Work and Power
Work Let’s look at some examples of moving a book where “work” is being done and “work” is not being done on the book. Move the book from the table to a higher height. Move the book from the higher height back the table. Sliding the book on the table Lifting the book and putting it back down
Work Physics definition – work is done on an object when the object’s energy is changed. Lifting the book – raising the gravitational potential energy Sliding the book – raising the kinetic energy As the book slides and stops, lowering the kinetic energy
Mathematical definitions of Work Work is scalar (magnitude only) Work = Force*Displacement – This causes a change in energy usually, especially when lifted a displacement – Only the force parallel to the motion Ex: Gravity does not do work on a box being slid across a table. Work = change in kinetic energy Work = change in potential energy
English vs. Physics Suppose you hold a textbook over your head: Is work being done? Though the English definition might suggest that you are doing work since you will get tired after a while, the physics definition says that no work is done on the book because there is no change in energy of the book Work is being done on my arm since I am using the chemical potential energy in the muscles.
Two categories of work 1)Work done to raise the energy of an object – This is called positive work – Ex: Raising an object off of a table is raising the gravitational potential energy of the book 2) Work done to lower the energy of an object – This is called negative work – Ex: A box sliding on a table stops due to friction. The friction is doing negative work on the box because it is taking away kinetic energy.
Units for Work Joule (rhymes with “cool”) is the unit for work… it is also the unit for energy (more about this tomorrow) 1 Joule would be like lifting an apple from the ground to a table top. (1 Newton weight up one meter). Stopping a truck going 60mph is takes about 1 million Joules of work.
Other Units for Energy (and Work) calorie and Calorie
Power Which takes more power: – Slowly raising a book to the table top? – Quickly raising the book to the table top?
The definition of work says nothing about “how long” the change in motion will occur in time. It takes the same amount of work to lift a box up the stairs if you run up the stairs in 4 seconds, or if you walk up the stairs in 30 seconds.
Power Power is the rate at which work is done. Something that is more powerful will do more work in the same amount of time as something that is not as powerful. Ex: An old microwave can heat up a hot pocket in about 3 minutes. A new microwave can heat up the hot pocket to the same temperature in about 2 and a half minutes. The new microwave is more powerful.
Power A car with more power can change its speed from a stop up to 60 mph in a faster amount of time than the same change in speed for a less powerful car of the same weight.
Units for Power Metric Units – Watt – One Watt of power is lifting an apple onto a table within one second. English Units – Horsepower – 1 horsepower is the same as 750 Watts
Power definition in mathematics Power is the rate of change of work: Power = work done/time
Gravitational potential energy Depends on the mass of the object and how high the object is away from a reference point (usually the ground or a table top) Mathematically: GPE = mgh, where g is 10 m/s 2
Kinetic Energy The energy of motion. Depends on the mass of the object as well as the speed of the object Mathematically: KE = ½ mv 2
Conceptual ? On KE A 4 kg bicycle changing its speed from 5 m/s to 10 m/s. A 4 kg bicycle changing its speed from 10 m/s to 15 m/s. Which requires more work and why?