CIE A Level Maths: Mechanics复习笔记4.1.2 Energy

There are many different forms of energy including, but not limited to, heat energy, light energy, chemical energy and nuclear energy. In this course we deal with a type of energy called mechanical energy which exists in two forms, kinetic energy (KE) and gravitational potential energy (GPE).

Kinetic Energy (KE)

What is kinetic energy?

• Kinetic Energy is the energy formed by an object’s movement.
• Kinetic energy is a scalar quantity, it can not be negative
• The work done by a resultant force that acts to move an object in a particular direction will be equal to the change in kinetic energy of the object

How is kinetic energy calculated?

• A particle can only have kinetic energy when it is moving
• If a particle with mass, m kg is moving with speed v m s^-1 then its kinetic energy can be calculated using the formula

• • If the particle is moving in two dimensions with the velocity vector v then kinetic energy can be calculated in two ways
    • Using the formula on each component individually and finding the sum of the KE in each component
    • Finding the magnitude of the velocity to get the speed and then using the formula for KE
• Kinetic energy is measured in joules (J)
  • 1 Kilojoule = 1000 joules (1 kJ = 1000 J)

How do we derive the formula for the change in kinetic energy?

• The work done by the resultant force is equal to the change in kinetic energy
  • This is the final kinetic energy minus the initial kinetic energy
  • The formula for the change in kinetic energy is

What is potential energy?

• Potential energy is the energy stored in a stationary object
• Gravitational potential energy (GPE) is the energy a particle possesses when it is at a fixed height and gravity is acting on it
• There are other types of potential energy but in this module only GPE is dealt with and so sometimes GPE is referred to as potential energy (PE)
• GPE will change as the vertical height of an object changes
  • The work done against gravity on a particle as it moves upwards is equal to its increase in GPE
  • The work done by gravity on a particle as it moves downwards is equal to its decrease in GPE

How is gravitational potential energy calculated?

• Gravitational potential energy is equal to the product of the force of the weight of an object and its vertical height, h , above a fixed point
• If the object is sitting on the ground or the point chosen as the fixed base level, the object will have no gravitational potential energy
• As the object moves upwards, its GPE will increase
• As the object moves downwards again, its GPE will decrease

• When mass is measured in kg, acceleration due to gravity is measured in m s^-2 and height is in metres, m, gravitational potential energy is measured in joules (J)
  • 1 kilojoule = 1000 joules (1 kJ = 1000 J)