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

A.     Mass and weight are not interchangeable; weight is a force (gravitational force exerted on mass)

B.     w = mg (weight = mass*gravitational acceleration), weight is in newtons (N)

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

A.     FN = mgcosθ

B.     w = mg

C.    F ǁ to plane = mgsinθ

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

A.     Pulleys change direction of tension (FT) of the rope that pulls on the object that the rope attaches to

B.     Pulleys can also decrease the force necessary to lift an object (Σ↑FT = m*g)

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

MCAT Study Guide Physics - Kim Matsumoto


More MCAT Study Guide Physics

1.

Ch. 2 Kinematics

2.

Ch. 3 Force

3.

Ch. 4 Center of Mass + Torque

4.

Ch. 5 Work, Power and Energy

5.

Ch. 6 Hydrodynamics

6.

Ch. 7 Electricity

7.

Ch. 8 Electrical Circuits

8.

Ch. 9 Simple Harmonic Motion

9.

Ch. 10 Sound Waves

10.

Ch. 11 Reflection + Refraction

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