Kinetic Energy (Oxford AQA IGCSE Combined Science Double Award)
Revision Note
Kinetic Energy
Energy in the kinetic 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 store
If an object speeds up, energy is transferred to its kinetic store
If an object slows down, energy is transferred away from its kinetic store
Kinetic energy of a moving car
The amount of energy in an object's kinetic store can be calculated using the equation:
Ek = ½ × m × v2
Where:
Ek = kinetic energy in joules (J)
m = mass of the object in kilograms (kg)
v = speed of the object in metres per second (m/s)
The equation tells us 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
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 velocity squared
Worked Example
Calculate the energy in the kinetic store of a vehicle of mass 1200 kg moving at a speed of 27 m/s.
Answer:
Step 1: List the known quantities
Mass of the vehicle, m = 1200 kg
Speed of the vehicle, v = 27 m/s
Step 2: Write down the equation for kinetic energy
EK = ½ × m × v2
Step 3: Calculate the kinetic energy
EK = ½ × 1200 × (27)2
EK = 437 400 J
Step 4: Round the final answer to 2 significant figures
EK = 440 000 J
Worked Example
A car of mass 1500 kg is travelling at 13 m/s (30 mph).
a) Show that if the speed of the car is doubled, the kinetic energy of the car is increased by a factor of 4.
b) Use your answer to explain why obeying speed limits on residential roads is important to the safety of pedestrians.
Answer:
Part a)
Step 1: List the known quantities
Mass,
Speed,
Step 2: Write out the kinetic energy equation
Step 3: Determine the kinetic energy of the car at 13 m/s
Step 4: Determine the kinetic energy of the car if the speed is doubled
Step 5: Show that the kinetic energy of the car has increased by a factor of 4
OR
The car has a kinetic energy of 126 750 J when travelling at a speed of 13 m/s, when the speed is doubled to 26 m/s the kinetic energy is increased by a factor of 4 to 507 000 J
Part b)
The faster a car is travelling the more energy it has in its kinetic store
For the car to come to a sudden stop (for example, if a pedestrian steps into the road), the energy in its kinetic store must be transferred by heating to the thermal store of the breaks
Since kinetic energy is proportional to the speed squared, even small increases in speed will have a large impact on the car's stopping distance
If the car is travelling too fast to be able to stop before hitting a pedestrian, some of the kinetic energy of the car will be transferred to the pedestrian upon impact
The greater the speed of the car at the point of collision, the greater the energy transferred and the more severe the injury
Examiner Tip
When performing calculations using the kinetic energy equation double-check that you have squared the speed. Forgetting to do this is the most common mistake that students make.
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