Parameters Affecting Speed

Planning

A factor which tremendously affects our daily lives is most certainly speed. In the morning, we take the car, the bus or the trains to arrive to work. These vehicles travel at extremely high velocities, which would be impossible to reach without machine power. Consequently, it is of enormous importance to know about the parameters which have an affect on speed. The automotive industry, for instance, needs to determine these factors in order to be able to produce faster, safer and overall better vehicles. This investigation will precisely deal with all of the possible aspects which can affect velocity in any sort of way.

Now let’s hypothesize that there is a car at the top of a hill. At the bottom of it, there is a bus waiting at a stop sign. What would the velocity be if the car began to move due to the failure of the brakes? And how much energy would the automobile have on impact? These questions can be easily answered with a couple of algebraic equations.

Let the height of the hill be 250 m and the mass of the car be 1000 Kg.

PE =    weight x height

PE =    10000 N x 250 m

PE =    2500000 J

So at the bottom of the hill all of this energy will have been converted to kinetic energy. Now I can find the velocity of the car…

            PE = KE

            m x g x h = ½ x m x v²

            v² =        2500000      

                          ½ x 1000

            v² = 5000

            v  = 70.7 m/s

The car would hit the bus at a speed of 70.7 m/s. Now with this result we can calculate other variables such as the acceleration of the vehicle down the hill. This can be done using the formula the following formula:

a = (v – u) / t

So let’s suppose that the whole journey to the bottom of the hill took about 30 seconds, then

            a = (v – u) / t

            a = (70.7 – 0) / 30

            a = 2.357 m/s²

So the car accelerated 2.357 m/s².

Naturally, the results that I have calculated are assuming a frictionless environment. This, of course, is not the case in our world. Friction is a force which opposes the movement of an object. Friction between solid surfaces depends on the type of surface. There is friction between the car wheels and the road. The road is generally rough and not at all slippery, so that when the car breaks it does not skid. Consequently, if the road were wet, it would be smoother and slippery, thus reducing friction. With oil, it would reduce even further since it is a better lubricant.

Another factor that can affect the speed of the car is its mass. As a matter of fact, I believe that, by having more mass, the automobile’s gravitational potential energy will be greater. As a result, its kinetic energy will be the same. Therefore the vehicle will have to have a greater velocity as well.

            Speed is also important in sports. For instance, a ski jumper at the top of the hill also needs to know the factors which affect velocity, since the greater the speed the farther he will go. However, in addition to his mass and the floor’s friction, also the air friction can affect his speed. This is called fluid friction (since it acts in both liquids and gases) and depends on the object’s surface area and speed. This type of friction increases as the contact area and velocity increase. So, if a ski jumper wants to travel far in the air, he will have to assume a streamlined, or better, an aerodynamic position which will minimize friction.

Parameters affecting speed are also crucial in theme parks. A roller-coaster ride has to be perfect in every small detail. Knowing the speed of the ride is a life or death situation, since if the roller-coaster were traveling too fast then maybe it would jump off its tracks, ending its journey in a spectacular crash. In these type of rides it is essential to know the gradient of the slope, since it is another influential factor on velocity. If the slope is steep, then the ride will naturally travel at a higher speed. While if the slope is gentle, then it will have a lower velocity and travel less faster. By creating a slope with a certain gradient, the theme park engineers can have the ride pretty much under control.

            As I have said before, in this experiment I will be investigating the parameters which affect speed. In order to do so, I will be using a trolley which will roll down a ramp of a pre-determined distance. In order to record the distance that the trolley has traveled over a certain time period, I will use an ultrasound sonar. This apparatus measures the distance through the use of ultrasound waves. The waves bounce off the object and travel back to the sensor which measures the distance it has traveled. This method is widely used, for instance, on ships. In fact, with the aid of sonar, ships traveling on seas can find out the depth of the sea floor so that they can avoid hitting any possible sandbanks or rocks which could cause damage to the ship. Another example could be the echoes heard in canyons. If somebody shouts, the sound travels to the wall and then bounces back. The ultrasound apparatus will be connected to a computer so that I can have very precise readings with small intervals.

            Before I actually begin to take down the results, I will do a few trial runs in order to see that everything is working perfectly, and that there is no malfunction with the computer programming or the ultra-sound device. Once I feel happy with all of the apparatus I shall commence recording my actual results.

In order to test the various factors, I will be changing the various parameters. For instance, I will increase the gradient of the bench each time 10 cm, each time testing it at least three times in order to have a pretty accurate result, whilst keeping the other factors constant. Then I will also pour different liquids on the bench in order to vary the friction, such as water, oil, etc.. Furthermore, I will also add masses to the trolley, in order to test the affects of weight on velocity. Finally, I will change the aerodynamics of the trolley by increasing its surface area. This can be done by adding a sheet of paper which can act as a sort of parachute. Naturally, this will also vary the weight of the trolley, but only by a minimal amount which shouldn’t have a tremendous negative effect on my results.

            I will firstly record all of my results in a table. It will be divided in three columns in which I will write the distance the trolley has traveled and the time taken for it to cover that distance as well as the average velocity at that precise moment. My table will look something like this:

I will be able to calculate the average speed at each point in time by using the following formula:

average velocity =     total displacement     

                                                                         total time taken

With the results in the table, I will then proceed to graph my results on a displacement-time graph, in which I predict that I will see in every graph an increase of speed shown by a straight line. Then I will also graph a velocity-time graph, in order to see the acceleration of the trolley at each point in time. Finally, I will also graph the average velocity against the parameter which I was verifying. So for instance, after having all of my results on the effects of mass on speed, then I will draw up a graph of speed versus mass of trolley. These graphs will give me the real answers to my investigation.

I believe that my results will show that all of these factors greatly affect speed. I will see that when the gradient of the slope is increased, so will the speed. However, this will not happen proportionally. Instead, I think that the speed will increase exponentially, as shown on the graph.

This idea will probably also be reflected in the graph of mass against speed. As a matter of fact, with a bigger mass, then the trolley’s gravitational potential energy will be greater. So if PE = KE then, the kinetic energy will also be greater and therefore it will have to travel at a greater speed. However, I don’t think that it will be exponential, but rather proportional. This means that we should see a straight line. The graph will look like this:

Finally, if various lubricants are poured onto the bench, I expect that the speed of the trolley will increase, however, I believe that it will not be uniformly in any sort of way. If graphed, the results would most certainly be in an irregular pattern. Consequently, I believe that I would have to use a scatter graph and from it draw a line, or better, a curve of best fit. This idea will probably also apply for the results regarding air friction.

Results:

Analyzing Evidence:

            In this investigation, I was looking at the factors which have an effect velocity. After having carried out the experiment numerous times and recorded my results, I came up with some graphs from which interesting conclusions can be made.

            First of all, let’s look at the relationship between velocity and height. Straight away, if we look at the tables, we can notice that the predicted values, calculated mathematically, are completely different from the actual results that I attained. This is due to various phenomena, most important of which is friction. As a matter of fact, even though the surface on which the trolley was being rolled down was rather smooth, it was not frictionless. This had the adverse effect of slowing down the trolley. In addition to this, also the air played a part in decreasing the ‘car’s’ speed. This is because the air particles in the air are hitting the car while it is rolling down, thus causing air resistance.

            Despite these small inaccuracies, the results still give us some valid proof and actually confirm my initial hypothesis. In fact, we can see that if we graph the height against the velocity of the trolley, we get a curving graph. This insinuates that there is an exponential increase. As a result, if we graph the height of the ramp against the square of the velocity, we get a straight line, through the origin. This last graph therefore suggest that the height of the ramp and the square of the velocity are directly proportional. This idea can be written as:

h α v²                          where h = height and v = velocity

or as

h =kv²                         where k = the constant or the gradient of the graph, which stays always the same

In simple words, this means that if we double the height of the ramp, the velocity of the car will quadruple, if we triple it, the velocity will be nine times as much. This theory is helpful because by knowing just one variable it is very easy to calculate the other. For instance:

If the velocity of the trolley is 1.1 m/s, calculate the height of the ramp.

Similarly, the relationship between the amount of kinetic energy and the velocity of the trolley is the same. That is the kinetic energy is directly proportional to the square of the velocity. Naturally, these theories are based on the idea that the other factors remain constant.

            Additionally, I also looked at the affects of mass on the velocity of the trolley and I must say that I found some quite interesting results. As a matter of fact, the most noticeable thing is that the velocities of the trolley with the extra masses, are usually lower than those without. This is probably due to the fact mentioned earlier: air resistance. In fact, with the extra masses, the surface area of the trolley is increased. This consequently creates a bigger area on which the resistance of the air will act, thus dramatically decreasing the trolley’s overall velocity.

            Nevertheless, there seems to be no true pattern or relationship between the mass and the velocity of the trolley. As a matter of fact, if we look at the graph, we see that there is no real pattern. There is a very slight positive correlation, however, in my opinion, it is not enough to base some sort of relationship on. This increase is simply due to my inaccuracy. Consequently, I believe that mass has no effect on the trolley’s velocity.

            Last, but not least, I analyzed the relationship between the amount of energy of the trolley and the height of the ramp. If we take a look at the graph we can easily see that as the height increases so does the kinetic energy and vice versa. Consequently, this would suggest that the height of the ramp is directly proportional to the energy of the trolley (h α KE). If one value increases so does the other in the same proportion.

On the whole, though, despite the few problems with accuracy, I should consider this experiment a success.

Evaluating evidence:

             As mentioned above, the experiment went well. Nevertheless, there are some slight modifications which would improve it further. The biggest problem that I had was friction. In fact, be it friction with the surface of the ramp, or the resistance of air, a lot of the trolley’s energy was lost, dispersed in the environment in the form of heat as well as sound energy – after all, the trolley did make noise rolling down the ramp. This lead to the few anomalous results. As a matter of fact, if we look at the speed of the trolley in the first trial at the height of 63.5 cm, we see that the velocity is 3.6 m/s. However, this is impossible since the calculated velocity is of 3.53 m/s. Consequently, this could only have been achieved if another force was applied upon the trolley, probably a slight push from my hand or a breeze of air.

In order to resolve this problem, the best thing to do would be to remove or at least, minimize the friction. This can be down in a number of ways. In regards to the ramps, it can be oiled or ‘iced’ i.e. place ice on it. This would dramatically reduce the amount of energy lost due to friction. Another way would be to use a jet of air or a magnet strong enough to levitate the trolley. As a result, the trolley’s wheels wouldn’t be touching the ramp anymore, thus getting rid of any possible friction. Many forms of transportation work on this principle, the Japanese bullet trains for instance.

The air resistance, on the other hand, can be cancelled by simply getting rid of the air. In fact, if the experiment were carried out in a vacuum, there would be no air particles and therefore there would be hardly any friction with the air. Another possible resolution could be to streamline the trolley. This would consist in reducing its surface area as much as possible as well as smoothing out the sharp, square edges of the trolley. Many modern day cars use this idea in order to minimize the air resistance and maximize its velocity.

Some further investigation could actually consist in testing these latter variables. If various substances are poured onto the ramp, this will modify the friction and consequently influence the trolley’s speed. Then, a relationship between the density of the substance and the velocity could be deduced. Similarly, the influence of surface area could also be investigated by adding pieces of cloth of various areas.

Another small problem which I encountered was that when I was recording the velocity of the trolley, I had to repeat some trials numerous times because the sonar would take bad readings. This was due to the fact that at the end of the ramp the trolley would jump off and ‘crash’. This was picked up by the computer and displayed some strange results. Consequently, I had to repeat the experiment quite a few times. A possible solution to this dilemma would be to add a flat plank on which the trolley would continue to roll on until it stopped. This would stop the trolley from jumping of the ramp, thus solving the problem of the strange readings. On the other hand, these ‘strange’ results could also have been due to the fact that the ultrasound apparatus didn’t pick up the trolley at the bottom of the distance. The sound waves could have been hitting a nearby cupboard or even the wall. However, I believe this was not the case since the ultrasound apparatus was inclined with the same angle of the ramp, and therefore, its sound waves should have traveled parallel to the ramp, thus ensuring that the trolley would be hit.

A last further experiment, could involve the analysis of the effect of gravity on the trolley’s velocity. This could not actually be done practically, since we cannot go to the Moon or to some other planet without a space shuttle and the necessary equipment, which only a nation could afford. Consequently, we would have to restrict ourselves to the simple math. Let’s, for instance see what would happen on Mars:

Mars has a gravity of 4 N/Kg

Therefore if,    

            mgh = ½mv²

            1 x 4 x 0.135 = ½ x 1 x v²

            0.54 = ½ v²

            1.08 = v²

            v = 1.04 m/s

So if we compare the velocity on Mars with the one on Earth, we see that the velocity on the ‘Red Planet’ is less. This suggests that with a lower gravity the velocity is also decreased. However, the actual relationship would have to be studied in depth in a further investigation.

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