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MCAT physics equations

### What assumption do we make with the BIG 5 equations? What are the 3 most frequently used equations?

That acceleration is constant (uniformly accelerated motion)

2. Missing d

3. Missing vf (v final, v)

5. Missing t

### For projection motion, we assume that the downward direction is...

NEGATIVE direction.

DOWNWARD = NEGATIVE DIRECTION.

###
PROJECTILE MOTION - Horizontal Motion

(in the x-direction)

Give the equation for:

1. Displacement

2. Velocity

3. Acceleration

1. d = v₀t (in the x-direction)

2. v₀x = vx (velocity is CONSTANT in the x-direction!!)

v₀x = v₀cosθ₀

3. ax = 0 (acceleration in the x-direction is ZERO!)

###
PROJECTILE MOTION - Vertical Motion

Give the equation for:

1. Displacement

2. Velocity

3. Acceleration

1. y = v₀yt + ½(-g)t² (in the y-direction)

2. vy = v₀y + (-g)t (in the y-direction)

v₀y = v₀sinθ₀

3. ay = -g (accerleration in the y-direction)

### What is the force due to gravity acting PARALLEL to the inclined plane? (sliding down the plane)

F = mgsinθ

θ = angle between incline and horizontal

### What is the force due to gravity acting PERPENDICULAR to the inclined plane?

F = mgcosθ

θ = angle between incline and horizontal

### Torque (τ)

τ = rFsinθ

r = distance from pivot point to F

F = force applied (Fapp)

θ = angle between r and F

### What does it mean to be in ROTATIONAL EQUILIBRIUM?

τcw = τccw

∴τnet = 0 (net torque = 0)

clockwise torque = counterclockwise torque

###
Is the inertia greater for a solid sphere or a hollow sphere?

If the same net torque was applied to each sphere, which would spin faster?

Hollow sphere has GREATER inertia than solid sphere.

Solid sphere would spin faster because it has less inertia!

### Work (W)

W = Fdcosθ

Unit = Joules (J)

F = force applied

d = displacement

θ = angle between F and d

Wmax occurs when θ = 0

### Conservation of Energy (when friction is taken into account)

KE₀ + PE₀ - Wf = KE + PE

Wf = work done by FRICTION!

### During a collision (short duration of interaction between 2 objects)...

1. Total momentum (p) is ALWAYS conserved!

2. KE is NOT always conserved!

### 1. Elastic collision

(think of 2 pool balls)

1. p is conserved

2. KE is ALSO conserved!

∴p₀ = pf

∴KE₀ = KEf

### 2. Inelastic collision

(think of a car crash)

1. p is conserved

2. KE is NOT conserved: one object becomes deformed; loss in energy

m₁v₀₁ + m₂v₀₂ = m₁v₁' + m₂v₂'

### 3. Perfectly inelastic collision

(think of 2 objects becoming stuck together)

1. p is conserved

2. objects get stuck together and move with the same v' (final velocity!)

m₁v₀₁ + m₂v₀₂ = (m₁ + m₂)v'

### During the collision, there is a short duration of interaction between the 2 objects so we can apply...

Newton's 3rd Law: action-reaction pair!

F₁₂ = F₂₁

### Pressure (P)

F/A

F = perpendicularly applied force

A = area

Unit = N/m₂ = Pascal (Pa)

1atm = 100 kPa

### Gauge Pressure (Pg)

Pressure felt at a particular depth = hydrostatic pressure

Pg = ρ g D

ρ = density of fluid

g = accl due to gravity

D = depth

### Total hydrostatic pressure (Ptotal)

Ptotal = Patm + Pg

Patm = pressure at the surface

Pg = gauge pressure

###
Buoyant Force (Fb)

*Archimedes Principle

Fb = ρ V g

ρ = density of fluid

V = Vsub = volume of object submerged = volume of fluid displaced

g = accl due to gravity

### Archimedes Principle

There is an upward acting force on an object that is rising, sinking, floating, or completely submerged in a fluid. This force is called the buoyant force (Fb) and it equals the weight of the fluid displaced.

### Case 2: Object is completely submerged and reaches the bottom of the tank

Fnet = Fn + Fb - Fg = 0

∴Fn = Fg - Fb

ρ object > ρ fluid

*Fn = normal force: weight of the object inside the fluid = apparent weight

### Case 4: Object is floating on the surface

Fnet = Fb - Fg = 0

∴Fb = Fg (= weight of object)

ρ V g = m g

ρ V = m = ρ₀V₀ (object)

ρ fluid > ρ object

V/V₀ = ρ₀/ρ = specific gravity

### What are the 4 conditions to have an IDEAL FLUID?

1. No or negligible viscosity.

2. Laminar flow (continuous, streamline flow).

3. Fluid must be incompressible.

4. Flow must be continuous.

### Bernoulli's equation (ideal fluid)

describes ideal fluid flow through a pipe

*looks similar to conservation of energy equation

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

*pgh is NOT gauge pressure, but the PE of the fluid at a certain height, h.

### Apply Bernoulli's equation to a HORIZONTAL PIPE.

Since h₁ = h₂, the equation looks like this:

P₁ + ½ρv₁² = P₂ + ½ρv₂²

### For a horizontal pipe, describe the relationships between pressure and velocity.

1. If v₁ > v₂, then P₁ < P₂.

2. If v₂ > v₁, then P₂ < P₁.

### Objects will move from _______ pressure to _______ pressure. Think of an example.

High P --> Low P

Think of air planes and the lift force!

### Coulomb's law (Electric force: force on a charged particle)

F = kQq/r²

k = Coulomb's constant = 9 ∗10⁹ Nm²/C²

Q = charge that applies force

q = test charged being acted on by Q

r = distance between 2 charges

Positive F = repelling force

Negative F = attractive force