
F = (mass) x (acceleration)
We are given the average speed of the nitrogen molecule, the time interval for it to rebound, and its mass. Let's calculate the answers step by step:
a) First, let's find the change in velocity using the average speed. Since the molecule rebounds with the same speed but moving in the opposite direction, the change in velocity is:
change in velocity = 2 x average speed = 2 x 686 m/s = 1372 m/s
Now we can calculate the average acceleration by dividing the change in velocity by the time interval:
a = (change in velocity) / (time interval) = 1372 m/s / (3.78×10-13 s)
(Note: divide the change in velocity by the given time interval)
b) With the average acceleration calculated, let's now calculate the average force exerted on the wall. We will use Newton's second law, F = (mass) x (acceleration):
F = (mass) x (acceleration) = (4.85×10-26 kg) x (acceleration)
(Note: multiply the given mass by the calculated acceleration)
Now, substitute the calculated value of acceleration into the equation:
F = (4.85×10-26 kg) x (1372 m/s / (3.78×10-13 s))
By solving this equation, we can find the average force exerted by the nitrogen molecule on the wall.