Definition and Mathematics of Work Newton's laws serve as a useful model for analyzing motion and making predictions about the final state of an object's motion. When a force acts upon an object to cause a displacement of the object, work was done upon the object. There are three key ingredients to work - force, displacement, and cause. There are several good examples of work - a horse pulling a plow through the field, a father pushing a grocery cart down the aisle of a grocery store, a freshman lifting a backpack full of books upon her shoulder. In each case described, there is a force exerted upon an object to cause that object to be displaced. W= F*d*cos θ where F is the force, d is the displacement, and the angle is defined as the angle between the force and the displacement vector. To Do Work, Forces Must Cause Displacements A vertical force can never cause a horizontal displacement; thus, a vertical force does not do work on a horizontally displaced object!! When a force is exerted on an object at an angle to the horizontal, only a part of the force contributes to a horizontal displacement. The Meaning of Theta Theta is ALWAYS defined as the angle between the force and the displacement vector. The Meaning of Negative Work On occasion, a force acts upon a moving object to hinder a displacement. Examples might include a car skidding to a stop on a roadway surface or a baseball runner sliding to a stop on the infield dirt. In such instances, the force acts in the direction opposite the objects motion in order to slow it down. The negative of negative work refers to the numerical value that results when values of F, d and theta are substituted into the work equation. Since the force vector is directly opposite the displacement vector, theta is 180 degrees. The cosine(180 degrees) is -1 and so a negative value results for the amount of work done upon the object. Units of Work The standard metric unit is the Joule (abbreviated J). One Joule is equivalent to one Newton of force causing a displacement of one meter( 1J= 1N*m) Any unit of force times any unit of displacement is equivalent to a unit of work. In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.
Work, Energy, and Power Lesson 2a (1/30)
Internal vs. External Forces
The force of gravity, electrical forces, and magnetic forces were examples of forces that could exist between two objects even when they are not physically touching.Certain forces when present and involved in doing work on objects will change the total mechanical energy of the object. there are other types of forces that can transform the energy of an object from potential energy to kinetic energy (or vice versa)called internal forces and external forces.
External forcesinclude the applied force, normal force, tension force, friction force, and air resistance force. Internal forces include the gravity forces, magnetic force, electrical force, and spring force.
When net work is done upon an object by an external force, the total mechanical energy (KE+PE) of that object is changed. If the work is positive work, then the object will gain energy. If the work is negative work, then the object will lose energy. The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. The work that is done will be equal to the change in mechanical energy of the object. Because external forces are capable of changing the total mechanical energy of an object, they are sometimes referred to as nonconservative forces.
When the only type of force doing net work upon an object is an internal force (ie- gravitational and spring forces), the TME of that object remains constant. In such cases, the object's energy changes form. For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remains constant. This is referred to as energy conservation. When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical is conserved. Because internal forces are capable of changing the form of energy without changing the total amount of mechanical energy, they are sometimes referred to as conservative forces.
Exercises:
A ball falls from a height of 2 meters in the absence of air resistance.
PE --> KE
A skier glides from location A to location B across a friction free ice.
PE --> KE
A baseball is traveling upward towards a man in the bleachers.
KE --> PE
A bungee cord begins to exert an upward force upon a falling bungee jumper.
KE --> PE
The spring of a dart gun exerts a force on a dart as it is launched from an initial rest position.
PE --> KE
Energy Analysis
Objective Estimate how much electrical energy you consume on a daily basis (ie: what does it cost my parents) 5 kWh
What to do?
Identify 10 electrical appliances you use on a daily basis and identify their power rating (in Watts).
Apple laptop charger= 60 W= .06 kW
Flat Iron= 25 W= .025 kW
iHome= 150 W= .150 kW
iPhone Charger= 10W =.10 kW
Blow Dryer= 1875 W= 1.875 kW
Vizio Tv= 110 W=.110 kW
Lamp= 60 W= .06 kW
Microwave= 950 W=.95 kW
Pencil Sharpener= 20 W= .02 kW
Apple Desktop Computer= 120W= .120kW
The power rating will be listed on the info label – typically on the back of or under the appliance. Often the power consumption is listed in terms of AMPERAGE (amperage measures the current of electricity consumed). The power rating (in Watts) may be calculated using the following formula:
Power (in Watts) = AMPS x 120 volts.
For example, a 12 AMP vacuum cleaner uses 12A x 120v = 1440 Watts of power.
Determine the total kWh (kilowatt-hours) of power that you consume with these ten appliances.
First estimate how many hours you use each appliance. For example, you may use your hairdryer every second day for 10 minutes – so on average you use it for 0.17h/d ¸ 2 = 0.085 h per day.
12h/d
.167h/d
2 h/d
6h/d
3h/d
3h/d
.33h/d
.167h/d
.0167h/d
12h/d
Calculate the kWh used per day by multiplying the wattage of the appliance by the hours used (per day).
.72 kWh
.0042 kWh
.30 kWh
.60 kWh
5.625 kWh
.330 kWh
.0198 kWh
.15865 kWh
.000334 kWh
1.44 kWh
Finally, determine the total kWh you use per day.
9.197984 kWh
What does this cost your parents?
$0.119164*9.197984= $1.10
Look at your household electric bill. Find two numbers:
the total dollar amount due
$265.38
kWh consumed that month
1424 kWh
Costs of Electricity.
Calculate the average cost per kWh by dividing the dollar amount by the kWh consumed. This is approximately what each kWh costs your family. (Note: this figure includes fees and taxes, too). The cost will probably be between $0.10-$0.20 per kWh – depending on how much electricity you use. Electricity costs more if you exceed a certain usage.
$0.186362
You can also look this value up on the bill itself.
$0.119164
Compare the two values. Why are they different?
Probably because PSE&G wants to make a profit.
Multiply the kWh you use per day by the cost per kWh to determine what you cost your parents.
9.197984* $0.119164= $1.10
Evaluate
Does the cost of electricity seem like a lot to you? Discuss this with your friends.
It doesn’t seem that much but in the long run it probably adds up. There are so many appliances that are left out so I’m sure that it is much more.
Keep in mind that this cost only reflects ten appliances. What do you think your total cost actually is? Are there major appliances that you may have excluded from your list of ten that would make a big difference?
I left out refrigerator, garage door, pool heater, etc. I am sure it costs much more than this. This definitely would have made a huge difference.
If you think your consumption is a lot – what can you change? Do you need/should change?
I should probably unplug my chargers and such. I always leave everything plugged in—it’s a very bad habit. However, I have gotten better at shutting off the lights.
I think that the electric bill can be a little overpriced. I think that it especially hard for those who have big families, who are constantly maximizing the amount of electricity used. Also, when children are younger, I feel like there are more lights on in the house and more use of electrical appliances (tv, video games). Ultimately, I feel like people underestimate and overlook how much each appliance costs, and are overall uneducated.
toc Work, Energy, and Power Lesson 1a (1/12)
Work, Energy, and Power Lesson 2a (1/30)
Energy Analysis
Definition and Mathematics of WorkTable of Contents
Newton's laws serve as a useful model for analyzing motion and making predictions about the final state of an object's motion.
When a force acts upon an object to cause a displacement of the object, work was done upon the object. There are three key ingredients to work - force, displacement, and cause. There are several good examples of work - a horse pulling a plow through the field, a father pushing a grocery cart down the aisle of a grocery store, a freshman lifting a backpack full of books upon her shoulder. In each case described, there is a force exerted upon an object to cause that object to be displaced.
W= F*d*cos θ
where F is the force, d is the displacement, and the angle is defined as the angle between the force and the displacement vector.
To Do Work, Forces Must Cause Displacements
A vertical force can never cause a horizontal displacement; thus, a vertical force does not do work on a horizontally displaced object!!
When a force is exerted on an object at an angle to the horizontal, only a part of the force contributes to a horizontal displacement.
The Meaning of Theta
Theta is ALWAYS defined as the angle between the force and the displacement vector.
The Meaning of Negative Work
On occasion, a force acts upon a moving object to hinder a displacement. Examples might include a car skidding to a stop on a roadway surface or a baseball runner sliding to a stop on the infield dirt. In such instances, the force acts in the direction opposite the objects motion in order to slow it down. The negative of negative work refers to the numerical value that results when values of F, d and theta are substituted into the work equation. Since the force vector is directly opposite the displacement vector, theta is 180 degrees. The cosine(180 degrees) is -1 and so a negative value results for the amount of work done upon the object.
Units of Work
The standard metric unit is the Joule (abbreviated J). One Joule is equivalent to one Newton of force causing a displacement of one meter( 1J= 1N*m)
Any unit of force times any unit of displacement is equivalent to a unit of work.
In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.
Work, Energy, and Power Lesson 2a (1/30)
Internal vs. External ForcesThe force of gravity, electrical forces, and magnetic forces were examples of forces that could exist between two objects even when they are not physically touching.Certain forces when present and involved in doing work on objects will change the total mechanical energy of the object. there are other types of forces that can transform the energy of an object from potential energy to kinetic energy (or vice versa)called internal forces and external forces.
External forces include the applied force, normal force, tension force, friction force, and air resistance force. Internal forces include the gravity forces, magnetic force, electrical force, and spring force.
When net work is done upon an object by an external force, the total mechanical energy (KE+PE) of that object is changed. If the work is positive work, then the object will gain energy. If the work is negative work, then the object will lose energy. The gain or loss in energy can be in the form of potential energy, kinetic energy, or both. The work that is done will be equal to the change in mechanical energy of the object. Because external forces are capable of changing the total mechanical energy of an object, they are sometimes referred to as nonconservative forces.
When the only type of force doing net work upon an object is an internal force (ie- gravitational and spring forces), the TME of that object remains constant. In such cases, the object's energy changes form. For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy of that object is transformed into kinetic energy. Yet, the sum of the kinetic and potential energies remains constant. This is referred to as energy conservation. When the only forces doing work are internal forces, energy changes forms - from kinetic to potential (or vice versa); yet the total amount of mechanical is conserved. Because internal forces are capable of changing the form of energy without changing the total amount of mechanical energy, they are sometimes referred to as conservative forces.
Exercises:
Energy Analysis
ObjectiveEstimate how much electrical energy you consume on a daily basis (ie: what does it cost my parents)
5 kWh
What to do?
- The power rating will be listed on the info label – typically on the back of or under the appliance. Often the power consumption is listed in terms of AMPERAGE (amperage measures the current of electricity consumed). The power rating (in Watts) may be calculated using the following formula:
Power (in Watts) = AMPS x 120 volts.For example, a 12 AMP vacuum cleaner uses 12A x 120v = 1440 Watts of power.
Evaluate
- If you think your consumption is a lot – what can you change? Do you need/should change?
- I should probably unplug my chargers and such. I always leave everything plugged in—it’s a very bad habit. However, I have gotten better at shutting off the lights.
I think that the electric bill can be a little overpriced. I think that it especially hard for those who have big families, who are constantly maximizing the amount of electricity used. Also, when children are younger, I feel like there are more lights on in the house and more use of electrical appliances (tv, video games). Ultimately, I feel like people underestimate and overlook how much each appliance costs, and are overall uneducated.