Work, Energy and Power

Aslevels Physics Notes

Topic 6: Work , Energy and Power

Energy

Energy is defined as the ability (or capacity) to do work. Energy is measured in joules. When a body has 300J of energy it means that it can do 300J of work.

Different forms of energy are shown in the table below:

 Conservation of energy

The law of conservation of energy states that the total energy of a closed system is constant. This means that energy can be transformed from one form to another but it can neither be created nor destroyed – the total energy of a closed system will be the same before an interaction as after it. When energy is transformed from one form to another either:

•  Work is done – for example, a man does work against gravity by lifting a large mass onto his shoulders. 

                  Or 

• Energy is radiated or received in the form of electromagnetic radiation – for example, internal energy is radiated away from the white hot filament of a lamp by infrared and light radiation. 

Gravitational potential energy

Consider a mass m is lifted through a height h. The weight of the mass is mg, where g is the gravitational field strength.

                               𝑤𝑜𝑟𝑘𝑑𝑜𝑛𝑒 = 𝑓𝑜𝑟𝑐𝑒 × 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑 = 𝑚𝑔∆ℎ 

Due to its new position, the body is now able to do extra work equal to 𝑚𝑔∆ℎ. It has gained extra potential energy, ∆𝑊 = 𝑚𝑔∆ℎ

                      𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒑𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍 𝒆𝒏𝒆𝒓𝒈𝒚 = 𝒎𝒈∆h

If the net force acting on an object in a particular situation has a constant value, or if it is appropriate to utilize an average force value, then: 

The net work done on an object is defined as the product of the net force on the object and its displacement in the direction of the net force. When the force and displacement are in the same direction, the work done by the stated force is given by:

                     𝑊 = 𝐹. 𝑆 

Where:

W is the work done by the stated force in joules (J)
 F is the magnitude of the stated force in newtons (N)
S is the magnitude of the displacement in meters (m)

Work is the area under a force – displacement graph.

Situations also occur in which a constant force acts at an angle 𝜃 to the direction of motion. A force acting at an angle will be less effective than the force acting solely in the direction of the displacement. The component of the force in the direction of the displacement, 𝐹𝑐𝑜𝑠𝜃, is used in calculating the work done in the required direction.

The efficiency of energy transformations

The percentage of energy that is transformed to a useful form by a device is known as the efficiency of that device. All practical energy transformations ‘lose’ some energy as heat. The effectiveness of a transfer from one energy form to another is expressed as:  

Mechanical energy

Mechanical energy is defined as the energy that a body possesses due to its position or motion. Kinetic energy, gravitational potential energy and elastic potential energy are all forms of mechaical energy.

Kinetic energy 

 An object in motion has the ability to do work and therefore is said to possess energy. This energy carried by a moving object is called kinetic energy (from the Greek word “kinesis’: literally meaning motion).

If a moving object of mass, m, and initial velocity u, experiences a constant net force, F, for time, t, then a uniform acceleration results. The velocity will increase to a final value, v. work will have been done during the time the force is applied.

From the definition of work, when the net applied force is in the direction of the displacement . 

𝑊 = 𝐹S 

Now substituting Newton’s second law 𝐹 = 𝑚𝑎 we get

𝑊 = 𝑚𝑎𝑆 

Using one of the equations of motion 

2𝑎𝑆 = 𝑣 ² − 𝑢²

𝑆 = 𝑣² − 𝑢²/ 2𝑎   

Power

Power (P) is the rate of doing work or transforming energy

Power is measured in joules per second. One joule per seond is 1 watt. The symbol for watt is W.

Power and velocity

Consider a car travelling at constant velocity v along a straight, level road. The engine must continue to do work against friction. If the firctional force is F, then the engine will supply an equal-sized force in the oposite direction. The work done by the engine, ∆𝑊, in time ∆𝑡 is 𝐹∆𝑆, where ∆𝑆 us the distance travelled in time ∆𝑡.