Newton’s Second Law

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 ΣFis 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 αΣF (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 α1/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 αΣF/ 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 = kg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 anyforce, 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)

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