Kinetic Energy (Cambridge (CIE) IGCSE Physics): Revision Note

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, $m=160\mathrm{g}$ 

• Speed of the cricket ball, $v=35\mathrm{m}/\mathrm{s}$

Step 2: Write down the equation for kinetic energy

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

Step 3: Convert the mass into kilograms

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mrow»«mi»m«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»160«/mn»«mn»1000«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»16«/mn»«mo»§#160;«/mo»«mi»kg«/mi»«/mrow»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math» [1 mark]

Step 4: Calculate the kinetic energy

$E_k=\frac{1}{2}\times 0.16\times {\left(35\right)}^2$ [1 mark]

$E_k=98\mathrm{J}$ [1 mark]

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).

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, $E_k=1400\mathrm{J}$

Step 2: Write down the equation for kinetic energy

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

Step 3: Rearrange for the speed, v

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics»«mrow»«mn»2«/mn»«msub»«mi»E«/mi»«mi»k«/mi»«/msub»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mi»m«/mi»«msup»«mi»v«/mi»«mn»2«/mn»«/msup»«/mrow»«annotation encoding=¨application/vnd.wiris.mtweb-params+json¨»{¨fontFamily¨:¨Times New Roman¨,¨fontSize¨:¨18¨,¨autoformat¨:true,¨toolbar¨:¨«toolbar ref=`general`»«tab ref=`general`»«removeItem ref=`setColor`/»«removeItem ref=`bold`/»«removeItem ref=`italic`/»«removeItem ref=`autoItalic`/»«removeItem ref=`setUnicode`/»«removeItem ref=`mtext` /»«removeItem ref=`rtl`/»«removeItem ref=`forceLigature`/»«removeItem ref=`setFontFamily` /»«removeItem ref=`setFontSize`/»«/tab»«/toolbar»¨}«/annotation»«/semantics»«/math»

$\frac{2E_k}{m}=v^2$

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

Step 4: Calculate the speed

$v=\sqrt{\frac{2\times 1400}{70}}$ [1 mark]

$v=6.3\mathrm{m}/\mathrm{s}$ (2 s.f.) [1 mark]

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.