Q1. A golf ball has a mass of 60 g and is struck by the golfer's number 1 wood (driver), leaving the tee at a speed of approximately 32 m/s (just over 70 miles an hour). Calculate the kinetic energy of the ball.


A. Straight away, look back at the equation and see what the units are. You are given the velocity in metres per second so this value does not have to be changed, however your golf ball is given in grams but the equation is expecting kilograms therefore you need to make a conversion before you can actually start "crunching" any numbers.The mass of 60 g is 0.06 kg and the velocity is 32 m/s. The kinetic energy is therefore half of the mass multiplied by the square of the velocity, in other words 0.03 multiplied by (32 squared):


Q2. A skydiver with a mass of 105 kg leaps from an aeroplane at a height of 1500 m. At a certain point during the fall (s)he is travelling at 45 m/s. Calculate the kinetic energy of the skydiver at this point.


A. A little bit sneaky, because you are given information that you don't need. You don't need to know the height that the skydiver falls from because height is not a variable in the equation. The other items that you need are the velocity and mass, both of which you are given.


The kinetic energy of the skydiver is half of the mass multiplied by the square of the velocity, let's put these into the equation and see what we come back with:



It is likely, in an example like this that you will be asked to quote your answer to a certain number of decimal places and probably to kJ or even MJ when the numbers start to get quite large. For example this answer in kilojoules would be approximately 106.3 kJ.


You will not always be given the necessary figures to perform the energy calculation. What you might be given is a value for the kinetic energy and you you will then probably be asked to work out the mass or the velocity of the object. This requires you to have a knowledge of transforming equations or how to construct and use an equation triangle.


Here is an example of such a question:


Q3. A motorcycle has a mass of 190 kg including the rider and is travelling at a certain speed. At this certain speed the combined motorcycle and rider has a kinetic energy of 25,000 J. From this information calculate the speed of the motorcycle in metres per second and state to one decimal place.


A. Look at the question, you are given everything you need apart from the velocity which the question is asking you to calculate. You are told in what units to calculate it and to what precision to state your answer. You have everything you need to answer this question. First of all you need to transpose the equation for kinetic energy to make velocity the subject:



In this particular equation, establishing "v" is probably the hardest thing you will be expected to do as it involves taking a square root at the very end. Study each line of the expression to satisfy yourself that you understand how each subsequent line was arrived at. When you are able to carry on substitute your values given to obtain your value for v.


Usually, the subject will be stated on the left-hand side of the expression, so in our substitutions which will now follow I will swap it around. Follow the substitutions carefully so that you are happy that you understand how the answer was obtained:



Q4. A bullet leaves the muzzle of a rifle at a velocity of 1500 m/s. It has a Kinetic Energy of 16875 J. What is the mass of the bullet in grams?


A. In cases such as this, you will be given all but one of the items required and will be expected to transpose the equation to find the unknown. In this case the unknown is mass 'm' so we transpose the KE equation in terms of mass. NB: watch the units.


From here it is just a matter of 'plugging in' the values we have to arrive at the answer...again remember the units.



The answer is expected in grams.....be sure to convert it and present it that way at the end.


Q5. A van with a mass of 2450 kg is travelling at a constant velocity and has a kinetic energy of 1,960,000 J. At what velocity is the van travelling?


A. This question requires you to manipulate the equation once again in terms of velocity:




Q6a. A certain make of motorcycle has a kerbside mass of 197Kg. Disregarding the mass of the rider, the motorcycle is travelling with a velocity of 26.8 m/s (approximately 60 mph). Given this information, calculate the energy, in Joules in the vehicle's Kinetic Energy store.


From the equation for kinetic energy, this is a straightforward "plug-in" of the values given.


Q6b. A certain make of large saloon car with a kerbside mass of 1696 kg is travelling along the road, possessing exactly the same amount of Kinetic Energy in its Kinetic Energy store, as the motorcycle. Calculate the velocity/speed of the saloon car.


A. This question requires the standard equation for Kinetic Energy to be rearranged in terms of velocity:



Inserting the information that we have, into this rearranged equation for 'v' gives us:



Which, for the sake of interest is approximately 20.4 mph.


Q7a. The car in question 6, now catches up with the motorcycle which means that they are both travelling with a velocity of 26.8 m/s (60 mph). What is the new Kinetic Energy of the car?


A. Again this is a simple "plug-in" directly into the unaltered equation:


Q7b. The motorcycle pulls up into a lay-by at the side of the road. What is the Gravitational Potential Energy of the motorcycle at this point?


A. A little bit of a trick question given the fact that we have been talking about Kinetic Energy. During the braking process, and coming to a halt the motorcycle loses all of its Kinetic Energy to other energy stores (due to friction on the brake pads / tyres on the road, heat generated dissipates into the environment, possibly some sound energy et cetera). The motorcycle is at a standstill but is on the ground, so its Gravitational Potential Energy will be zero.


Q8. The driver of the saloon car in question 6, together with the vehicle have a combined mass of 1816 kg. The vehicle is travelling along at 13.4 m/s (which is approximately 30 mph) with a Kinetic Energy of 163,040.48 J. The driver stops, collects a passenger and then pulls away, returning to 13.4 m/s, but the vehicle now has a Kinetic Energy of 167,888.6 J. Taking the acceleration due to gravity to be 9.8 Newtons per kilogram, calculate the weight of the passenger in Newtons.


A. This time you're given some new information, the acceleration due to gravity in Newtons per Kilogram, so be sure to use it somewhere in your answer.


The extra energy in the Kinetic Energy store has come from the fact that the passenger collected has added to the overall mass. If we subtract the lower energy from the higher energy we can calculate the increase. Once we have the increase we can plug this into the Kinetic Energy equation rearranged in terms of mass and then apply the acceleration due to gravity to convert the additional mass into Newtons (weight).


The additional kinetic energy is given by:



We now rearrange the standard Kinetic Energy equation in terms of mass:



We could also have approached this question by calculating the new mass of the combined car and 2 passengers, and then by using the new value for Kinetic Energy we could have established the new mass, from which we would take the old mass to give the difference. In either case it would be 54 kg.


This of course, isn't the end of the matter. We have calculated the mass of the passenger but now we must calculate his/her weight in Newtons by multiplying the mass by the acceleration due to gravity:


Q9. A motorcar, with a mass of 725 kg is travelling at 35.5 m/s. Calculate its kinetic energy.



To be fair, they don't come much simpler than this one, but you can bet that the ones you will see on the exam paper will be a little bit more demanding. As well as gravitational potential energy, you will need to be able to "transpose" the equation for kinetic energy to make any other variable the subject. Very often you will be given questions which will demand this.


Q10. A bullet with a mass of 14 g leaves the muzzle of a rifle at a velocity of 552 m/s. Calculate its kinetic energy as it leaves the gun.



A. There was a tiny catch in this one, I hope you spotted that the mass of the bullet was given in grams not kilograms and you made the appropriate conversion?


Q11. An Airbus A380 holiday jet flying to the USA is travelling at 250m/s with a total Kinetic Energy of 18,750,000,000J (18,750 MJ). Calculate the mass of the jet (including all passengers and cargo).


A. The numbers look scary, it’s no different to the ones you have already seen, but there is a “transposition” to be done first:




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