Calculating Air Resistance for a 5kg Rock Falling at 7m/s2

[mike2007]

A 5kg rock falls with an acceleration of 7m/s2. What is the magnitude of the force of air resistance acting on the rock at this instant?

 

[Doc Al]

First identify all the forces acting on the rock, then apply Newton's 2nd law.

 

[mike2007]

this is what i did so far but i do not know how to get the air resistance.
F = ma
m = 5kg
a = 7m/s
F= 35N
Is that gravitational acceleration? and how do i get air resistance

 

[mike2007]

the only two forces are acceleration due to gravity which is 9.8m/s downdard and air resistance which is ?

 

[Doc Al]

No, that's not gravitational acceleration--the acceleration due to gravity (g) is 9.8 m/s^2 downward.

What you've done--whether you realize it or not--is apply Newton's 2nd law to calculate the net force on the rock. Now you have to identify the individual forces that act on the rock. Air resistance is one of those forces; what's the other?

 

[Doc Al]

the only two forces are acceleration due to gravity which is 9.8m/s downdard and air resistance which is ?

Let's phrase that more precisely: There are two forces acting on the rock:
(1) gravity, which acts down; what's that equal to?
(2) air resistance; which way does that force act?

Now set up an equation adding these two forces to get the net force, then solve for the force of air resistance. Remember: direction, and thus signs, matter!

 

[mike2007]

Ok i see. Here goes
Net force = 35N
gravitational force
F= ma
= 5*9.81
=49.05N

air resistance = 49.05-35
= 14.05N upward
?? am i even more lost now?

 

[Doc Al]

You have it exactly right.

I recommend that for problems like this you draw yourself a diagram showing all the forces. In this case, you'd have the gravitational force (mg) going down and the air resistance (call it R) going up. Since the net force is ma = 35N down, you would have:

ma = -mg + R
-35N = -49.05N + R

so: R = 49.05N - 35N = 14N

Note that I use negative for down and positive for up.