Energy in Mechanical Day 1

Energy• Energy is defined as the ability to do work.

• Energy like work is also measured in Joules.

• Work is the means by which energy changes forms.

• Mechanical energy can be divided into two basic forms: Kinetic and Potential.

Kinetic Energy

• An object in motion can do work.– A moving hammer can do work on a nail.

– Hot exhaust gas leaving a jet engine can do work on an airplane.

• Energy that is due to mass in motion is called Kinetic Energy.

Formula for KE

• KE – Kinetic Energy (Joules)

• m – mass (kg)

• v – velocity (m/s)

KE=1

2mv2

Example Problem 1: After a serve, a 0.27 kg volleyball is moving at 22 m/s. What is the kinetic energy of the volleyball?

Givensm = 0.27 kgv = 22 m/s

Formula

KE=1

2mv2

Work:

KE = ½ (0.27)(22)2 = 65.3 Joules

The kinetic energy of the volleyball is 65.3 Joules.

Potential EnergyPotential Energy is the energy an object has based on its position or condition.

An object held above ground level has gravitational potential energy because it wants to be at ground level (it would fall if it was released).

Potential EnergyA stretched spring has elastic potential energy because it wants to be back at its equilibrium position.

Formulas for PE

PE=mgh•PE – Potential Energy (Joules)•m – mass (kg)•g – acceleration of gravity (m/s2)•h – height raised above ground level or any arbitrary base level (m).

Gravitational Potential Energy:

Example Problem 2: A 20 kg rock is sitting on the edge of a cliff that is 50 m above the ground. What is the gravitational potential energy of the rock?

Givensm = 20 kgg = 9.8 m/s2

h = 50 m

Formula

Work:

PEg = (20)(9.8)(50) = 9800 Joules

The gravitational PE of the rock is 9800 Joules.

PE=mgh

Formulas for PE

PEElastic

=1

2kx2

•PE – potential energy (Joules)•k – spring constant or force constant (N/m)•x – displacement from equilibrium (m)

Elastic Potential Energy:

Example Problem 3: A spring is stretched 10 cm from its equilibrium position. What is the elastic potential energy of the spring? (k = 2500 N/m)

Givensk = 2500 N/mx = 0.1 m

Formula

Work:

PEe = ½ (2500)(0.1)2 = 12.5 Joules

The elastic PE of the spring is 12.5 Joules.

PEElastic

=1

2kx2

Work – Energy Theorem

The Work – Energy Theorem says that the net work done is equal to the change in kinetic energy, or the net work done is equal to the change in potential energy.

Work – Energy Theorem

• W – Work (Joules)∀ ∆KE – change in kinetic energy (final KE – initial KE) (Joules)

∀ ∆PE – change in potential energy (final PE – initial PE) (Joules)

W =∆ KE

W =∆ PE

Work – Energy Theorem

• This means that when work is done to make an object move to a certain velocity, its kinetic energy changes by an amount equal to the work done.

• Or, when work is done raising an object to higher elevation, its potential energy changes by an amount equal to the work done.

Energy in Mechanical Day 2

Conservation of Energy

The Law of Conservation of Energy states:

“In a closed, isolated system, energy is conserved – it cannot be created or destroyed. Energy can change form, but the total amount of energy in the system does not change.”

Conservation of Energy This means Potential Energy can be converted into Kinetic Energy and vice versa.

Conservation of Energy

Example Problem 4: A 50 kg skier is standing at the top of a 30 m hill. What would his speed be at the bottom of the hill?

Givensm = 50 kgg = 9.8 m/s2

h = 30 m

Formulas

KE=1

2mv2

Work:

PE = (50)(9.8)(30) = 14700 J

14700 = ½ (50)v2

PE=mgh

v =24.25 m/s

Example Problem 5: A 100 kg skier is going 70 m/s at the bottom of the hill. What is the height of the hill?

Givensm = 100 kgv = 70 m/sg = 9.8 m/s2

Formulas

KE=1

2mv2

Work:

KE = ½ (100)(70)2 = 245000 J

245000 = (100)(9.8)h

PE=mgh

h = 250 m

Total Mechanical Energy

At any time, the total mechanical energy of a system is sum of the kinetic energy and potential energy.

KEinitial + PEinitial = KEfinal + PEfinal

Conservation of Energy

• At the endpoints, the pendulum has a maximum potential energy and zero kinetic energy.

• At equilibrium, the pendulum has a maximum kinetic energy and depending on the arbitrary base line used, it either has no potential energy or a minimum amount of potential energy.

Bernoulli’s PrincipleBernoulli’s Principle states:

“As the velocity of a fluid increases, the pressure in the fluid decreases.”

Bernoulli’s Principle is derived from the principle of conservation of energy.

If the velocity (kinetic energy) increases, the pressure (fluid’s potential energy) must decrease.

Bernoulli’s Principle

A simple demonstration of Bernoulli’s principle is to hold a sheet of paper just below your bottom lip and blow across the top of the paper. Try it . . .

The paper lifts because the pressure on the top of the paper is less than the pressure underneath the paper.

Bernoulli’s Principle

Bernoulli’s principle explains how this speed and pressure difference above and below an

airplane wing

can cause

lift.