# Newton's second law of motion states

From above we know that Newton's Second Law of Motion mentions that, that acceleration(an effect) is the result of the application of an net external force(which becomes the cause).Thus, one thing that we can really interpret is the relationship between these two quantities is that of cause & effect. Furthermore, form the above proved relation we know that force (F) is equal to the vector product of a scalar quantity, the mass (m), and a vector quantity,the acceleration (?a), which implies that the directional motion of the acceleration is in same direction as that of the net force. Thus, we can say that although acceleration is the measurement of the change in velocity of a body, it is strictly determined by the external force applied (F) and the total mass of the body (m); and we all know it is expressed as the "time rate change of velocity".

Having said this in my extended essay I would like to investigate how this change in the application of force & changing the mass of an automobile will affect its acceleration when in motion. Also, how this application of force helps derive the efficiency of an automobile, which is very important in the making of an automobile. Obviously, when an automobile is designed all the forces acting on it are taken into consideration like the drag force, the weight, the frictional force between the car & the tyre. One of the most important forces which need to be overcome is the frictional forces in the engine parts. Thus, this forms an important part for the automobile for its daily ride.

In this experiment I will investigate the Newton's Second Law as applied in the manufacture of an ideal automobile. According to Newton's Second law of Motion F = mDa, F is the force applied on the body, m is the mass of the body, & a is the acceleration produced on the body. In this experiment we will use a low friction cart of mass m, which will be pulled be a string running through a pulley, & connected with a system of weights on the other end. Due to the weight on the other end a tension will be created in the string which will in turn pull the cart. The main objective of the experiment is to understand the relation between the acceleration, mass of the cart & force acting on it, & how it can be used to improve the efficiency of the engine.

In the above shown diagram, one of the forces acting on the cart will be gravitational pull on the cart, this will be balanced by the normal reaction acting on the cart, and hence there will be no vertical motion in the cart. Now, in case of the mass m2 attached on the other end of the pulley, acceleration due to gravity g will act. Thus, there will be vertical motion in the direction of the gravity. This motion, according to Newton's Third Law, will produce an equal & opposite force in the string, namely the tension T, which in turn will produce a reaction in the motion of the cart, which will result in horizontal acceleration a in the cart.

Thus, from the above derived formula we already know that

Thus from the above formula obtained & the above made diagram, an inverse relation is obtained between the acceleration & the total mass of the cart, & a direct relation between the acceleration & the mass attached on the other end.

One immediate conclusion from the above mentioned formula is that as the weight of the cart increases the acceleration produced in it will go under constant decrease for a particular value of the force acting on the cart, whereas in case of the of the increasing force, the acceleration will go under a constant increase for a particular value of weight. Thus, as we increase the mass of the, the acceleration will go under decrease, & to keep this acceleration constant we will have to increase the force acting on the cart. Now, this increase in force will only happen from the internal engine of the car. But, if the force is increased, then the engine will have to work more, which means that there is going to be a large amount of wear & tear in the engine parts of the automobile. There will be more friction between the engine parts, & there will be less heat dissipation[2], resulting in maximum heat loss to the outside & less to the engine, resulting in low engine efficiency. Also, more of this wear & tear will also be related to the type of fuel in use. If the oil in use does not lubricate the engine properly, then due to increase in the heat produced in the engine due to the daily use, there might a high amount of wear & tear, which will obviously reduce the life of the car engine, & will have to be replaced at regular intervals, which would be very expensive.

Engine efficiency is one of the prime important factors in the design of an automobile, as the engine form the core of an automobile. The greater the efficiency, there is a high possibility of the automobile performing better, because the fuel consumption will decrease, that is the amount of fuel used to travel per unit distance. But if the case is otherwise, where the fuel consumption is increasing then it is a matter of concern, as the emissions from the automobile will also increase. This won't be welcome to the current situation of global warming as automobile emissions are a very big source of it. Greater fuel consumption will also affect the fuel economy, because more the fuel consumption, more the amount of money wasted. Thus, if this is to be reduced, than the only possible way is to increase the engine efficiency.

Engine Efficiency = Useful Power Total Power

Here, the Useful Power will be "time rate change of work done in accordance to the mass added on the cart". Therefore the Useful Power = Work done by the carttime =(m1+M)a x S1t. Here S1 is the distance through which the cart moves on the platform. This distance has been taken as 0.5000m.

And the Total Power will be "time rate change of work done in accordance to the force acting on the cart". Therefore the power output = force applied on the cart x Displacementtime =m2g x S2t. Here S2 is the distance through which mass on the hook attached on the other end of the pulley falls. The distance S2 is the height of the platform the length of the hook to which the mass were attached.

### EXPERIMENTAL MATERIALS:-

The software used in the experiment is: Vernier lab pro, verneir photogates, & logger pro for collection of data & Microsoft Office Excel for the calculation of data.

The basic materials required for the experiment are two photogates, a low friction cart, a long piece of string, some weights, a weighing scale, a piece of stick & two stands.

At first I had thought of using a normal wooden cart with sets of wheel, but decided against it for the simple reason that, there would probably not have been enough place to add the weight as I had decided, & I also in case the stick attaching the wheels & the trolley broke, then I would have to get a completely new cart, which would rather affect my readings, due to changes in the making of the cart. Thus, I decided to make the below shown cart with the help of Technica set, which provided me with many varieties, for the design of my cart. The choice of this basic cart with the wide sized set of wheels was the most simple & basic, as it provided me with complete balance when the cart is in motion, & also, to provide with support as the amount of load added to the cart would have broken the piece of stick which attach the wheels, had the wheel base been narrow, & also the possibility of sagging of the cart along the centre was there, which would have affected my readings. In the experiment the cart used is a low friction cart so that it does not interfere much in the investigation of the effect of changing force & weight on the acceleration & the motion of the cart. One more thing necessary in the cart, is the wheel alignment. Unless the wheel alignment is not proper, there are high chances of error in the collected data, due to non-uniform motion in the cart & also there is the possibility that the cart might not move in the straight direction which will be a problem because it will not pass through the second photogate, thus increasing the time taken in the collection of data.

### EXPERIMENTAL SETUP:-

The experimental setup is shown in the above image.

To start, weight the initial mass of the car. This weight will remain constant throughout the experiment. Next setup the two photogates at a distance of 5 to 10cms, in my case more than this was not possible as the length of the USB cable used to connect the two photogates was not long enough. Hold them in place with the help of the stands. Also make sure that that they are parallel to each other as well as the ground. This will avoid the error in the readings, because if the photogates are not aligned then there is a possibility that stick will not pass through the photogate & hence the readings will have to been taken again, which would be really very time consuming. Connect the second photogate to the first photogate, & the first photogate to the lab pro, which will be connected to the laptop. Once you connect to the laptop, you will see three graphs on the screen, namely distance vs time, velocity vs time, & acceleration vs time. Make sure that the gates are unblocked, so that it will read when the stick passes through the sensors. Also, when setting up the photogates make sure that they are at a height where, when the mass is added to the photogates, it does not interfere with the sensors, otherwise there will be a problem in the readings due to the discrepancies created because of the changed point, and make sure that they are not too high that the stick does not pass through it. This can be checked by once passing the cart slowly through the photogate. If the light blinks once & stays off, that means that the height is proper, but if it blinks more than once, it is an indicator that the photogate height needs to be adjusted. I have assured a large distance between the second photogate & the end of the platform, so as to avoid the cart form toppling over the platform so as not cause any physical damage, which would have otherwise lead to uncertainties in the experiment.

Next attach a string to the front of the cart. But make sure that the string is attached in a manner which does not increase the weight on the front of the car. Also make sure that area on the cart where the weight is going to be added is in the centre, which if kept on one side, will unbalance the cart resulting in non-uniform motion which will affect the cart motion & the collection of data. Then pass the string through the pulley, but, make sure that base of the car, that is the point where the string is attached to the cart, & the top of the pulley should be in line, which means that the string should be parallel to the track. Also one more thing of importance is the length of the string used, because if the string is too long than probably the cart might not pass through the second photogate, & if it is too short than it might flow off the table due to the force which might cause physical damage to the cart. To avoid physical damage to the cart I placed a large box, with a heavy weight inside it so that the cart after hitting the box will stop completely & not flow off the table. But make sure that the boxes are placed on both sides, & not very near to the string attached to the cart, otherwise it might interfere with the motion, like making it slow suddenly, which will be problematic to the readings collected as the required reading might not be collected.

Then I attached the piece of stick to the cart, at a place where the stick does not affect the placement of the mass on the cart. Make sure that the stick is long enough to pass through the photogates which will placed at a height from the ground, so that the stick will pass through the sensors, so that data can be recorded. Also before attaching the stick, measure the length of the stick, & make sure that length is constant throughout the experiment, otherwise the height of the photogate will have to be adjusted for each reading, which will rather be time consuming & will result in random error in the readings. This is also to ensure that the readings for the velocity show change in value due to difference in time & not due to difference in the length of the string.

On the other end of the pulley I attached sets of weights. For better results, I used mass of the same value to avoid any discrepancies in the calculations & readings. In this experiments, the mass of the weights used are 50gm each, in both cases, where it is added to the cart as well as on the other end. On the cart I made sure that the weights are kept at the centre of the cart, or, if placed on the sides of the cart, same amounts of weights are placed on both the sides, so as to balance the weight of the cart.

Before starting I checked whether the track is level, this, I did by applying a small force on the cart in one direction & then applying the same in the other direction. Since the cart moved almost the same distance in both the direction, I concluded the platform was level. Also to keep the motion a straight line motion I placed a piece of string on both sides of the cart, which acted as the rails of the track through which the cart moved.

### HOW TO PERFORM?

Once the setup is done, I am ready to perform the experiment.

Firstly I made sure that all the equipments are fine & working properly. This was done by doing a test run, wherein data for five runs with the same force acting on them & the same weight added to the cart were collected, to make sure that there is no incongruity in the readings. For that the following method will be used,

1. Place the cart before the first photogate, & for the test reading do not add any weight on the cart, as well as, add minimal weight on the other end of the pulley.
2. Before starting make sure that the cart is in line with the threads placed along the sides of the track , to assure this, just leave the car once & see if passes through both the photogates without any problem.
3. Once assured that the cart is in line, again perform the same task, but this time with the photogates.
4. Set the cart before the first photogate.
5. Next, I press on the logger pro graphing software.
6. A message saying "waiting for data collection" appeared on the screen.
7. Next, I left the cart & let it pass through both the photogates. I took enough time to leave the cart but not long enough so that the graph goes above 3-4 seconds to show the first reading.
8. Once it shows that the cart has passed through both photogates, I pressed so that it can record a graph between the two defined points, because if I didn't, then while bringing back the cart back along the track, it again showed a change in displacement, & further points on the graph were plotted, which was erroneous for calculation purposes.
9. On the screen a graph of distance vs time appeared, showing a straight line. I repeated the steps, & since I obsevered parallel & straight lines l conclude that the experimental setup was proper.

After the test run was successful, I proceeded to perform the experiment with different sets of weight & forces applied on the cart. Also to avoid random errors in the graph calculations, I decided to take five sets of readings for each set of mass added to the cart & force applied on the cart. Since systematic error was constant throughout the experiment, I have not taken into consideration, during the calculations. Also, as these blocks of mass were of specific quantity, I have avoided taking any uncertainty which might have been present in the values of the mass.

### COLLECTION OF DATA:-

Here I have presented all my readings in terms of a tabular form. For each set of weight added to the cart I have shown a table of values which represent the time at which the cart entered & left the photogates, later on, these values have been averaged to reduce the random uncertainty & this values have been further used to calculate the values for velocity & acceleration. As mentioned above the length of the stick was kept constant throughout the experiment & that is 10.5cm 0.1cm as well as the initial mass of the cart which is 194.0 0.1gm

On the basis of the values obtained, the following graphs were plotted:

As can be seen in the above graph, the force acting on the cart for a constant value of the mass attached to the cart results in an increase in the acceleration of the cart. Thus if we increase the force which the engine applies in case of an automobile, then we will see that its acceleration increases. But for that the efficiency of the engine will have to be increased, which requires many efficiency improving methods & materials like lean fuel technique, turbochargers, & direct fuel injection techniques. This aspect of the investigation has taken later into account. These accelerations produced are on a very small scale, as the force acting on the cart is also very small. But if these forces are to act on a large mass like that of a car, truck, & other forms of automobile, then care should be taken that it is accurate otherwise, the increased acceleration might unbalance the car, but also result in collision & damage to its parts, & in some cases might result in death of the people in the car.

Next, let's have a look at the below graph:

In the above graph we see that as the weight of the cart increases, the acceleration produced goes under an almost constant decrease. Thus we see that the acceleration produced in carts is more than that in a truck. One more thing which we can say is that leaner & lighter the structure, lesser the opposition & resistance & more the acceleration produced in the car. This is the philosophy which the automakers have taken into account design the widely seen racecars. Also due to a leaner structure the braking distance will be less, as will have less momentum, which is very helpful when designing a racecar. But the only problem is that when driving at high speed, if sudden brakes are applied, there might be a chance of the car toppling over, due to the unbalance caused in the centre of gravity of the car. But these problems is more prominent in automobiles where the centre of gravity is high, it is not prominent in racecars with a low centre of gravity, although there are chances of accidents, due to the very sudden change in the momentum.

### ENGINE EFFICINECY:-

As expressed above, the formula to find the engine efficiency is as below,

Engine Efficiency = Useful Power Total Power = (m1+M)a x S2tm2g x S1t = [(m1+M)a] x S2m2g x S1 = W1W2

The effect on engine efficiency is show below in a tabular format, along with a graph to represent the relation between the mass added to the cart & the engine efficiency, as well as the relation between the force acting on the cart & the engine efficiency.

Work done by force acting on the cart, moving through the distance S2 (W2)

Work done by the cart in moving the distance S1 (W1)

Thus after having a look at the above shown value, we see that engine efficiency is around 60%. This is very high as compared to the normal efficiency of the regular automobile as seen on the road, for the simple reason that the cart does not have an engine, so there is no loss in terms of heat, which uses up the major chunk of the energy provided to it. Also, before performing my experiment, I had made sure that all the parts in use were lubricated, to provide me with minimum friction in between internal parts of the cart. Even then, an efficiency of 60% is not very high when considered in theoretical terms. In practical terms, the loss in my case would have been mainly due to frictional loss as the mass added to the cart increased, & due to air resistance, which it might have encountered during its straight line motion.

Above is a diagram which represents the loss in energy in different parts of the engine in the automobile, after 100% percent fuel energy is supplied to it. On an average only 15%-20% of the total fuel energy provided to the automobile is ever used in the normal running of the automobile, & in using the normal accessories, provided in the automobile, the large part of the energy is wasted in engines work & driveline inefficiencies & idling.[3] Thus, in the current conditions, when the world is plagued with many such environmental problems, improving the fuel inefficiency has an enormous potential. On an average, the large part of the engine wasted in automobiles is for the following reasons:

### Standby or Idling Loss:

It refers to the loss of energy when the automobile is in standby mode with the engine still running, which results in high loss of energy. But, currently techniques like Integrated Starter/Generator have helped improve the efficiency by 8%, by automatically turning off the engine when not in use, & it starts, when the accelerator is pressed.

### Engine Loss:

The use of gasoline in car engines has resulted in high loss of energy in terms of heat in the internal combustion Engine (ICE). It is almost uses 62% of the total energy which is extremely high, which also includes loss due to friction in engine parts. Now in the above performed experiment we saw that when the parts were properly lubricated, the motion was smooth with minimum resistance. Thus in the same manner if we can, if the engines are lubricated, the loss of energy due to friction will be minimized to a great extent, & to reduce the loss of energy in terms of burning of fuel, the use of lean fuel techniques, & to improve the efficiency of the engine, we can use turbocharger & direct fuel injection methods, which due to higher compression rates, & efficient fuel intake reduces the amount of heat produced, thereby using that energy to deliver a higher performance with a low fuel intake, which will obviously help resolve the problem of the extra emissions over the years, which have been observed from automobiles..

1. http://www.citycollegiate.com/force_motion_Xb.htm
2. http://www.efficient-mileage.com/engine-oil.html
3. http://www.fueleconomy.gov/FEG/atv.shtml

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