PHYS 1210 - Energy and Energy Resources (Chapter 7)

Work is defined as

Force x displacement

Work done is zero when

Force is perpendicular to displacement

Energy is defined as

Ability to do work

The SI unit of work is

Joule

Positive work is done when

Force is along displacement

Negative work is done when

Force and displacement are opposite

Kinetic energy depends on

Mass and velocity

Potential energy depends on

Height and mass

Work-energy theorem states

Net work = change in kinetic energy

Mechanical energy is

KE + PE

Conservative Forces ….

Depend only on initial and final positions

Friction is a…

Non-conservative force

Mechanical energy is conserved when…

Only conservative forces act

Power is defined as

Work/time

If work done is positive, the speed of object…

Increases

A force of 50 N moves an object 10 m in the same direction. Work done is…

500 J

A 2 kg object moves with velocity 3 m/s. Its kinetic energy is…

9 J

A 5 kg object is lifted to a height of 10 m(g = 10 m/s²). Potential energy is…

500 J

A machine does 200 J of work in 4 seconds. Power is…

50 W

A spring has k = 200 N/m and is compressed by 0.1 m. Energy stored is…

1 J

What is Energy?

The ability to do work

What is Work?

The energy transferred to or from a system by a force that acts on it

What is the Dimensional Formula for Work?

[M¹L² T^-2 ]

__ J = __ Nm = __ kg m²/s²

1 ; 1 ; 1

What is Work? (formula)

Force x Displacement

Formula for Work Done

W = F x d = ____

W = Fdcosθ

Components of Work Done Formula:

What is W?

Work

Components of Work Done Formula:

What is F?

Applied Force

Components of Work Done Formula:

What is d?

Displacement

Components of Work Done Formula:

What is θ?

The angle

What is Positive Work?

0° < θ > 180°

When the force and displacement are in the same direction

What is Negative Work?

90° < θ > 180°

When the force and displacement are in opposite directions

What is Zero Work?

(θ = 90°)

When the force is perpendicular to the displacement or when there is no displacement

What is Net Work?

The sum of work done by all external forces

Formula for Net Work

W_net = F_netdcosθ

Formula for Kinetic Energy

KE = 1/2 mv²

Components of Kinetic Energy Formula:

What is m?

Mass (kg)

Components of Kinetic Energy Formula:

What is v?

Velocity (m/s)

What is the SI unit of Kinetic Energy?

Joule

Formula for Potential Energy

PE = mgh

Components of Potential Energy Formula:

What is m?

Mass (kg)

Components of Potential Energy Formula:

What is g?

9.8 N/kg

Components of Potential Energy Formula:

What is h?

Height (m)

Formula for Mechanical Energy

E_mec = E_kin + E_pot

E_{mec = 1/2mv² + mgh}

Formula for Work-Energy Theorem

W_total= K = ½ mv_f² - ½ mvi²

A ___ force is a force whose work depends only on the object’s initial and final positions, not on the path taken

conservative

Examples of Conserved Force

Gravity (dropping a ball), elastic spring forces (trampolines), and electrostatic forces

A ___ force is one for which work depends on the path

nonconservative

Example of a Nonconservative Force

Friction

Mechanical energy remains ___ when conservative forces are acting on the system

conserved

Conservation of energy equation when only conservative force is acting on the system:

KEi + PEi = KEf + PEf

Conservation of energy equation when conservative and nonconservative force is acting on the system:

KEi + PEi + Wnc = KEf + PEf

What are these examples of?

Gravitational Force, Spring Force, Electromagnetic Force

Conservative Force

What are these examples of?

Friction, Air Resistance, Viscous Force

Nonconservative Force