Work, Energy and Power

Work, Energy and Power Fortbend ISD

work mechanical energy energy transformations potential energy kinetic energy law of conservation of energy power work heat efficiency horsepower joule energy Vocabulary Terms

Review • Newtons Laws • Used to analyze motion of an object • Force and mass  acceleration • Acceleration  velocity over time • Used to predict final state of an object's motion What are other ways to look at motion?

Motion Based on Work and Energy • Objective: • Understand and calculate the effect of work on the energy of an object (or system of objects) • Predict the resulting velocity and/or height of the object from energy information

Work • A force acting upon an object to cause a displacement • For a force to qualify • 1. Displacement MUST happen • 2. Force MUST cause the displacement What are some examples of work?

A teacher applies a force to a wall and becomes exhausted. No. The wall is not displaced. Work or NOT? • A book falls off a table and free falls to the ground. • Yes! The is a downward force (gravity) which acts on the book to displace it. • A waiter carries a tray full of meals above his head by one arm across the room. • No. There is an upward force, and there is a horizontal displacement but the force does not cause the displacement • A rocket accelerates through space. • Yes the expelled gas is the force which accelerates the rocket through space.

Work Concept • Work is defined as a force acting upon an object to cause a displacement • Mathematically, work can be expressed by the following equation. • W= F x d cos q ( cos 00 = 1) • where F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vector

Work Calculations W = F x d W=F x d cos 300 W= F x d =15Kg(10m/s2) x 5m = 100N x 5m = 100N x 5m x 0.87 = 500 N m = 413 N m = 750 N m

Summary • Work is a force acting upon an object to cause a displacement. • three quantities must be known in order to calculate the amount of work. • Force • Displacement • Angle between the force and the displacement.

Ramp Example • Ramp 10 m long and 1 m high • Push 100 kg all the way up ramp • Would require mg = 980 N (220 lb) of force to lift directly (brute strength) • Work done is (980 N)(1 m) = 980 N·m in direct lift • Extend over 10 m, and only 98 N (22 lb) is needed • Something we can actually provide • Excludes frictional forces/losses 1 m

James Joule • British physicist James Joule is best known for his work in electricity and thermodynamics Together with the physicist William Thomson (later Baron Kelvin), Joule found that the temperature of a gas falls when it expands without doing any work. This principle, which became known as the Joule-Thomson effect, underlies the operation of common refrigeration and air conditioning systems. • The metric system unit of energy is the joule (J), after James Joule.

Mechanical • Mechanical energyis the energy which is possessed by an object due to its motion or its stored energy of position • Kinetic energy : is the energy of motion • Potential Energy : an object can store energy as the result of its position or elastic source • http://www.schooltube.com/video/c4ea045957576318dbbe/

Gravitational Potential Energy • After an object has been lifted to a height, work is done. This energy becomes stored in the object. • Energy is the ability for an object to do work. W = F x d • PE or Ug = mgh Potential Energy is maximum at the maximum HEIGHT

Potential Energy Calculation • How much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 m • PE or Ug = mgh • PE or Ug = (5Kg)(10 m/s2)(4.5 m) • PE or Ug = 225 Kg m2/s2 • PE or Ug = 225 J

Kinetic Energy • Once the object start moving it is called kinetic energy. One way you can tell that this is energy is by looking at a generator. • KE = 1/2mv2 Kinetic Energy is maximum at the lowest HEIGHT

Kinetic Energy Calculation • Find the kinetic energy of an 4 Kg object moving at 5m/s. • KE = 1/2 mv2 • KE = ½ (4Kg)(5m/s) 2 • KE = 50 Kg m 2 /s 2 • KE = 50 J

Roller Coaster – KE and PE • TOP: all potential • potential gradually changes to kinetic as the car accelerates • at the bottom of the lowest hill • maximum of kinetic energy • a minimum of potential energy • No more energy than original energy

Elastic potential energy

Spring constant Calculation A tired squirrel (mass of 1 kg) does push-ups by applying a force to elevate its center-of-mass by 5 cm. (A) Determine the number of push-ups which a tired squirrel must do in order to do a mere 5.0 Joules of work. (B) Determine the squirrel’s spring constant.

Spring Constant Calculation • W = F x d = 10 N*(.05m)=.5 N m • W = .5 J (each push up) • 10 pushups = 5 J • PE = ½ k x 2 • .5 J = ½ k (.05m) 2 • .5 J = ½ k (.003m 2) • .5 J = .0015 m 2 • 333.3 J/m 2 = k

Power! • Power is the rate that we use energy. • Power = Work or Energy / Time • P = W/t = F x d/t = F v • The units for power : • Watts • J/s • Kg m2 / s2 /s • N m / s

Power Calculation • A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart. • P = F x d / t • P = 30 N (10 m) / 5 s • P = 60 N m /s • P = 60 watts

Summary • Energy is the ability to move • Potential is stored energy (Statics) • Dependant on height • Kinetic is moving energy (Dynamics) • Dependant on velocity • Springs store energy dependant on distance and constant

Practice Problems • 13. A 500.0 kg pig is standing at the top of a muddy hill on a rainy day. The hill is 100.0 m long with a vertical drop of 30.0 m. The pig slips and begins to slide down the hill. What is the pig’s speed at the bottom of the hill? • 15. A 2.00 kg ball is dropped from the top of a 10.0 m high building. Calculate the potential AND kinetic energies at: (a) 10.0 m (b) 5.00 m (c) 0.00 m. • 16. A 10.0 g pebble is placed in a sling shot with a spring constant of 200.0 N/m and is stretched back 0.500 m. What is the maximum velocity the pebble will acquire?

Practice Problem

Work, Energy and Power