Kinetic Energy (Cambridge International IGCSE Physics)

Spec point — 1.7.2 · Recall and use the equation for kinetic energy Ek = 1/2 mv^2

Kinetic energy

Extended Tier Only

• Energy in an object's kinetic energy store is defined as:

The amount of energy an object has as a result of its mass and speed

• This means that any object in motion has energy in its kinetic energy store

  • If an object speeds up, energy is transferred to its kinetic energy store
  • If an object slows down, energy is transferred away from its kinetic energy store

A moving car has energy in its kinetic energy store

Kinetic energy equation

• The amount of energy in an object's kinetic energy store can be calculated using the equation:

$E_{k}=\frac{1}{2}mv^{2}$

• Where:

  • $E_{k}$ = kinetic energy, measured in joules (J)
  • $m$ = mass of the object, measured in kilograms (kg)
  • $v$ = speed of the object, measured in metres per second (m/s)

• The kinetic energy equation demonstrates that if the mass of an object is doubled for a given speed, then its kinetic energy will double

  • This is because kinetic energy is directly proportional to mass

$E_{k}\propto m$

• If the speed of the object is doubled for a given mass, it will have four times the kinetic energy

  • This is because kinetic energy is directly proportional to speed squared

$E_{k}\propto v^{2}$

• Since kinetic energy is directly proportional to speed squared, doubling the kinetic energy does not double the speed; it increases it by a factor of $\sqrt{2}$ (approximately 1.41)
• The change in an object's kinetic energy can be calculated using:

$\Delta E_{k}=\frac{1}{2}mv^{2}-\frac{1}{2}\mu^{2}$

• Where:

  • $v$ = final speed of the object, measured in metres per second (m/s)
  • $u$ = initial speed of the object, measured in metres per second (m/s)

Worked Example Calculate the kinetic energy stored in a cricket ball of mass 160 g moving at a speed of 35 m/s.

[3]

Answer:

Step 1: List the known quantities

• Mass of the cricket ball, $m=160g$
• Speed of the cricket ball, $v=35m/s$

Step 2: Write down the equation for kinetic energy

$E_{k}=\frac{1}{2}mv^{2}$

Step 3: Convert the mass into kilograms

m=160 / 1000=0.16 kg [1 mark]

Step 4: Calculate the kinetic energy

E_ k=1 half×0.16×(35)²* [1 mark]

$E_{k}=98J$* [1 mark]

Exam Hint When performing calculations using the kinetic energy equation, always double-check that you have squared the speed, even when the term $v^{2}$ has been written down. Also ensure that you have included the 1/2 factor in your calculation. Forgetting to do these two steps are the most common mistakes that students make.

Remember that the units of kinetic energy are joules (J).

Worked Example A cyclist and a bicycle have a total mass of 70 kg and a kinetic energy of 1400 J. Calculate their speed.

[3]

Answer:

Step 1: List the known quantities

• Total mass of cyclist and bicycle, $m=70\mathrm{kg}$
• Kinetic energy, $E_{k}=1400J$

Step 2: Write down the equation for kinetic energy

$E_{k}=\frac{1}{2}mv^{2}$

Step 3: Rearrange for the speed, v

2 E_ k=m v²

$\frac{2E_{k}}{m}=v^{2}$

$v=\sqrt{\frac{2E_{k}}{m}}$ [1 mark]

Step 4: Calculate the speed

$v=\sqrt{\frac{2\times1400}{70}}$* [1 mark]

$v=6.3m/s$* (2 s.f.) [1 mark]

Exam Hint You will most likely need to rearrange the kinetic energy equation in your IGCSE exam. The kinetic energy equation is one of the more difficult rearrangements at IGCSE.