Find out the breaking distance of a trolley car going down a ramp when an independent factor is changed.
Physics Investigation
By Christopher Stylianou
Aim
The aim is to find out the breaking distance of a trolley car going down a ramp when an independent factor is changed.
Factors
All the independent variables, which could affect the investigation of Breaking Distance, are:
> Speed of Vehicle- By changing the speed of the trolley car, it could change the Breaking Distance.
> Friction of Wheels- By changing the amount of frictions on the wheels, it could change the Breaking Distance.
> Surface Material- By changing the surface material the trolley is travelling on, it could change the Breaking Distance.
> Gradient of Slope- By changing the gradient of the slope, it could change the Breaking Distance.
> The Breaking Force- By changing the breaking force applied to the trolley car, it could change the Breaking Distance.
> Mass of the Vehicle- By changing the mass of the trolley car, it could change the Breaking Distance.
Investigation
I have decided with the research I have below to investigate the change of breaking force independent variable. This is because I can use a range of different weights applied to the trolley car as it travels down the slope. E.g.: - 100g of breaking force, 120g of breaking force etc... Then, by marking where the breaking force is applied and where the trolley car actually stops, I can work out how far the trolley car has travelled. I can work out the Potential Energy at the beginning of the ramp, where the breaking force is applied and the Kinetic Energy at where the breaking force is applied to see how much work is done in stopping the vehicle. Lastly, I can work out the de-acceleration of the trolley car and see whether it increases or decreases when the breaking force is increased.
Research
* Breaking Force - The force that is applied to a vehicle that is moving to slow or even stop the vehicle.
* Potential Energy - The Energy a mass has because of its position or condition. E.g.: - A trolley car weighing 1kg is rolled down a ramp 20 meters high. When the trolley car is at the top of the ramp the Potential Energy is,
Ep = mgh
Where m = the mass of the trolley car (10kg), g = the gravitational pull (10N/kg) and h = the height of the ramp (20m).
Ep = 10kg x 10N/kg x 20m
Ep = 2000 Joules
So the Potential Energy acting on the trolley car at the top of the ramp is 2000 Joules. When the trolley car is at the bottom of the ramp there is no Potential energy as it has been converted into Kinetic Energy (see below).
* Kinetic Energy - The Energy a mass has because of its motion. E.g.: - A trolley car weighing 10kg is rolling down a ramp at 20 meters per second to the earth. When the trolley is at the bottom of the ramp the Kinetic Energy is,
Ek = 1/2 x m x v²
Where m = the mass of the trolley car (10kg) and v = the velocity of the trolley car (20m/s).
Ek = 1/2 x 10kg x 20m/s²
Ek = 5kg x 400m/s
Ek = 2000 Joules
So the Kinetic Energy acting on the trolley car at the bottom of the ramp is 2000 Joules. When the trolley car was at the top of the ramp there is no Kinetic Energy as there is no motion.
* To work out the Kinetic Energy or Potential Energy of a mass that is not at the top of the ramp or at the bottom we can use Potential Energy equation.
Ep = mgh
So if the trolley car (10kg) was 15 meters high from a drop of 20m then the Potential Energy is,
Ep = 10kg x 10N/kg x 15m
Ep = 1500 Joules
So if Potential Energy is 1500 Joules, then the remainder from the beginning 2000 Joules is 500 Joules. This is the Kinetic Energy on the trolley car. This is because no force can be lost or gained but these figures could be incorrect as some of the force is converted into heat.
* To calculate out the work done in braking the trolley car, we use the equation
Braking Force (N) x Distance Travelled (m) = Constant (Joules).
So if a trolley car had a braking force of 200g and travelled 10m after the ...
This is a preview of the whole essay
So if Potential Energy is 1500 Joules, then the remainder from the beginning 2000 Joules is 500 Joules. This is the Kinetic Energy on the trolley car. This is because no force can be lost or gained but these figures could be incorrect as some of the force is converted into heat.
* To calculate out the work done in braking the trolley car, we use the equation
Braking Force (N) x Distance Travelled (m) = Constant (Joules).
So if a trolley car had a braking force of 200g and travelled 10m after the force was applied before it stopped, then the work done braking is:
Force (200g = 2 Newton Force) x Distance Travelled (10 meters)
2N Force x 10m = 20 Joules.
This means that it took 20 Joules to stop the trolley car from moving down the ramp.
* To work out de-acceleration of a moving vehicle, you divide the change in speed by time. E.g.: - A trolley car is rolling down a ramp at 20m per second. The breaks are applied and the trolley car stops 4 seconds later
De-acceleration = Change in Speed (20m/s - 0m/s = 20m/s) ÷ Time Taken (4s)
De-acceleration = 20m/s ÷ 4s
De-acceleration = 5m/s
Prediction
I predict that the more breaking force is added to the vehicle, the less distance it will travel. I predicted this by using the research above and matching it with the preliminary experiment which we did earlier in the Year. The experiment we did then was to find the distance it took for a trolley car with 50g, 100g and 150g. The trolley car travelled at 1m/s and these were our results.
Mass of Breaking Force
(g)
Distance Travelled After Breaking is Applied (to nearest 0.1m)
50
2.6
00
.9
50
.5
The results show that the breaking distance decreases, as the breaking force increase so I believe this will happen in this investigation. Below is a graph with the Predicted outcome.
I also can predict that as the breaking force increases so will the de-acceleration. This is because as more breaking force is applied, the quicker the trolley car will stop as the counter-force becomes greater. Here is a graph to show my predicted results
Plan: -
Apparatus: - 2 x 100g Weights
9 x 10g Weights
1 x Trolley Ramp
1 x Trolley Car
1 x 3m String and a Pin
1 x Ticker timer plus tape
1 x Power Pack
1 x Stand
1 x Clamp
1 x Boss Clamp
1 x Pulley wheel
1 x Stop Clock
Metre Sticks
Method: -
Before collecting the results, set up the apparatus as shown in the diagram. Place the trolley car at the top of the ramp and let it roll down freely to see if the ramp side catches the car as it travels down. If so, try checking and cleaning the wheels and axis of the trolley car and if that doesn't work, swap it for another trolley car. Then record the weight of the trolley car. Attach the ticker timer to trolley car and let the vehicle roll down the ramp to work out the average speed without any breaking forces applied (1 metre). To work this out we use the formula,
Average Speed of Trolley Car (m/s) = Distance Travelled (m) ÷ Time Taken (s)
Counting the amount of dots there are on the tape, we can tell how long it took the trolley car to go down the ramp. There are 5 dots to every 1/10th of a second. The distance travelled is the length of the ramp. After this, attach the string with the weights of 10g on to the trolley car and allow trolley to roll down the ramp. Where the breaking force is applied (1 metre), make a mark on the ramp to tell us where to start measuring from. Then we start the experiment.
Collect Results
. Place 100g of weight on the breaking force.
2. Start the trolley car at the top of the ramp, let the vehicle roll down the ramp
3. When the vehicle reaches the start of the breaking force, start the stop clock.
4. After the breaking force is applied and the vehicle stops, stop the clock and measure how far from the start of breaking force to where the back wheel of the trolley car has reached and record this distance and time. Also measure how high the ramp is at this point.
5. Add 10g of weight to breaking force and repeat 1 to 3.
6. Do this until 250g of breaking force is recorded.
7. Repeat experiment until no anomalous results occur.
Fair Test: -
To make it a fair test you must carry out these precautions: -
* The measuring is accurate of the breaking distance.
* The right amount of weight is used.
* The trolley car is not changed during experiment.
* The trolley car is not pushed down the ramp with force.
* The ramp gradient/height does not change.
* The other factors that could affect the results are not changed.
Safety: -
To make it a fair test you must carry out these precautions: -
* Bags and Stalls are put on the sides of the room, out of the way of any experiment.
* The normal Science Labs rules must be obeyed.
* Be careful and make sure weights don't drop on the floor.
Results: -
Before experiment carried out:
* Mass of the trolley car = 970.0 grams
* Height at top of ramp = 27.2cm
* Height where braking force applied = 18.0cm
* Average speed of trolley car before breaking force applied: -
Ticker timer tape
There are 16 x 1/10 and 2 x 1/10 which equals:
(16 x 0.1) = 1.6 + (2/50 which is also 0.02 x 2) = 0.04
.6 + 0.04 = 1.64s
Put this into the equation:
Average speed of trolley car (m/s) = Distance travelled (m) ÷ Time Taken (s)
m ÷ 1.64s = 0.610m/s
Results of experiment Breaking Distance and Time:
(X = Anomalous Result)
Mass of Breaking Force (g)
Results 1
Results 2
Result 3
Average
Distance Travelled (mm)
Time (s)
Distance Travelled (mm)
Time (s)
Distance Travelled (mm)
Time (s)
Distance Travelled (mm)
Time (s)
00
835
.80
841
.82
-
-
838.0
.810
10
631
.61
633
.66
-
-
632.0
.635
20
523
.39
520
.38
-
-
521.5
.385
30
440
.33
438
.26
-
-
439.0
.295
40
350
.16
354
.21
-
-
352.0
.185
50
295
.06
301
.12
-
-
298.0
.090
60
210 X
0.56 X
270
.01
274
.03
272.0
.020
70
296 X
.05 X
261
0.95
263
0.99
262.0
0.970
80
248
0.91
251
0.94
-
-
249.5
0.925
90
237
0.83
236
0.79
-
-
236.5
0.810
200
215
0.67
219
0.72
-
-
217.0
0.695
210
85
0.65
84
0.57
-
-
84.5
0.610
220
64
0.51
64
0.52
-
-
64.0
0.515
230
32
0.46
87 X
0.66 X
40
0.48
36.0
0.470
240
27
0.40
30
0.45
-
-
28.5
0.425
250
15
0.29
10
0.25
-
-
12.5
0.270
Taking a look at these results I can see that as the mass of the braking force increase, the time and distance travelled decrease. Once I have drawn the graphs I can add this to my conclusion.
Results of experiment stopping height:
Mass of Breaking Force (g)
Results 1 Height (mm)
Results 2 Height (mm)
Result 3 Height (mm)
Average Height (mm)
00
90
88
-
89.0
10
11
10
-
10.5
20
25
26
-
25.5
30
30
32
-
31.0
40
44
40
-
42.0
50
49
48
-
48.5
60
56 X
52
51
51.5
70
45 X
54
53
53.5
80
54
55
-
54.5
90
56
56
-
56.0
200
58
57
-
57.5
210
59
59
-
59.0
220
62
62
-
62.0
230
66
59 X
65
65.5
240
68
67
-
67.5
250
71
69
-
70.0
Taking a look at these results I can say that as the mass of the breaking force increase the height of the trolley car stopping increases. This means that the trolley car must be stopping higher up the ramp when the braking force is increased.
Results of experiment de-acceleration:
Mass of Breaking Force (g)
Results 1 De-acceleration (m/s)
Results 2 De-acceleration (m/s)
Result 3 De-acceleration (m/s)
Average De-acceleration (m/s)
00
0.34
0.34
-
0.340
10
0.38
0.37
-
0.375
20
0.44
0.44
-
0.440
30
0.46
0.48
-
0.470
40
0.53
0.50
-
0.515
50
0.58
0.54
-
0.560
60
.09 X
0.60
0.59
0.595
70
0.58 X
0.64
0.62
0.630
80
0.67
0.65
-
0.660
90
0.73
0.77
-
0.750
200
0.91
0.85
-
0.880
210
0.94
.07
-
.005
220
.20
.17
-
.185
230
.33
0.92 X
.27
.300
240
.53
.36
-
.445
250
2.10
2.44
-
2.270
This table shows that as the mass of the breaking force increase, the speed of de-acceleration also increases. I will plot these results on a graph to show this.
Results of experiment Potential Energy and Kinetic Energy:
Mass of Trolley Car (g)
Potential Energy at start of ramp (Joules)
Potential Energy at braking force applied (Joules)
Kinetic Energy at braking force applied (Joules)
970
2.6384
.7460
0.8924
These results show that the trolley car has 2.6384 Joules of Potential Energy at the start of the ramp, 1.7460 Joules of Potential Energy where the brakes are applied and 0.8924 Joules of Kinetic Energy when the brakes are applied.
Conclusion
The line of best fit on graph 1 shows us that the braking force and the distance travelled after the force was applied are almost inversely proportional. This means that if the breaking force doubles then the distance travelled halves and visa-versa. This happens as the breaking force applied provides more counter force against the movement of the trolley, as it increases, so the trolley car will lose its momentum force quicker and travels a shorter distance. The results are almost directly inversely proportional though, as with the errors that happen with the experiment or complete accuracy of the results cannot always be correct, as it is impossible to do with the apparatus provided to get such accurate results. To show this, if we work out the work done in braking by using the equation,
Force x Distance Travelled = Constant.
It should equal the same answer as the constant kinetic energy the trolley has when the brakes are applied, i.e. 0.8924 Joules, but this is not the case. An example from the results to show this is: -
Force (100g = 1 Newton Force) x Distance Travelled (Average of distance
travelled = 838.0mm = 0.8380 meters)
N Force x 0.8380m = 0.8380 Joules.
Another example is: -
Force (180g = 1.8 Newton Force) x Distance Travelled (Average of distance
travelled = 249.5mm = 0.2495 meters)
.8N Force x 0.2495m = 0.4491 Joules.
Graph 2's line of best fit shows us that as the braking force applied to the trolley car increases, so does the de-acceleration speed of the trolley car in a directly proportional trend. This is because as the breaking force increases, the quicker the trolley car stops as it has more counter force to counter act the momentum of the trolley going down the ramp. This also means the trolley car travels less distance as it loses its momentum quicker. This supports and proves my prediction is correct as I predicted using my preliminary work that as the braking force increases, the distance the trolley car will travel decreases and so the speed of de-acceleration increases.
Evaluation
In this investigation I believe that I have gone deep enough to get some justified results with accuracy and with this produce a well supported conclusion. We investigated 16 different mass of braking force and we repeated each result twice to get an average result. After we did this we noticed that there were 3 anomalous results (circle of the graphs) so we repeat it again to get to disregard these results in the investigation. These anomalous results may have occurred as one of the main factors that could affect the final results could have changed accidentally, i.e.: - the trolley might have gain more speed by being pushes down the ramp or that some momentum was lost due to friction in the wheels of the trolley car or on the ramp. However, I believe we managed to keep all the main factors under control over the whole experiment. We did this by cleared the ramp of any debris or dust that could add friction to the trolley car wheels. We labelled all the equipment we used so none of it got changed or swapped accidentally during the experiment. The mass of the trolley car was kept the same and the wheels were cleaned and well oiled to make sure no extra friction was being added that could affect the final results. However, I don't believe that they are part of a new trend in this investigation, but if I was to change a different independent variable then they might be.
I believe our results were accurate enough for this investigation to provide reliable, usable results for my analysis and conclusion. All my results seem to lie just next to or on the line of best fit drawn on the graphs and this has help me produce a firm, well supported conclusion. But, as I said in the conclusion we can only draw an almost inversely proportional graph, unless we measured everything to precision using expensive 100% accurate equipment, but there is no need for this. Maybe if we followed this investigation up that could be looked into and added to the method. I could also used data login techniques to get much more accurate times by using sensor to tell when the vehicle passes the braking point and how long after it takes for it to stop. I could carry out the experiment again using a different method to get the same results. Instead of using pullies and weights on strings attached to the trolley car, I could attach a piece of flat rope and thread it through a friction block with different mass's on it to add more or less friction to the vehicle to stop it. Here is a diagram of the experiment: -
From this, I would be able to get the same results that I have achieved from the method I have carried out for this investigation and could compare them to make sure this is true. I could also concentrate on working out just one result of this experiment, i.e.: - de-acceleration, energy used to stop the vehicle or the distance the vehicle travels. By doing this I could extend my experiment and find out a bigger range of results to support the conclusion even more so.
I got my research from the Physics GCSE textbook, past preliminary work and class work note in my exercise book.