Kinetic and Potential Energy

Energy is the capacity to do work!

Work is done to transfer energy! (Work = force x displacement along the line of action of the force).

Work and energy in physics are of the same nature, and have the same unit: Joules (J).

If after the work is done, energy is stored in an object, we call it potential energy; like when we raise an object, gravitational potential energy (GPE) is saved, or when we stretch a spring, elastic potential energy is saved in it. 

Closed system: a number of objects interacting with each other that are isolated from anything else around them. 

Principle of conservation of energy: in a closed system, energy is neither created nor destroyed, it is only converted from one form to another. 

Kinetic Energy:

Any moving object has KE.

Example 1:

Meena has a KE of 100 J when riding her bicycle. Her mass is 50 kg. Calculate her speed.

P5.1-1 KE & GPE interchange

Kinetic and potential energy interchange when an object falls or is thrown up:

Image above shows an object falling, as the GPE decreases, KE increases. 

Example 2:

A crane lifts a load of mass 3 tonnes. The work done by the crane on the weight of the load is 9MJ. Calculate the height that the load is lifted. Take g = 10 m/s².

Example 3:

A car of mass 1 tonne, is moving with a speed of 40 m/s. The driver applies the brakes to bring the car to complete stop. If the force applied by the brakes is 16 kN: 

1. calculate the distance it takes the car to stop;
2. what happens to the KE of the car as it stops.

P5.1-2 Heat and Temperature

When an object is being heated, thermal energy is transferred to it. 

Temperature is just a conventional number that we use to show how hot or cold an object is! 

Recall that specific heat capacity is the amount of energy required to change the temperature of 1 kg of a material by 1 degree.

To raise temperature of water by 1^oC, we need 10 times more energy compared to steel. 

Water can take a lot of heat energy in rather small amounts of its mass. This makes it a good material to cool car engines, or a nuclear reactor! Since 1^oC change in water temperature, can mean lot more temperature change in a metal! Also it can transfer heat energy to radiators of a house without losing too much temperature. 

Energy transfers

When water boils in an electric kettle, electrical energy is transferred to heating element of the kettle which in turn heats the water. But some of the heat is lost to the surroundings, and some as noise. These are called dissipated energy or wasted energy! 

Electrical energy is calculated from power x time; where power = PD x current

Example 4:

An electric kettle is connected to mains of 230 V and draws 7.8 A of current. If it takes 3 minutes to boil a certain amount of water, initially at 15 ^oC, find the mass of the water in the kettle. Specific heat capacity of water: 4200 J/kg ^oC.

Kilowatt-hour

To use smaller numbers for energy used by households, school, etc. we use kilowatt-hour instead of joules. Watt is the unit for power, but when multiplied by a unit of time, it gives energy. 

P5.1-2-a Transfer of thermal energy:

Thermal energy can transferred in three ways:

1. Conduction: increase in temperature increases the vibration of particles of a material which leads to this energy being transferred to other parts of the object or other objects.
2. Convection: when a radiator in a room warms the air around it, the particles of air get further away from each other, which leads to density of air to decrease. This part of air then raises and get replaced by colder air, which in turn will raise again and get replaced by some colder air, and eventually warm up the whole room. Same happens in fluids e.g. when warming water in a pan. 
3. Radiation: infrared radiation

P5.1-3 Elastic potential energy

Energy stored in a spring when it is stretched or compressed.

Example 5:

A retractable pen is placed on its head on a desk and pressed down on its spring so that its centre of mass is lowered by 4.8 mm. The pen is then released and it jumps up vertically. 

1. Calculate the height which the centre of mass of the pen jumps after release. Ignore air resistance and other forms of energy transfers to the surroundings.
2. Explain why in reality the height will be less.

The spring constant = 263 N/m; mass of the pen 0.9 g; gravitational acceleration = 10 m/s². 

Solution

Answer to part b) some of the energy stored in the spring will be converted to heat, sound, and the pen itself experiences some air resistance while it moves up.

P5.2 Power and Efficiency 

Normally when we convert one form of energy to another, some of the original energy is converted to some other forms that were not intended! Example 5 above shows this. 

Other examples:

• When an electric motor raises a lift: some of the energy goes to heat and sound. To reduce this we lubricate the components to reduce friction;
• When we heat our homes, some the heat is wasted through wall and windows. To reduce this we insulate the walls and use double glazing on windows. The insulation boards put in the wall cavity has shiny foil on both sides. Shiny object reflect infrared radiation and reduce heat transfer. 

Insulation reduces heat loss by conduction. The lower the thermal conductivity and the thicker the better!

A wool jumper traps air, wool and air are both good insulators. Trapped air reduces heat loss by conduction and convection.

P5.2-1 Energy Efficiency 

In the fraction above, energy can be replaced by power too!

Example 1:

If the efficiency of a diesel car is 15%, and the useful energy output is 45kJ, calculate the total energy input.