Investigating the Effect of Mass and Speed of a Moving Object on Its Stopping Time The investigation is about the mass and speed of a moving object and how this affects its stopping distance due to the changes in energy needed to brake. Since I cannot measure the speed and energy accurately I shall change the definition of my investigation. The problem/task I will be investigating is how the mass of a moving object ? a trolley, affects its stopping distance. [image] [image] Stopping Distance m In order for a moving vehicle to stop a Braking Force is needed. The friction between the wheel and the ground usually does this. But in this experiment the trolley has no brakes therefore a weight is attached to the trolley to stop it when the string attached to the weight tightens and provides an opposing force to the movement of the trolley. Force is the factor that pushes or pulls an object. Forces can change the speed and direction of an object as well as changing its shape. The size of a force is measured in Newtons (N). Work is done when an applied force moves or acts upon an object, against and opposing a force. Work is equal to the energy transferred and is measured in Joules ? J. The equation for Work is Force x Distance
KE is the type of energy all moving objects transfer is measured in J. The faster the object is moving the more force is needed to stop it. This can be explained by saying that the faster the object is moving the more kinetic energy it has and therefore it will need more work to stop it. According to the conservation law all energy cannot be created or destroyed. Also to stop a movement the same amount energy used to move it must be used to stop it. If it has a greater mass then a greater amount of force is needed to push the object therefore it needs a greater amount of work to stop it. Therefore the work done is equal to the KE. Other factors are the velocity of the trolley and the force. Work = Force x Distance Kinetic Energy = ½ x mass x Velocity2 I can calculate the work needed to stop the car by multiplying the force (weight) by the stopping distance. I can calculate the kinetic energy needed by halving the mass and multiplying it by the velocity squared. If I assume all the energy at the start is used as kinetic energy (none lost to air resistance, heat, etc.) Then I can say the following: Initial kinetic energy ? Work done by brakes ½ x m x v2 ? brake force x stopping distance ½ x m x v2 ? F x S S = ½ x m x v2 F Stopping distance ? Mass. I can say this because of the following. [image][image]S = m x v2 2xF The bracketed part of this equation is a constant. This is why I can say s (stopping distance) is directly proportional to the m (mass). I can use the above knowledge to help me plan what I will do in my experiment. Prediction -???- I predict that as the mass of trolley increases it?s braking distance will increase. I know that the mass and the stopping distance or displacement are directly proportion because of the information above. [image] [image] S = m x v2 2xF The bracketed part of this equation is a constant. This is why I can say s is directly proportional to the m. Using this piece of information I predict that the best fit lone on a stopping distance against mass graph will look like this: [image] The scientific information I used to create the basis of the above prediction came from the page above. Preliminary Work -??????- A preliminary experiment was carried out in order to find the weight to be used as the Braking Force. The apparatus was setup as shown below on the next page. The Apparatus:
Weights (1N each)
Pulley
Trolley
Stool
String
Boards
Balance
The weight was altered and the result between where the string tightened and where the trolley stopped was recorded as the stopping distance the weight was recorded as the Braking Force. The trolley?s mass was changed by adding different numbers of slabs on the top. I will try the maximum number of slabs (5) and the minimum number (0) to see if I can get a range of results. [image] Boards Stool Wheels String [image][image][image][image] Weight ? Braking Force [image][image] Trolley [image] Braking Force (N) Stopping Distance ? no mass (cm) Stopping Distance ? 5 mass (cm) Therefore: 5N 71 Off the track The braking force is too small. 6N 55 138 The stopping distance is recordable this force could be used. 7N Stuttered movement, unreadable 51cm This force is to heavy the results were hard to record accurately as the differences were too small. The braking force (weight) will be 6N because the distances were measurable. Fair Test -??? Before I create the method I shall find what factors may affect the experiment, which is the most significant of those and how I will control them. The mass is the variable and so it will change. This will cause the velocity to change because the gpe is greater for a greater mass and will give and greater KE, which in turn will increase velocity. The gpe is affecting the velocity of the trolley because there is a slanted board. The slanted board is there so that we do not need to push it, which we would be inaccurate. This changing in gpe, velocity and mass is solved by the following equation: ? The energy lost to heat from friction will be minuscule so it will not be taken to account also it would be hard to measure. It can be assumed that all the gpe is transferred to KE. gpe (Gravitational Potential Energy) ? KE (Kinetic Energy) gpe = KE m x g x h = ½ x m x v2 [image][image]m x g x h = ½ x m x v2 Therefore the mass of the trolley will not affect the gpe whereas the height of the ramp will. I will therefore keep the height the same. ? I should keep the trolley the same as its mass may vary. Therefore the mass of the trolley will be consistent throughout the experiment. The mass is going to be the variable in this experiment and will be altered by adding pre-weighed slabs. ? The board must be kept perfectly flat in order that no energy is wasted on a bump. The same boards must be used since the friction between the trolley and the boards may vary. If the friction changes, the results will be invalid because the greater the force of friction, the shorter the stopping distance will be. ? The slanted board must be kept on the same angle. If there was a greater angle/height, there would be a greater gpe and so an unfair and invalid result would be obtained. ? The braking force must be the same. The amount of force that will be used was calculated in the preliminary experiment. Diagram -?? Mass String Wheels Stool Boards Trolley 6N [image] The apparatus will be setup as shown above. The mass on the trolley will be varied from 0 ? 5 (the mass of each slab will be measured on a balance). The braking force will be kept constant at 6N. The trolley will be released from the top of the first board. The distances will be recorded between where the thread tightens and where the trolley stops. I will record the stopping distance by setting the length of the string so that it will tighten when the trolley reaches the flat board. I will draw a line where it stops and measure the distance with a metre ruler. I will take 5 recordings. The first with no mass on the trolley and then with 1 then 2 then 3 then 4, and finally 5 masses. I will repeat each mass 3 times to increase the reliability and to try to ensure that there are no anomalous results. The precautions I need to take are listed in the fair test section. Safety -?- I will keep away from the weight so that it does not drop on my foot and place bags at the end of the board to stop the trolley if it goes off, which it should not according to my preliminary results. Obtaining the Evidence The results I shall take will be the following: ? The mass of each of the 5 slabs. ? The mass of the trolley. ? I shall calculate the mass of the trolley and the specific number of slabs to be put on it. ? I shall perform each experiment three times to check for reliability. ? I shall measure the stopping distance each time. ? Then I shall calculate the averages. The only change I made to the actual method was that the pulleys were connected under the stool rather than above it. The figures below show the masses of each of the five slabs that were used to add mass to the trolley. 1 ? 776g 2 ? 774g 3 ? 775g 4 ? 771g 5 ? 772g The Trolley?s mass was 844g The table below shows the results of the experiment using 6N, which includes the apparatus which is 1N plus the 5 masses of 5N. 1 2 3 Masses Used Total Mass of Trolley (g) Stopping Distance (cm) Stopping Distance (cm) Stopping Distance (cm) Trolley 844 37 31 35 Trolley + 1 1620 60 61 57 Trolley + 1+2 2394 80 84 81 Trolley + 1+2+3 3169 109 108 112 Trolley + 1+2+3+4 3940 129 127 135 Trolley + 1+2+3+4+5 4712 153 156 149 Averages Mass (g) Average Stopping Distance (CM) 844 34 1620 59 2394 82 3169 110 3940 130 4712 153 Average results will be put into a graph so the relationship between an increase in mass and stopping distance can be observed. I did not push the trolley or give it extra force; I just allowed it to move under the force of gravity. This ensured the results would be accurate and fair. I made sure that as I released the trolley that it would move in a straight line and therefore not move off the board. Analysis and Conclusion From my results I can see that as the mass increases the stopping distance does too. I found the relationship between the mass and stopping distance is directly proportional. This is because as the mass increases the gpe increases when placed on the ramp. As the trolley moves down the ramp the gpe is converted to KE. Therefore the greater the mass the greater KE the trolley will have. For the trolley to stop, there must be an equal and opposite force to the movement. Therefore a trolley with greater kinetic energy will need a greater braking force to oppose the movement. As the braking force is the same throughout each experiment the increase in energy has transferred lost by another means before the trolley will stop. This is why the trolley has a longer stopping distance when there is a greater mass. [image] [image] S = m x v2 2xF The above equation is Stopping Distance (S) is equal to mass multiplied to the velocity squared over force multiplied by two. The bracketed part is a constant. Therefore the stopping distance and the mass are directly proportional to one another. The graph shows this, as it is a straight line. Therefore I can say that the above equation is correct. Though in my prediction, I stated and drew a predicted graph showing the line going through the origin, this was not so in my graph results as it went through at about 20cm on the y axis (stopping distance). I can find a substitute the mass, v2, and the force to get a theoretical stopping distance and I could compare this with my actual results. Mass: Total Mass of Trolley (g) 844 1620 2394 3169 3940 4712 Force: 6N (braking force) v2: I could find the velocity squared by using the formula: gpe = KE, h x g x m = ½ x m x v2 Now I will substitute the mass and height: 0.20m x 10 × 0.844 = 0.5 x m x v2 = 1.688 = ½ x m x v2 v2 = (1.688 / 0.5) / 0.844 v2 = 4 Since v2 is a constant, I do not need to figure the velocity squared for every mass. 0 2xF Theoretical stopping distance = mass x v2 2xF = m x 4 / (2 x F) = m x 4 / (2 × 6) = m x 4 / 12 = m x 0.33 = 0.844 × 0.42 S = 0.28133?m = 28cm I can replace the mass for each trolley mass and therefore create Theoretical Stopping Distances (tsd). I will create a table containing the masses the tsd and the Average Stopping Distance (asd). Mass (g) Average Stoppping Distance (cm) Theoretical Stopping Distance (cm) 844 34 28.13333333 1620 59 54 2394 82 79.8 3169 110 105.6333333 3940 130 131.3333333 4712 153 157.0666667 I can round the above figures of the tsd to: 28cm 54cm 80cm 106cm 131cm 157cm. I can now draw another line onto my graph, which holds my actual results too. Evaluation I think the method was a good way of carrying out the investigation. If it was done correctly and without mistakes it could be very successful. But there are things that could alter the results and make them inaccurate, which is listed below. From my graph I can see that all my results fit the best-fit line well. But since the results I used were averages any anomalous results were hidden. I had an anomalous result of the trolley mass of 3940g on the third experiment. The distance was 135cm, which was 6 ? 7 cm different from the first two experiments. The mass of 3169g was a slight anomaly, all of them touched the line in some way except for this. I would think that the reason that this result may be inaccurate is because: Ø The movement not in a straight line. Ø The speed may have changed. Ø Method/Measurements (human) Errors. To solve the above problems I would: Ø Create a rail track to keep the movement straight. Barriers would not work because if the trolley made contact and extra large amount of friction will be added and make a large change to the results. The friction on the rail track would be larger than that on a normal board but it would help the accuracy. Ø The speed change is unstoppable therefore all I could do is monitor is. I could measure this by attaching the end of the trolley to a strip of paper in a ticker tape machine. Ø All I could do to stop making any method or measurement errors is to be more careful As you can see on the graph, the tsd line of best fit and the asd line of best fit are very similar. In one case a point asd passes through the line of best fit of the tsd. The two lines cross at this point. The difference in the two lines could be because of small uncontrollable things such as energy lost through heat from friction, inaccurate measuring and uneven surfaces. the theoretical line passes through the origin, not the real line. According to my graph (asd line) that at a mass of 0g the stopping distance is 8cm, which is clearly impossible. My graph, asd line, look very similar to the simple predicted graph, except for it not passing through the origin. But the theoretical line is almost identical. I think my results support the conclusion I have made very well. Improvement/Extensions However I could try it with: More slabs upon the trolley, Different heights to change the amount gpe transferred to KE for movement, Different surfaces to see how friction changes stopping distance, And more accurate apparatus to check that the patterns shown in this experiment are correct and generally to make the experiment more accurate. Further work could be done to this experiment like using light gates to measure the velocity of the trolley as it passes down the ramp. The light gate would be placed and different points and it could measure the time taken to pass them. Then the stopping distance measured and the time taken could be used to get the velocity = distance/time. Using this I could find the acceleration using the formula: Acceleration = change of velocity time taken for change. E.g. Acceleration = (50-20) m/s = 6m/s2 5s Using this I could use the formula, Force = Mass x Acceleration, and find the force.

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