# Investigation to Determine how the Height of a slope Affects the Speed of an Object Travelling Down the Slope

Investigation to Determine how the Height of a slope Affects the Speed of an Object Travelling Down the Slope

## Prediction

I predict that the higher the slope the faster the speed of the object travelling down the slope. This is because the higher the slope, the more gravitational potential energy an object has when it is at the top of the slope and as the object travels down the slope gravitational potential energy is being converted in kinetic energy so the more gravitational potential energy the object has at the top, the greater the kinetic energy at the bottom and the greater the kinetic energy the greater the speed.

g.p.e.=mgh                                           k.e.=½mv²

g.p.e. is gravitational potential energy    k.e. is kinetic energy

m is the mass of the object                      m is the mass of the object

g is the gravitational field strength           v is the velocity of the object

h is the height the object is at

These formulas show that gravitational potential energy is related to height and that kinetic energy is related to speed. Because of the laws of conservation of energy, energy is never lost, only converted to different forms, the gravitational potential energy at the top of the slope is roughly the same as the kinetic energy at the bottom although some energy is converted to heat because of friction. This allows me to work out a formula that links the speed or velocity of an object to the height it started at.

g.p.e.=k.e.                        sub in equations

mgh=½mv²                        divide by mass

gh=½v²                        multiply by 2

v²=2gh                        square root

v=√2gh                        sub in gravitational field strength of earth

v=√20h                        This is the equation linking speed to height

I am going to plot two graphs for my experiment; the first will be velocity against height and the second will be velocity squared against height. I predict that the first graph will have a curved line getting steeper because velocity is not directly proportional to height, velocity squared is directly proportional height so the line on the second graph will be a diagonal straight line.

## Trial Experiment

The purpose of doing a trial experiment is so that you can decide what would be the best possible method. It allows you to decide what apparatus to use and what measurements to use to make the final experiment more accurate. I am going to use my trial experiment to help me determine three things, what heights to use in the final experiment, what run-off distance to use and how to get the object to roll in a straight line.

The reason I am using the trial experiment to find what heights to use is because the heights you choose can greatly alter the accuracy of your experiment, for example if the slope is too high the object will travel too fast across the run-off distance for you to time and the results will not be accurate. If, on the other hand, the slope is too low the object may stop before it reaches the end of the run-off distance because of friction. I will start with the height of the slope at 2cm and use a variety of different heights up to about 50cm.

I am trying to find out what the best run-off distance to use is because if it is too short the results will not be accurate because the object will complete it too quickly to record accurately and if it is too long the results will not be accurate because either the marble will stop completely or it will slow down so much that the speed on the run-off distance will be a lot slower than the speed of the object at the bottom of the slope and that is what we are trying to work out. I will start with the run-off distance as 1m and change it if it is necessary.

Getting the object to roll in a straight line is important because if it crosses the run-off distance diagonally than it will have travelled a lot further than what the run-off distance has been recorded as and the speed will be calculated to e slower than what it actually should be. I will start by using a pipe that has been cut in half and is semi-circular as the slope so that the object rolls down the middle of it and I will stick down two rulers either side with a gap just big enough for the object to fit through on the run-off distance to make sure it carries on rolling in a straight line.

The object I will use for my trial experiment will be a marble and the slope will be held up by a clamp and stand. Also I will use a barrier at the end of the run-off distance to help me know when it has reached the end.

What the trial experiment told me

After the first seven results I recorded I decided that the run-off distance was too short for the results to be accurate so I lengthened it to 150cm. This is the length of the distance I will use for my final experiment. I ...