Physics

A · B = [A][B]cosθ

You get a scalar product.

A x B = [A][B]sinθ

You get a vector product.

• Displacement: includes the magnitude and direction of only the net change from start to finish
• Distance: a scalar quantity that takes into account to length traveled

• Velocity: magnitude of measured rate of change of displacement per unit of time (vector quantity)
• Speed: rate of actual distance traveled divided by a given unit of time

v = lim(as Δt → 0) Δx/Δt

kg·m/s²

Newton's second law of thermodynamics

• F = ma
• m: mass
• a: acceleration

F_g = (Gm₁m₂)/(r²)

• G: 6.67x10^-11 N·m²/kg²
• r: distance between the two object of m₁ and m₂

Exists between two objects at rest. It is an equal and opposite force acting on object.

0 ≤ f_s ≤ μ_sN

• μ_s: coefficient if static friction
• N: normal force (component of force perpendicular to the plan between object on at rest and surface)

Exists between two objects sliding along a surface. 

f_k = μ_fN

• μ_f: coefficient if kinetc friction
• N: normal force (component of force perpendicular to the plan between object on at rest and surface)

μ_s > μ_k

A measure of gravitational on an objects mass.

F_g = mg

g: 9.8 m/s²

A = Δv / Δt

v = v₀ + at

x = v₀t + at²/2

v² = v₀² + 2ax

x = vt

• F_g,ll = mgsinθ = ma
• F_{g,(perpendicular)} = mgcosθ = N

F_c = mv²/r

(centripetal acceleration)

• Note:
• Centrifugal force is antiparrallel to centripetal force

Exists only when the vector sum of all forces is 0

Fixed pivot point

Application of force at some distance from the fulcrum.

τ = r x F = (r)(F)sinθ

r: distance of applied force from fulcrum

• Counterclockwise (-)
• Clockwise (+)

• n = F_{g,seesaw + blocks}
• N = (m_seesaw + m₁ + m₂)g

Kinetic Energy: energy of motion

K = (1/2)mv²

It is NOT related to velocity, but it IS related to speed.

The faster something is, the more kinetic energy it has, hense K = (1/2)mv²

Potential Energy: energy with the potential to do work of stationary objects

U = (1/2)mgh

When a spring is stretched from it's equilibrium length, the spring has spring potential energy determined by the following equation:

U = (1/2)kx²

• k: spring constant (high k means spring is stiffer)
• x: magnitude of displacement from the equilibrium length

The sum of the objects potential and kinetic energy.

E = U + K

This is if the system is conserved (no energy leaves system due to things like friction, heat, light)

• Conservative Forces: those that are path independent and do not dissipate energy
• -gravitational
• -electrostatic

If the net change is 0, then the forces are conserved.

• Forces that dissipate mechanical energy as thermal or chemical energy:
• -friction
• -air resistance

ΔE = ΔU + ΔK = 0 = W

(work is measured in J)

W_{nonconservative} = ΔE = ΔU + ΔK

(work is measured in J)

Work: it is not a form of energy, but the process by which energy is transferred from one system to another

W = F · d = Fdcosθ

θ: the angle between force vector and displacement vector

(work is measured in J)

In a P vs V diagram, this is when no work is done. This means volume does not change, ONLY pressure.

Isobaric: when pressure is constant, and only volume changes.

W = PΔV

The area under a P vs. V line is work.

(work is measured in J)

It would be the area under the curve. Try cutting it up into shapes who's areas you know and calculating the area.

(work is measured in J)

• (+): work is done by a system
• (-): work is done on a system

(work is measured in J)

Power: rate at which energy is transferred from one system to another.

P = W/t = ΔE/t

(work is measured in J)

Mechanical application for relating energy and work. The net work done by forces acting on an object result in equal change in the objects kinetic energy:

• W_net = ΔK = K_f - K_i
• Knowing the magnitude of forces acting on an object allows you to calculate the work.

(work is measured in J)

Mechanical Advantage: ratio of magnitudes of the force exerted on an object by a simple machine (F_out) to the force applied on a simple machine (F_in).

Mechanical Advantage = F_out/F_in

Efficiency = W_out/W_in = [(load)(load distance)]/[(effort)(effort distance)]

• load: weight (mass x gravity)
• load distance: object height lifted
• effort: force required to lift crate
• effort distance: how much rope must be pulled (height raised x number of pulleys)

You don't always get 100% efficiency because of nonconservative forces.

• Inclined plane
• Wedge
• Pulley
• Liver
• Wheel and axle
• Screw

The force used to pull up the pulley is F = ma. The tensions on the pulley cancel force done by gravity if it was still but increase as tension increases, giving:

F_net = ma = xT - mg

x: number of ropes used