Changes in Energy

This section explains changes in energy covering, energy in moving objects, kinetic energy, elastic potential energy, gravitational potential energy and changes in thermal energy. 

Energy in Moving Objects

Energy is the ability to do work. When an object moves, it possesses energy due to its motion, known as kinetic energy. Other forms of energy that can change include elastic potential energy, gravitational potential energy, and thermal energy.

Kinetic Energy

Kinetic energy ($KE$) is the energy an object has due to its motion. The amount of kinetic energy depends on the object's mass and velocity.

Formula for Kinetic Energy

$$KE = \frac{1}{2} m v^2$$

Where:

• $KE$ = kinetic energy (Joules, J)
• $m$ = mass (kilograms, kg)
• $v$ = velocity (metres per second, m/s)

Example Calculation

A car of mass 1,000 kg is moving at a velocity of 20 m/s. Calculate its kinetic energy.

$$KE = \frac{1}{2} \times 1000 \times (20)^2$$

$$KE = 0.5 \times 1000 \times 400$$

$$KE = 200,000 J$$ 

So, the car has 200,000 Joules of kinetic energy.

Elastic Potential Energy

Elastic potential energy is the energy stored in a stretched or compressed elastic object, such as a spring or rubber band.

Formula for Elastic Potential Energy

$$E_e = \frac{1}{2} k e^2$$

Where:

• $E_e$​ = elastic potential energy (Joules, J)
• $k$ = spring constant (Newtons per metre, N/m)
• $e$ = extension (metres, m)

Example Calculation

A spring with a spring constant of 200 N/m is stretched by 0.1 m. Calculate the elastic potential energy stored.

$$E_e = \frac{1}{2} \times 200 \times (0.1)^2$$

$$E_e = 0.5 \times 200 \times 0.01$$

$$E_e = 1 J$$

So, the spring stores 1 Joule of elastic potential energy.

Gravitational Potential Energy

Gravitational potential energy ($GPE$) is the energy stored in an object due to its height above the ground.

Formula for Gravitational Potential Energy

$$GPE = mgh$$

Where:

• $GPE$ = gravitational potential energy (Joules, J)
• $m$ = mass (kilograms, kg)
• $g$ = gravitational field strength (on Earth, 9.8 m/s29.8 \text{ m/s}^29.8 m/s2)
• $h$ = height (metres, m)

Example Calculation

A book of mass 2 kg is lifted to a height of 1.5 m. Calculate its gravitational potential energy.

$$GPE = 2 \times 9.8 \times 1.5$$

$$GPE = 2 \times 14.7$$

$$GPE = 29.4 J$$ 

So, the book has 29.4 Joules of gravitational potential energy.

Changes in Thermal Energy

Thermal energy is related to the temperature of an object. When heat is added to or removed from a substance, its thermal energy changes.

Formula for Changes in Thermal Energy

$$\Delta E = mc\Delta\theta$$

Where:

• $\Delta E$ = change in thermal energy (Joules, J)
• $m$ = mass (kilograms, kg)
• $c$ = specific heat capacity (J/kg°C)
• $\Delta\theta$ = temperature change (°C)

Example Calculation

A 0.5 kg piece of metal is heated, increasing its temperature by 10°C. If the metal has a specific heat capacity of 900 J/kg°C, calculate the thermal energy change.

$$\Delta E = 0.5 \times 900 \times 10$$

$$\Delta E = 4500 J$$ 

So, the metal gains 4,500 Joules of thermal energy.

This guide covers essential formulas and examples for changes in energy. Understanding these concepts is crucial for solving energy-related problems in GCSE Physics.