Work and Energy - Notes

Work and Energy

Unit 3: Energy and Society

• Canada is a leading energy producer and user.

• Energy is used for transportation, heating, cooling, industrial production, and leisure.

• Most energy in Canada comes from coal, crude oil, natural gas, and radioactive elements like uranium.

• Extracting these resources causes environmental problems and contributes to climate change due to gas emissions.

Introduction to Energy - The Big Ideas

• The sun is the primary energy source.

• Energy is transformed multiple times before use.

• Energy exists in many forms and easily converts between them.

• Energy cannot be created or destroyed (conservation of energy).

• Energy can be stored and used later.

• Energy conversion always results in some energy transforming into thermal energy (heat) that disperses into the surroundings.

Forms of Energy

• Kinetic Energy: Energy of motion.

• Gravitational Potential Energy: Energy due to an object's position above another (e.g., height).

• Electrical Energy: Energy provided by electricity.

• Chemical Energy: Energy stored in chemical bonds.

• Nuclear Energy: Energy stored in the nucleus of an atom.

• Elastic Energy: Energy stored in stretched, compressed, or distorted objects.

• Thermal Energy: Energy of vibrating or moving molecules.

• Radiant Energy: Energy of electromagnetic waves (including light).

• Sound Energy: Vibrational energy carried by sound waves.

• Potential Energy: Stored energy.

Energy Transformation Examples

• Fireworks: Chemical potential energy → radiant energy, thermal energy, sound energy.

• Flashlight: Chemical potential energy (battery) → radiant energy, thermal energy.

Energy Transformations - Examples

Learning Goals

• Define work and energy.

• Describe the three conditions necessary for work to occur.

• Describe the difference between positive, negative, and zero work.

• List the three conditions which would result in zero work.

• Identify situations where work is done against the force of gravity.

• Energy can be transformed from one form to another and transferred from one object to another.

So Far…

• Newton's laws analyze the motion of objects.

• Force and mass determine acceleration.

• Acceleration determines velocity or displacement over time.

• Newton's laws are a useful model for analyzing motion and making predictions.

Now…

• Motion will be examined from the perspective of work and energy.

• The effect of work on an object's energy will be investigated.

• Resulting velocity and/or height can be predicted from energy information.

Energy Defined

• Energy: The ability to do work or accomplish a task; can be stored and used later; always conserved.

• Work: Energy transferred to an object when a force moves it through a distance.

Thinking About Work and Energy

• Pushing a wall hard enough to break a sweat, but the wall doesn't move:

  • Energy expended (chemical energy in the body used).

  • No energy transferred to the wall.

  • No “useful” work done on the wall.

  • Connection: Doing useful work and energy.

Mechanical Work

• Energy can be transferred into or out of a system by an external force.

  • System loses energy: force does negative work.

  • System gains energy: force does positive work.

• Energy is a scalar quantity; positive or negative work indicates a gain or loss of energy.

• Mechanical work is done on an object when a force displaces the object in the direction of the force or a component of the force.

• Work is not energy itself, but rather it is a transfer of mechanical energy.

Work

• Work:
  The amount of energy transferred from an object when acted upon by a force over some displacement.

Work Conditions

• Case 1: Work is done if the object you push moves a distance in the direction towards which you are pushing.

• Case 2: No work is done if the force you exert doesn't make the object move - no motion.

• Case 3: No work is done if the force you exert doesn’t make the object move in the same direction as the force you exerted.

Work - Mathematically

• Work is done when a force F applied to an object causes it to have a displacement Δd in the same direction as the applied force.

• Formula:

  W = F \Delta d \cos(\theta)

  • F is the force (N).

  • Δd is the displacement (m).

  • \theta is the angle between the force and the direction of displacement.

• Work is a scalar quantity with units of Joules (J).

• 1 J = 1 N \cdot m

Units of Energy

• The SI derived unit of Energy is the Joule

• 1 J = 1 kg \frac{m^2}{s^2}

• Other units:

  • 1 erg = 1 g \cdot \frac{cm^2}{s^2} = 1 × 10^{-7} J

  • 1 cal = 4.184 J

  • 1 kWh = 3.6 × 10^6 J

Work Example 1: θ = 0°

• Ms. Varghese applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a frictionless surface. Find the work done on the box.

• The mass of the box does not affect the work done on the box. It will affect the acceleration of the box when the work is done on it.

• In this simple case when θ = 0°, you can write
  W = FΔd

Work Example 2: θ = 90°

• Ms. Varghese applies a vertical force of magnitude 40.0 N on a 10.0 kg box as it slides 15.0 m across a frictionless surface. Find the work done on the box.

• Ms. Varghese is not increasing the speed of the box and thus its mechanical energy.

• Forces applied at right angles to the motion don’t count when it comes to work done on the box.

Work Example 3: θ = 60°

*Ms. Varghese applies a force of magnitude 40.0 N at a 60.0^o angle with the horizontal to push a 10.0 kg box 15.0 m across a frictionless surface. Find the work done on the box.
*The box won’t accelerate as much.

Work by Forces at an Angle

• The only portion of the force that counts towards the work done is that component of the force in the direction of the motion:.

• The work done is using the formula W = F \Delta d \cos(\theta)

Work Example 4: θ = 180°

• Ms. Varghese applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a surface. The frictional force is 10.0 N. Find the work done by friction on the box.

• If there is a frictional force, it will do negative work on the object, i.e., reduce its total mechanical energy.

Examples of Work?

• Just because you feel like you are doing ‘work’, it doesn’t mean that you are doing mechanical work according to the physics definition of the term.

• Read the following five statements and determine whether or not they represent examples of work.

  • Leaning against a box that is too heavy to move

    • NO. The box is not displaced. A force must cause a displacement in order for work to be done.

  • A book falls off a table and free falls to the ground.

    • YES. There is a force (gravity) which acts on the book which causes it to be displaced in a downward direction (i.e., "fall").

  • A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed.

    • NO. There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

  • A rocket accelerates through space

    • YES There is a force (the expelled gases push on the rocket) which causes the rocket to be displaced through space.

Work - Summary

Work - Summary

• Work is positive when the direction of force is the same as the direction of motion. The object gains energy

  • Example: you do positive work on a box when you lift it up to the table.

• Work is negative when the direction of force is opposite to the direction of motion. The object loses energy

  • Example: gravity does negative work on the box when it is lifted up to the table.

• If you are careful about angles, the equation will take care of this for you because cos(180°)=-1.

Work Done On or Work Done By

• Work done by (something/someone/a force):

• Work done on an object:

Work Example 5

• Ms. Varghese applies a horizontal force of magnitude 40.0 N to push a 10.0 kg box 15.0 m across a surface. The frictional force is 10.0 N. Find the work done on the box.

• Free body diagram:

  • F_N - Normal Force

  • F_g - Force of gravity

  • F_f - Force of friction

  • F_A - Applied Force

Graphing Work Done

• If you have a graph of F vs Δd, you can determine Work by calculating the Area under the graph of F-Δd graph

Mechanical Work

• The mechanical work on an object is the amount of mechanical energy transferred to that object by a force acting on an object that moves it a displacement

Work Example 6: Work Done To Change Speed

A curler applies a force of 15 N on a curling stone and accelerates the stone from rest to a speed of 8.00 m/s in 3.5 s. Assuming that the ice surface is level and frictionless, how much mechanical work does the curler do on the stone?

Power

• Power is the rate at which work is performed or energy is transferred:

  • P = \frac{W}{t}

• It has the units of J/s or Watts (W)

• (We will discuss Power again in a later lesson)

Worksheets:

• Energy, Work, and Types of Energy

• Mechanical Work & Power

Kinetic Energy

• The energy of motion.

• Types of Kinetic Energy:

  • Bulk Kinetic: Energy that is due to motion of an entire object (i.e a rolling cue ball).

  • Sound: Energy transmitted from molecule to molecule within a medium.

  • Radiant: Energy that is transmitted via electromagnetic (EM) waves such as radio, light, x-rays, etc.

  • Electric: Energy associated with moving electric charges.

• This Included thermal/heat energy

Potential Energy

• Stored energy due to an object’s state. It is energy that has the potential to do work.

• Types of potential energy:

  • Gravitational: The stored energy of an object due to its position height above a surface.

  • Chemical: Energy stored within the molecules of a substance.

  • Nuclear: Energy stored within the nucleus of an atom.

  • Elastic Potential: Energy stored by bending or compressing an elastic material (spring).

  • Electric Potential: Stored energy of charged objects due to their position and charge.

  • Magnetic Potential: Stored energy of magnetized objects.

Bowling Ball Example

• Case 1: Consider picking up a bowling ball

  • If we consider the energy as the potential to break my toe, on the ground, it has to no to low energy.

  • When 1 pick it up to a height of 1m, it now has a much higher potential to break my toe

  • Therefore there has been a change in energy, work has been done.

• Case 2: Now that I have the bowling ball at a height of 1m, 1 walk 2m right. Did I do work?

  • The energy available to break my toe at the start would be the same after 1 walked 2m

  • Therefore I did not do any work -- there was no change in energy.

Bowling Ball Example Calculations

*Consider picking up a bowling ball 1 m with 100 N of force

• F = 100 N

• \Delta d = 1 m

• \theta = 0°

  W = F \Delta d \cos{\theta}

  W = (100N)(1m) \cos{0°}
  W = 100 J
  *Now that I have the bowling ball at a height of 1m, 1 walk 2m right.

• F = 100 N

• \Delta d = 2 m

• \theta = 90°

  W = F \Delta d \cos{\theta}
  W = 0

Calories

• A calorie is the amount of heat necessary to raise the temperature of 1 g of water by 1 (at a pressure of 1 atm)

• Food energy is measured in kilocalories (or Calories with a capital C)

• (More on this is a later lesson on Heat)

Energy Use and Production

• As a result, we are constantly searching for cleaner and “greener” ways of producing electricity

• For example, one promising solution is to use wind to produce electricity. Wind turbines provide an environmentally friendlier way of generating electricity.

  • Large groups of turbines, called wind farms, may provide electricity for an entire community

• Note: Wind turbines are not without controversy…. (e.g., location as well as health effects)

• Other alternative energy technologies include solar cells, geothermal systems, tidal turbines, and biofuels