Chapter 5 Work, Power and Energy

Objectives Section 1 – Work Recognize the difference between the scientific and ordinary definitions of work Define work by relating it to force and displacement Identify where work is being performed in a variety of situations Calculate the net work done when many forces are applied to an object

Objectives Section 2 – Energy Identify several forms of energy Calculate kinetic energy for an object Apply in the work-kinetic energy theorem to solve problems Distinguish between kinetic and potential energy Classify different types of potential energy Calculate the potential energy associated with an object’s position

Objectives Section 3 – Conservation of Energy Identify situations in which conservation of mechanical energy is valid Recognize the forms that conserved energy can take Solve problems using conservation of mechanical energy

Objectives Section 4 – Power Relate the concepts of energy, time and power Calculate power in two different ways Explain the effect of machines on work and power

Work Work – the product of force and displacement, as long as they are both in the same direction. This is a vector times a vector. In this case, a vector times a vector gives a scalar. Work is measured in Joules (J) which is the same as a Newton x meter.

Example How much work is done on an object if a force of 30 Newtons displaces the object 200 meters?

What happens if the force and displacement are not in the same direction? Where θ is the angle between the two vectors Note: We’ll talk about where the cosine magically comes from in class.

Example: As Alex pulls his red wagon down the sidewalk, the handle of the wagon makes an angle of 60o with the pavement. If Alex exerts a force of 100 Newtons along the direction of the handle, how much work is done when the displacement of the wagon is 20 meters along the ground? 100 N 60o 20 m

100 N 60o 20 m

Example: A constant force of 50 Newtons is applied over a distance of 10 meters. Draw a graph to represent this information. Calculate the work done by this force. Calculate the area under the graph. How do they compare? F (N) 50 d (m) 10

The work can be found by calculating the area under the graph. If given a graph of Force vs. Displacement The work can be found by calculating the area under the graph.

That’s enough for now…

Lets assume you own a moving company that employs two workers. Employee one moves ten boxes and gets the job done by lunch. Employee two moves ten boxes but takes his time and finishes by 5pm. Who does more work? Who would you pay more?

While there is no correct answer here, there is an added piece that work alone does not address. Time is the added piece.

Power Power is the rate at which work is done. Unit:

Example: If 3000 Joules of work is performed on an object in 1.0 minute, what is the power expended on the object?

Example: A 200 Newton force is applied to an object that moves in the direction of the force. If the object travels with a constant velocity of 10 m/s, calculate the power expended on the object.

Energy When work is done on an object, the energy of the object is changed.

Kinetic Energy

The work done on the object changes a quantity called kinetic energy that is related to the mass and the square of the speed of the object. This is known as the work-energy theorem.

Example: A 10kg object subjected to a 20 Newton force moves across a horizontal frictionless surface in the direction of the force. Before the force was applied, the speed of the object was 2.0 meters per second. When the force is removed, the object is traveling at 6.0 meters per second. Calculate the following quantities: (a) KE1 (b) KE2 (c) ΔKE (d) W and (e) distance.

That’s enough for today…

Gravitational Potential Energy Lifting a book from the floor to the table applies a force over a distance therefore work is done on the book but the kinetic energy is unchanged. In this case the force of gravity is overcome by work.

Example: A 2.0 kilogram mass is lifted to a height of 10 meters above the surface of the Earth. Calculate the change in the gravitational potential energy of the object.

Conservation of Energy Energy can not be created or destroyed. In the system, the sum of the potential energy and kinetic energy will be conserved; a change in one is accompanied by an opposite change in the other.

Example: A 2.0 kg ball is tossed with a velocity of 4.0 m/s straight into the air. How high does the ball travel upwards? Calculate the initial kinetic energy of the ball. Calculate the potential energy of the ball at it’s peak. Givens:

or

Roller Coaster m=1.0 kg v1 = 4.0m/s h1 = 10 m h1 = 5 m h1 = 4 m Calculate the total energy and the velocity at the top of each hill.

v1 = 4.0m/s m=1.0 kg h1 = 10 m h1 = 5 m h1 = 4 m h1 = 2 m

Pendulum Simple Harmonic Motion – In the absence of friction the pendulum will swing back and forth continuously.

Example: A pendulum whose bob weighs 12 Newtons is lifted a vertical height of 0.40 meter from its equilibrium position. Calculate the change in potential energy between maximum height and equilibrium height, the gain in kinetic energy, and the velocity at the equilibrium point.