MCAT Study Guide Physics Ch. 3 – Dynamics 2017-08-15T06:45:05+00:00

## I.          3.1:  MASS, FORCE, AND NEWTON’S LAWS:  study of dynamics

### A.     Force

Push or pull exerted by one object on another (i.e. tension, friction, gravitational electrostatic, air resistance)

### B.     Newton’s laws

1.     1:  An object at rest stays at rest, an object in motion stays in motion (if a = 0, v is constant; no net force, no acceleration)

a)     Law of inertia

b)     Mass of an object is the quantitative measurement of its inertia

2.     2:  F = m*a

[kg*m/s2 = N]

a)     F refers to net force, or the sum of all forces

3.     3:  With every force, there is an equal and opposite force

a)     If object 1 exerts a force, F1-on-2, on object 2, object 2 will exert a force, F2-on-1, on object 1

b)     These forces are equal but in opposite directions; are called an action-reaction pair

### C.    Things to remember about Newton’s laws:

1.     1st law vs 3rd law:  1st law implies forces are on a single object; 3rd law implies each force must be on a different object (on the objects of the action-reaction pair)

2.     3rd law:  if 2 forces are equal and opposite, it does not automatically mean they are an action-reaction pair; these forces have to act on each other in order to be this

3.     3rd law:  although the 2 forces must be equal, their effects are not necessarily equal (remember, if the mass of one is different, its acceleration will be different too)

## II.          3.2:  NEWTON’S LAW OF GRAVITATION

### C.    Newton’s law of gravitation:

1.     Every object exerts gravitational pull on every other object

a)     Is proportional to the product of the object’s masses

b)     Inverse-square law:  inversely proportional to the square of the distance between them (between the centers of the objects)

c)     Constant of proportionality is G (universal gravitational constant)

d)     Fgrav = G(Mm)/r2    (r = distance between centers)

e)     Combine  Fgrav = G(Mm)/r2 with w = mg (w = Fgrav):

(1)   mg = G(Mm)/r2

(2)   g = GM/r2 → the value of gravitational acceleration on earth = 10 m/s2

## III.          3.3:  FRICTION

### A.     Normal force (N, FN)

The opposite force exerted against an object exerting a force (usually gravitational); EX – book on table

1.     Action-reaction pairs:

a)     Reaction force to Ftable-on-book is Fbook-on-table

b)     Reaction force to to Fearth-on-book is Fbook-on-earth

c)     Reaction force to Ftable-on-book is not Fearth-on-book

2.     Remember:  action-reaction pairs always act on different objects!!

3.     Normal force is the perpendicular component of the contact force exerted by a surface on an object

4.     FN = m*a  (usually mass*gravitational acceleration)

### B.     2 types of friction

1.     Kinetic (sliding) friction – the mechanical friction between 2 surfaces due to roughness

a)     Coefficient of kinetic friction (μk) – depends on what the surfaces are made of, experimentally determined, no units

b)     Ff =  μkFN  → force of kinetic friction, not vector! Magnitude only

(1)   The direction of kinetic friction is always parallel to surface and opposite of velocity

2.     Static friction – the attraction between electrical atoms of 1 surface with those of another

a)     Maximum coefficient of static friction (μs) → on MCAT, this is always > than μk!

(1)   Starting to push something is always harder than continuing to push it

b)     Ff, max =  μsFN   → this is the max, because any force less than max will do nothing

(1)   If Ff, max = 200 N, and you exert 100 N, the static friction will only be 100 N

## IV.          3.4:  INCLINED PLANE

### D.    EX:

Block mass m = 4 kg is placed at the top of a frictionless ramp of incline angle 30º and length 10m.

1.     What is the block’s acceleration down the ramp?

a)     F = m*a; a = F/m

b)     a = mgsinθ/m = gsinθ = (10 m/s2)(0.5) = 5 m/s2

2.     How long will it take for the block to slide to the bottom?

a)     T = ?; a = 5; d = 10 v0 = 0

b)     d = v0t + ½at2

c)     10 = 0 + ½(5)t2

d)     10 = 2.5t2

e)     4 = t2; t = 2 s

## V.          3.5:  PULLEYS

### C.    EX:

Multiple pulley system

1.     To pull the plank up at constant speed, how much force is needed?

2.     If v is constant, a=0, therefore net force = 0

3.     Therefore, Σ FT↑ = M*a

4.     FT↑ = FT↓

5.     6FT = M*g

### D.    EX:

1 pulley, 2 masses:  if m = 5kg and M = 10 kg what is acceleration when released from rest?

1.     Draw a force diagram

2.     Choose direction to call (+); usually which direction the objects will move

3.     Find FNET  and set it equal to m*a

4.     Figure out the m*a for each

5.     FNET(m) = m*a = FT – m*g

6.     FNET(m) = M*a = M*g – FT

7.     Add equations together:

a)     M*g – m*g = M*a + m*a

b)     g(M – m) = a (M + m)

c)     a = G(M – m)/(M + m)

d)     a = 5g/15 = g/3

## VI.         3.6:  SUMMARY OF FORMULAS:

• FNET = m*a
• w = m*g
• Fgrav = G*Mm/r2 → w = Fgrav = m*g → m*g = G*Mm/r2 g = GM/r2
• Ff = μkFN
• Ff, max = μsFN s, max > μk)
• Fgrav, ‖ to inclined plane = mg*sinθ # 10.

#### Ch. 11 Reflection + Refraction

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