Average acceleration problem

[okool]

Homework Statement

The average speed of a nitrogen molecule in air is about 6.70 multiplied by 102 m/s, and its mass is about 4.68 multiplied by 10-26 kg.

(a) If it takes 1.80 multiplied by 10-13 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in an opposite direction (assumed to be the negative direction), what is the average acceleration of the molecule during this time interval?


(b) What average force does the molecule exert on the wall?

Homework Equations

I have no idea

The Attempt at a Solution

I don't even know how to attempt

 

[Delphi51]

We can't help much without seeing some effort from you.
It is accelerated motion. Have you any formulas for accelerated motion? Look for one with a change in velocity, Δv or Vf - Vi in it because you are given those values.

 

[okool]

Obviously I've already exhausted all the resources I have and all the methods I've tried do not work or else I would not be here...the only formula I have with that is v^2-v_0^2=2a(x-x_0) but I don't have x...not sure what v and v_0 are either..

 

[Delphi51]

There is a decent set of equations here: http://hyperphysics.phy-astr.gsu.edu/hbase/acons.html

Note that it uses V and Vo instead of Vf and Vi.
It says "acceleration is the slope on the velocity graph", which means a = Δv/Δt, a nice variation on the formulas it has with the V and Vo. Think of Δv as Vf - Vi. And Δt is just t if you are starting out at time zero.

There is a nice set of formulas and their derivations here:
http://en.wikiversity.org/wiki/Motion_-_Kinematics#Motion_with_constant_acceleration

 

[asteriatic]

this problem.

As a scientist, it is important to have a strong foundation in basic physics principles and equations in order to solve problems like this. In this case, we can use the equation for average acceleration:

Average acceleration = (final velocity - initial velocity) / time interval

(a) To find the average acceleration of the nitrogen molecule, we first need to calculate the final velocity. Since the molecule rebounds with the same speed in the opposite direction, its final velocity will be -6.70 x 10^2 m/s. The initial velocity is 6.70 x 10^2 m/s, and the time interval is 1.80 x 10^-13 s. Plugging these values into the equation, we get:

Average acceleration = (-6.70 x 10^2 m/s - 6.70 x 10^2 m/s) / (1.80 x 10^-13 s)

= -2 x 10^15 m/s^2

Therefore, the average acceleration of the nitrogen molecule during this time interval is -2 x 10^15 m/s^2. This means that the molecule is decelerating at a very high rate.

(b) To find the average force exerted by the molecule on the wall, we can use Newton's second law of motion:

Force = mass x acceleration

The mass of the nitrogen molecule is 4.68 x 10^-26 kg, and we just calculated the average acceleration to be -2 x 10^15 m/s^2. Plugging these values into the equation, we get:

Force = (4.68 x 10^-26 kg) x (-2 x 10^15 m/s^2)

= -9.36 x 10^-11 N

Therefore, the average force exerted by the nitrogen molecule on the wall is -9.36 x 10^-11 N, which means that the molecule is exerting a very small force on the wall.

In conclusion, by using basic physics principles and equations, we were able to find the average acceleration and force of a nitrogen molecule bouncing off a wall. It is important for scientists to have a strong understanding of these principles in order to solve problems and make accurate calculations.