Mechanics Topic 2.3 Work, Energy and Power

Learning Outcomes 2.3.1Outline what is meant by work Determine the work done by a non-constant force by interpreting a force–displacement graph Solve problems involving the work done by a force Outline what is meant by kinetic energy Outline what is meant by change in gravitational potential energy State the principle of conservation of energy List different forms of energy and describe examples of the transformation of energy from one form to another Distinguish between elastic and inelastic collisions Define power Define and apply the concept of efficiency Solve problems involving momentum, work, energy and power.

Work Learning Outcomes 2.3.1Outline what is meant by work Determine the work done by a non-constant force by interpreting a force–displacement graph Solve problems involving the work done by a force.

Work A simple definition of work is the force multiplied by the displacement moved However this does not take in to account of the case when the force applied is not in the direction of the motion Here we have to calculate the component of the force doing the work in the direction moved i.e. Work is equal to the magnitude of the component of the force in the direction moved multiplied by the displacement moved

Work  F s

More on Work Even though Work is the product of two vector quantities, it is a scalar quantity This type of product is called Dot Product. The SI unit of work is the newton-metre (Nm) and it is called the joule (J) This is a derived unit. Express it in terms of the fundamental units

Motive and Resistive Work If θ is < 90, work done by the force is positive: it helps the motion: Motive work. If θ is > 90, work is negative: it resists the motion: Resistive work If θ is = 90: no work is done  F s

Test your Knowledge! In all four situations shown below, the object is subject to the same force F and has the same displacement to the right. Rank the situations in order of the work done by the force on the object form most positive to most negative

Be a Thinker!

Force-displacement Graphs The area under any force-displacement graph is the work done force displacement Area = work done

The case of a spring

Apply your Knowledge!

Work done by gravity

Force of gravity as a Conservative force To lift the object from position A to position E, the picture represents two path: A to E directly A to B to C to D then to E In both cases, the work done by gravity is mg∆h The work done by gravity is independent of the path followed We say that the force is a conservative force Weight is a conservative force

Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points The work depends only upon the initial and final positions of the object Examples of conservative forces include: Gravity Spring force Electromagnetic forces

Force of gravity as a conservative force The work done by the weight of the skier depends on the vertical distance between her initial and final position (10 m) and not on the actual path followed by the skier.

Nonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. Examples of nonconservative forces friction, air drag

Friction Depends on the Path The blue path (B) is shorter than the red path (A) The work required is less on the blue path than on the red path Friction depends on the path and so is a nonconservative force

Test your Knowledge The following figure presents three different paths for a car to reach the top of a hill. Rank the paths in order of the work done by the weight of the car from the greatest to smallest.

Be a Thinker!

Energy Learning Outcomes 2.3.4Outline what is meant by kinetic energy Outline what is meant by change in gravitational potential energy State the principle of conservation of energy List different forms of energy and describe examples of the transformation of energy from one form to another.

What is Energy? Very hard to define because it is not tangible ! Often referred to as ability to do work You possess energy; therefore you can do work Work and energy are closely related and can be used interchangeably Energy is needed to do work Work changes the energy of the object.  W = ΔE

Forms of Energy There are many forms of energy: Mechanical energy  Kinetic  Potential Thermal Chemical Electrical Nuclear Sound Light

The Principle of Conservation of Energy Energy can be transformed from one form to another, but it cannot be created nor destroyed, i.e. the total energy of a system is constant

Energy Transformations Energy can be transformed from one form to another In the case of a lamp: transforms electrical energy into thermal energy (heat) and radiant energy (light) In the case of a fan: transforms electrical energy into mechanical energy and heat In the case of a photoelectric cell: transforms the radiant energy into electric energy

Mechanical Energy Mechanical Energy of a system consists of the sum of its Kinetic and Potential energies.

Kinetic Energy

Be a Thinker! What is the shape of the KE-V graph? How should be plotted on the y and x axes to obtain a straight line? There is more than one answer What would be the slope for each case?

Be a Thinker!

Work-Kinetic Energy Theorem

Work and Kinetic Energy

Apply your Knowledge!

Be a Thinker!

Mechanical Potential Energy The 2 nd form of Mechanical energy Potential energy is associated with the position of the object within some system Two forms of mechanical potential energy: Gravitational potential energy Elastic potential energy

Gravitational Potential Energy Gravitational Potential Energy is the energy associated with the relative position of an object in the gravitational field Every mass has a gravitational potential by virtue of its position But a question poses itself: position with respect to what?

Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen: This is the reference. The choice of the reference is arbitrary The gravitational potential energy is then = mgh where h is the height of the object from the reference position

The choice of the reference A mass rests on the table at a 1 m from the floor and 2 m below the ceiling If the reference is the table, then the PE of the mass is: Zero If the reference is the floor, then the PE of the mass is: PE= 2 x 10 x 1 = 20 J If the reference is the ceiling, then the PE of the mass is: PE= 2 x 10 x -2 = -40 J

Relationship between GPE and Work done by gravity

Work done by conservative force

Elastic Potential Energy

Mechanical Energy The mechanical energy of a system (ME) is the sum of the gravitational potential energy, elastic potential energy, and kinetic energy of all components in the system ME= GPE + Pe + KE

Principle of Conservation of Mechanical Energy In the abscence of non- conservative forces (ex. Friction, air drag), the mechanical energy of the system is conserved. In other words, if the forces acting on the system are force of gravity and/or spring force, then the mechanical energy of the system is conserved ME sys before = ME sys after

Conservation of Mechanical Energy

Using Principle of Conservation of Mechanical Energy Falling objects and roller coaster rides are situations where E p + E k = constant if we ignore the effects of air resistance and friction. Inclined planes and falling objects can often be solved more simply using this principle rather than the kinematics equations

Be a Thinker!

Transformation of Energy The electrical energy is converted as follows: Throughout the journey, part of the electrical energy is converted to heat and sound energy. Between the ground floor and the first floor: The electric energy is mainly converted to kinetic energy and some goes to increasing GPE. Between the first floor and the 9 th floor: The Kinetic energy is constant, so the electrical energy is converted mainly to gravitational potential energy. Between the 9 th floor and the 10 th floor: The electrical energy is mainly converted into thermal energy due to the braking system. Some of the energy is converted into increasing the GPE

2.3.8Distinguish between elastic and inelastic collisions Define power Define and apply the concept of efficiency Solve problems involving momentum, work, energy and power. Learning Outcomes!

Power

Apply your Knowledge!

Power and Velocity

Apply your Knowledge!

Be a Thinker!

Efficiency Efficiency is defined as the ratio of the useful output to the total input This can be calculated using energy or power values as long as you are consistent Efficiency is normally expressed as a percentage

Efficiency example

Efficiency Example

Kinetic energy and Momentum In all collisions and explosions momentum is conserved, but generally there is a loss of kinetic energy, usually to internal energy (heat) and to a small extent to sound In an inelastic collision there is a loss of kinetic energy (momentum is still conserved) In an elastic collision the kinetic energy is conserved (as well as momentum)

Elastic and Inelastic Collisions

Be a Thinker!

Apply your Knowledge!