4.1.23

# Conservation of Energy

Test yourself

## Conservation of Energy

One of the fundamental laws of physics is that energy cannot be created or destroyed, only transferred from one form to another.

### Law of energy conservation

• This law means that if you measured all the energy in the universe, it would be exactly the same whether you took the measurement now, in 10 billion years, or just after the big bang!

### Energy in = energy out

• For a machine that converts energy from one form to another, the energy in must equal the energy out.
• In the case of a kettle:
• Electrical energy in = heat energy to water + sound energy + heat energy wasted

### Energy before = energy after

• For a collision or an explosion, the total energy before must equal the total energy after.
• In the case of an inelastic collision, some kinetic energy is converted to other forms and lost from the system.

## Types of Energy

There are many forms of energy found in physics problems. Two key examples are kinetic energy and gravitational potential energy.

### Kinetic energy

• The equation for the kinetic energy of an object is:
• $E_k = \frac12 m v^2$
• It is the energy involved in moving.

### Gravitational potential energy

• The equation for the gravitational potential energy of an object is:
• $\Delta E_p = m g \Delta h$
• It is the potential energy of an object in a gravitational field.

## Common Energy Problems

Energy conservation problems are very common in physics. Use the conservation of energy to solve them.

### Projectile

• A projectile thrown into the air starts off with purely kinetic energy.
• The kinetic energy gradually transfers to gravitational potential energy.
• At the top of the throw all the energy has become gravitational potential energy.
• We can use the equation:
• kinetic energy at bottom = gravitational potential energy at top
• $\frac12 m v^2 = m g \Delta h$

### Climbing stairs

• A machine carries an object up a flight of stairs.
• The work done by the machine must equal the gravitational potential energy of the object at the top of the stairs.
• We can use the equation:
• work done by machine = gravitational potential energy at top
• $W = m g \Delta h$

### Slingshot

• Work is done to pull a slingshot back. The object is fired from the slingshot.
• Work done is converted to elastic potential energy, which is converted to kinetic energy.
• We can use the equation:
• work done = elastic potential energy at start = kinetic energy at finish
• $W = \frac12 k (\Delta L)^2 = \frac12 m v^2$