miércoles, 23 de noviembre de 2011

Mechanical Energy


Did you put a book in your backpack this morning? If so, the you did work on the book. Recall that work is done when a force moves an object.
Energy is the ability to do work or cause change upon other objects
When you do work on an object, some of your energy is transferred to that object.
You can think of work as the transfer of energy. When energy is transferred, the object upon which the work is done gains energy.
Energy is measured in joules (the same units as work).

What is mechanical energy?

*The energy acquired by the objects upon which work is done is known as mechanical energy.
*Mechanical energy = Potential energy + kinetic energy
*Total mechanical energy is the energy possessed by an object due to either its motion or its stored energy of position


*Energy that results from the position (height) or shape (mass) of an object is called potential energy
*Gravitational potential energy depends on the MASS and the HEIGHT
*When you lift a book up to your desk from the floor you transfer energy to it.
*The energy you transfer is stored and it might be used later if the book falls.

Calculating Gravitational potential energy

PEgrav = mass • gravity • height
PEgrav = m *• g • h
PEgrav = (# kg ) * (# m/s/s) * (# m)
In the above equation,
- m represents the mass of the object,
- h represents the height of the object and
- g represents the gravitational field strength (9.8 m/s^2 on Earth) - sometimes referred to as the acceleration of gravity.

We measure PEgrav in Joules

PEgrav = Joules
Like work, the standard metric unit of measurement for potential energy is the Joule.


The energy an object has due to its motion is called kinetic energy. For example:

*Moving objects, like cars and motorcycles have one type of energy: kinetic energy.
*A moving object can do work when it strikes another object and moves it.
* A swinging hammer does work on a nail as it drives the nail intro the piece of wood.
*The hammer has energy because it can do work.

Factors affecting kinetic energy

*The faster an object moves, the more kinetic energy it has. Example: A tennis ball that travels at a much greater speed would hurt more.

*A ball rolls across the ground and hits you in the foot. (tennis ball vs bowling ball). The bowling ball has more kinetic energy because it has a greater mass.

Calculating kinetic energy

m = mass of object
v = speed of object

This equation reveals that the kinetic energy of an object is directly proportional to the mass and the square of its speed.

Do changes in speed and mass have the same effect on the kinetic energy?
*Changing the speed of the wagon will have a greater effect on its kinetic energy than changing its mass by the same factor.
*Doubling the mass of the wagon will double its kinetic energy.
*Doubling the speed of the wagon will quadruple its kinetic energy.

Kinetic energy is dependent upon the square of the speed.
*For a twofold increase in speed, the kinetic energy will increase by a factor of four.
*For a threefold increase in speed, the kinetic energy will increase by a factor of nine.
*For a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen.

Kinetic Energy = Joules
Like work and potential energy, the standard metric unit of measurement for kinetic energy is the Joule.

Transformations from potential energy to kinetic energy

Rubber band

When you stretch a rubber band, you give it elastic potential energy. If you let it go, the rubber band flies across the room. When the rubber band is moving, it has kinetic energy.
The potential energy of the stretched rubber has transformed to the kinetic energy of the moving rubber band.

A lift motor

When you lift a heavy object against the gravitational field, you exert energy or give the object energy as you lift it. This potential energy later becomes kinetic energy if you let go of the object and it falls. A lift motor provides gravitational potential energy when lifting the car to higher floors. If the cable was cut the potential energy gained by the car would be transferred into kinetic energy as the car fell back towards the Earth, It would have maximum potential energy at the highest floor and maximum kinetic energy when it hit the Earth at the ground floor

Fallling Tennis ball

As the height of the ball decreases, it loses potential energy.
At the same time, its kinetic energy increases because its speed increases.
Its potential energy is transformed into kinetic energy.


Print this review and solve it this friday 25 inside the classroom.

1. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

2. Suppose a boy is pulling a 10-kg wagon at a speed if 1 m/s. What is the kinetic energy of the wagon?

3. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.

4. If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? Show your procedure.

5. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike and the rider is 85 kg. Find the kinetic energy of the bike and rider.

6. Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed?

In the following descriptions, the only forces doing work upon the objects are internal forces - gravitational and spring forces.
Thus, energy is transformed from KE to PE (or vice versa) while the total amount of mechanical energy is conserved.
Read each description and indicate whether energy is transformed from KE to PE or from PE to KE.

7. A ball falls from a height of 2 meters in the absence of air resistance.
PE to KE
The ball is losing height (falling) and gaining speed. Thus, the internal or conservative force (gravity) transforms the energy from PE (height) to KE (speed).

8. A skier glides from location A to location B across a friction free ice.

PE to KE
The skier is losing height (the final location is lower than the starting location) and gaining speed (the skier is faster at B than at A). Thus, the internal force or conservative (gravity) transforms the energy from PE (height) to KE (speed).

9. A baseball is traveling upward towards a man in the bleachers.

KE to PE
The ball is gaining height (rising) and losing speed (slowing down). Thus, the internal or conservative force (gravity) transforms the energy from KE (speed) to PE (height).

10. A bungee cord begins to exert an upward force upon a falling bungee jumper.

KE to PE
The jumper is losing speed (slowing down) and the bungee cord is stretching. Thus, the internal or conservative force (spring) transforms the energy from KE (speed) to PE (a stretched "spring"). One might also argue that the gravitational PE is decreasing due to the loss of height.

11. The spring of a dart gun exerts a force on a dart as it is launched from an initial rest position.
PE to KE
The spring changes from a compressed state to a relaxed state and the dart starts moving. Thus, the internal or conservative force (spring) transforms the energy from PE (a compressed spring) to KE (speed).

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