1. Newton’s Second Law
“ Forces do not cause motion. Forces cause accelerations”

2. Newton’s 2nd Law
Recall
acceleration is the rate of change of velocity – either speed or direction
ΣF is the sum of all the forces acting on an object – it is not the name of any one particular force.
Therefore, you can’t apply a net force to an object, you can only apply a force that may result in a net force.
If the sum of all the forces acting is NOT = 0, then we say there is a net force acting on an object.
Newton’s 2nd Law: a net force causes a mass to accelerate
to change its state of motion
to do something different than it’s already doing
A constant (consistent amount of) net force causes a constant acceleration
Any size net force, no matter how small, causes any size mass, no matter how big, to accelerate.

3. The Math of Newton’s 2nd Law…
a α ΣF (direct) so, for the same mass,
as ΣF changes, the a changes by the same multiple
Ex: If ΣF = 3 N causes a = 8 m/s2,
then if ΣF = 9 N on the same m, the a = _____
a α 1/m (inverse) so, for the same ΣF,
as m changes, the a changes by the inverse multiple
Ex: If m = 10 kg has an a = 4 m/s2,
then if m = 5 kg with same ΣF, the a = _____
But we can combine these 2 proportions to get
a α ΣF / m
where the constant to make the proportion an equation has a value of 1, so
a = (1) ΣF / m
or just a = ΣF / m
or more commonly, ΣF = ma

4. The Units of the ΣFnet = ma equation:
1 Newton = 1 kg1m/s2
so then if a = ΣFnet / m
the units are: = N / kg
= kgm/s2 kg
= m/s2 , which makes sense for a
or if m = ΣFnet / a
the units are: = N / m/s2
m/s2
= kg , which makes sense for m
All of this applies to Fg = mg too! See it ?!?!?
ΣFnet = ma is a more generic form, good for any force, whereas Fg = mg is only appropriate to determine the force of gravity (weight) using the acceleration due to gravity (g).

5. Friction Friction Ff is a force that acts between 2 touching objects
always parallel to the 2 surfaces in contact
always opposite the direction of (attempted) motion
so make sure you make it negative when placed in the ΣF eq’n

6. 3 Types of Friction between Solid Surfaces
1. Static - Ffs – opposes the start of motion
For any 2 given surfaces, it has a range of values:
0 < Ffs < max when motion begins
2. Kinetic (or Sliding) - Ffk – opposes the actual motion
Has a constant value for any 2 given surfaces
Contrary to popular belief, does NOT depend on
Amount of surface area touching
Relative speed between the 2 surfaces
3. Rolling – like with a ball – we don’t cover this…
There is a 4th type of friction that is not between solids… more to come soon.

7. The math of friction: Ff = μFN
so the amount of friction depends on 2 things:
1. μ is the Greek letter mu
it represents the coefficient of friction
“the nature of the 2 surfaces in contact…”
it has no units: μ = Ff / FN would cancel the only units of Newton/Newton
its value is determined experimentally by the 2 materials in contact (see chart)
Note: static friction is generally greater than kinetic friction for any 2 surfaces. This explains why it’s harder to get an object moving than it is to keep it moving! (Not due to inertia!)

8. Coefficients of Friction (approximate)
2 Surfaces in Contact
μ for static friction (μs)
μ for kinetic friction (μk)
Wood on wood
Up to .5 .2
Ice on ice
Up to .2
.03
Lubricated steel on steel
.07
Dry steel on steel
Up to .9 .6
Rubber on dry concrete
Up to 1.2 .8
Rubber on wet concrete
Up to .8 .5
Rubber on dry asphalt
Up to .75
Rubber on wet asphalt
Up to .7
.25
Teflon on Teflon
Up to .04
.04

9. (The math of friction: Ff = μFN)
(so the amount of friction depends on 2 things:)
2. FN is the normal force
Recall this is the perpendicular supporting force of a surface that’s under an object
Determined by how much the 2 surfaces are pressed together as they try to move across each other
So while FN is not the weight, the weight will often play some role here
This is a magnitude only equation – it only determines the size of the force of friction. Ff’s direction is always negative, but we don’t deal with that when using this equation.

10. Pressure… it’s different than Force
Pressure - the amount of force per unit of area
The math
Eq’n: Pressure = Force/Area or P = F/A
Units: Pascals = Newtons/meters2 or Pa = N/m2
(common units in our system are lbs/in2)
Examples
Petite woman’s high heel vs large man’s dress shoe:
He might be 2x’s as heavy (F),
but her heel might only cover 1/100th the area (A)…
so that’s 50x’s more pressure (P) from woman’s heel!
Bed of nails…
As painful as 400 nails may seem,
compare it to only 100 nails
or to only 10 nails
or to just 1 nail… Ouch!

11. 4th Type of Friction: Fluid Friction
Friction doesn’t only occur between solid surfaces –
it occurs between fluids too.
A fluid is anything that flows
so liquids and gases are both fluids.
Opposite of Solid Friction, it does depend on
Speed the object is moving
Surface area of the object
Examples: running through water
shooting a gun under water (Myth Busters)
Air resistance…see handout