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Kinetic and Potential Energy
Introduction

In this scenario we are going to explore how a car on a ramp reacts to the force of gravity.

We are going to do this by looking at a scenario of a car on a fairground style roller coaster.

Finally, we will look at a GCSE exam question where we can apply what we have learned.

Background

​The concept of energy is central here.  When we do work we are expending energy.  When a body is travelling at speed is has kinetic energy due to its speed.  When an object is at a height above the ground it has energy, called potential energy that can be realised by letting the object fall.  Commonly one form of energy can appear in a different form.  When we push a car up hill, we expend energy on the car which gains potential energy.  We expect that in ideal conditions energy will be conserved.  We don't see this in practice because there are usually ways in which energy escapes from the system, typically there may be work against friction which heats surfaces, energy might be converted to sound, or might raise the temperature of something.  For example, in a waterfall, the water at the top has potential energy it falls and gains kinetic energy, it then lands in the pool at the bottom where it loses its kinetic energy which heats the water.  So, the temperature of the water at the top of a waterfall is lower than that at the bottom.

In this scenario we are going to only consider the ideal case, where there are no losses to friction and other possible energy leaks.  As all these different forms of energy are measured using the same units 'Joules' (J).

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Notice that the yellow car is high on the ramp at the left.

Press ‘Start’, the car will start to roll down the ramp, then up and over the hump, and up the final slope where it will be halted.

You can see the car’s speed and height at any point on the central speedometer and height meter.

Speed and Height
  • Can you estimate the car’s fastest speed from the speedometer

  • Can you estimate the car’s lowest position from the height meter?

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You can re-run the e-scenario by using the Reset button and then the Start button.

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  • What is the height when the car is going the fastest?

  • What is the height when the car is going the slowest?

Energy

You will have noticed that the car is slowest when it is highest and fastest when it is lowest.

In this e-scenario there is no slowing force either from friction with the ramp or air resistance.

The speed is governed by the energy.  The car has potential energy due to its height, and kinetic or movement energy due to its speed.  As there is no energy lost to friction:

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   Total energy = constant = Potential + Kinetic energy.

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Potential Energy

The potential energy (PE) = mgh

Where m = mass of car

g = acceleration due to gravity (9.81 m/s²) and

h = height.

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The result has the units of energy, i.e. Joules.

The mass of our yellow car is 2kg.

What is its potential energy at its highest point?

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The potential energy (PE) = mgh

Where m = 2kg

g = 9.81 m/s2

h = 5.1m

 

Therefore: PE = 2 x 9.81 x 5.1 Joules = 100 J

Kinetic Energy

The kinetic energy (KE) = 0.5mv²  (half ‘m’ v’ squared)

Where m = mass of car

v = speed of the car

The mass of our yellow car is 2kg.

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What is its kinetic energy at its highest point?

What is its kinetic energy at its lowest point?​​

The light gates

The light gates time how long it takes the car to pass through and displays this time in seconds.

A beam of light is shone across the gate.  When the car passes through the gate it breaks this beam, the light gate timer starts when the beam is broken and stops when the beam is restored.

You can see the unbroken beam in the screenshot above and the beam of light being broken by the car in the screen shot below.

Speed of car using light gates

The speed of the car can be approximated by using the length of the car (0.9m) and the time taken to go through a light gate.

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The speed is given by:

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    Speed = distance / time

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For example, the car’s speed through the left gate = 0.9/0.1 m/s = 9 m/s

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Note that timings and the meters in the simulation are only approximate. They are not accurate due to many factors including your computer’s specifications.

Exam Questions

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AQA May 25 Foundation Paper 1

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If you have difficulty answering this, try the e-scenario again taking note of the changes in the potential and kinetic energies.

Remember the PE is dependent on the height, and the KE is dependent on the speed.  Without friction and air resistance, KE + PE is constant.

If you have difficulty answering this, go back to the description of the light gates.

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