The average speed of a Nitrogen molecule in air is about 858 m/s, and its mass is about 4.68 × 10−26 kg.
If it takes 2.6 × 10−13 s for a nitrogen
molecule to hit a wall and rebound with
the same speed but in the opposite direc-
tion, what is the magnitude of the average
acceleration of the molecule during this time interval?
see other post.
To find the magnitude of the average acceleration of the nitrogen molecule during the given time interval, we can use the equation for average acceleration:
Average acceleration = (final velocity - initial velocity) / time taken
In this case, the final velocity is the opposite of the initial velocity, and the mass of the nitrogen molecule is required.
First, let's find the initial velocity of the nitrogen molecule. Given that the average speed of the molecule is 858 m/s, the initial velocity would be half of the average speed since the molecule rebounds with the same speed but in the opposite direction:
Initial velocity = average speed / 2 = 858 m/s / 2 = 429 m/s
Next, we need to determine the final velocity of the molecule. Since the molecule rebounds with the same speed but in the opposite direction, the final velocity would be the negative of the initial velocity:
Final velocity = - initial velocity = -429 m/s
Given the time taken for the nitrogen molecule to hit the wall and rebound is 2.6 × 10^(-13) s, we have all the required values to calculate the average acceleration.
Average acceleration = (final velocity - initial velocity) / time taken
= (-429 m/s - 429 m/s) / (2.6 × 10^(-13) s)
= -858 m/s / (2.6 × 10^(-13) s)
To simplify this calculation further, we'll express -858 m/s in scientific notation:
-858 m/s = -8.58 × 10^2 m/s
Substituting these values into the equation, we get:
Average acceleration = (-8.58 × 10^2 m/s) / (2.6 × 10^(-13) s)
Now, to divide these two quantities with the same base but different exponents, we subtract the exponents and keep the base:
Average acceleration = -8.58 × 10^2 / 2.6 × 10^(-13-1)
Finally, simplifying the expression:
Average acceleration = -8.58 × 10^2 / (2.6 × 10^(-14))
= -8.58 × 10^2 × (10^14 / 2.6)
= -8.58 × 10^2 × 3.85 × 10^13
= -33.093 × 10^15 m/s^2
Therefore, the magnitude of the average acceleration of the nitrogen molecule during this time interval is approximately 33.093 × 10^15 m/s^2.