Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? Physics Depth Study: “How initial velocity affects stopping distance” Paul Parackal Year 11 Mr Chandra Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? “How does initial velocity affect stopping distance of a vehicle?” Aim: To observe how stopping distance increases with varying initial velocities. Hypothesis: The stopping distance of a vehicle will increase as initial velocity increases, due to a higher kinetic energy being only slowed by an unchanged frictional force. Independent Variable: - Velocity of the vehicle Dependant Variable: - Stopping distance of vehicle Controlled Variable: - Frictional force Equipment Required: - Electronic scale - 2 x (1m ruler) - Plank of wood (greater than 40 cm in length) - Protractor - Cardboard piece (15 cm in length) (as wide as plank of wood) - Sticky tape - Vehicle (with rubber wheels) - Marker Introduction: This experiment is designed to observe the effect velocity has on the stopping distance of a vehicle. The extension of this aim, is to observe whether kinetic energy increase will also increase in the stopping distance of a vehicle. The experimental method takes this into account and requires the calculation of the kinetic energy, to observe kinetic energy in relation to stopping distance. The experiment will be repeated three times in total, with each experiment having 4 different heights, and for each height 3 different consistent results. This is to ensure that experiment can be considered reliable. Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? Method: 1. Gathered all equipment as required. Assembled equipment as per diagram(s). 2. Placed the vehicle on the electronic scale and recorded weight. 3. Placed the vehicle at the first mark. 4. Ensured the front wheels touched the line. 5. Released the vehicle from the mark. 6. Measured the distance travelled after the vehicle stopped with the ruler. Recorded measured result. *note* Disregarded all results, where the car had not travelled in a straight line. 7. Repeated steps 5-7 three times in total. 8. Placed the vehicle at the next mark. 9. Repeated 5-7 three times in total. Then proceeded to step 11. 10. Repeated steps 9-10 until 10,20,30 and 40 cm heights lengths had 3 results each. 11. For reliability, repeated steps 4-11, until experiment had been done 3 times in total. 12. Averaged each set of results. Calculated 4 results total. *note* One ‘set’ is the results collected from a single height. (i.e, averaged the averages) 13. Using the kinetic formula (v^2=2as), calculated the velocity off the ramp. Repeated for all heights, resulting in 4 total velocities. Used the formula for calculating kinetic energy (0.5 * (mass(kg)) * (velocity^2 (m/s)), calculated kinetic energy for all velocities. Recorded results calculated. 14. Using weight (calculated in step 3), calculated normal force and multiplied by kinetic coefficient of friction (0.8), to get frictional force. 15. Tabelled all results, and graphed all appropriate graphs. Paul Parackal Year 11 Diagram 1: Diagram 2: How does initial velocity affect stopping distance of a vehicle? Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? Results: Weight of Vehicle: - 108.440(g) or 0.10844(kgs) Frictional Force: - 0.850N (left, in the diagram) Velocity: Kinetic Energy: Results From Experiment: 1st Trial: 2nd Trial: Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? 3rd Trial: Graphs: *note* take the averages from all the trials and average those to get 4 final results where applicable. Distance Travelled Over Velocity of Vehicle: Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? Kinetic Energy over Velocity of Vehicle: Distance Travelled over Kinetic Energy: Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? Analysis: As the only experimental results that were measured were with the ruler, because of the lack of outliers within the results there seems to be no errors regarding experimental results. Perhaps one uncertainty is if the car’s movement wasn’t completely straight, it might result in small discrepancies of the distance travelled. All the graphs show a linear line/pattern and thus means that kinetic energy and velocity, velocity and stopping distance and kinetic energy and stopping distance are all proportional to each other and can directly affect each other. The calculation of the kinetic energy is accurate through the use of the kinematic formula: - KE = ½ * m * v^2 The calculation of the velocity is accurate through the use of the kinematic formula: - v^2 = 2 * a * s - v^2 = 2 * (g sin𝜣) * s Discussion: Trends, Patterns and Relationships: There are clear trends and relationships that can be observed from the graphs above. The trends/patterns/relationships are as follows: - As the velocity increases, so does the kinetic energy of the vehicle. Kinetic energy is defined as the energy an object possess as it is in motion. Therefore kinetic energy is proportional to the speed of an object. Therefore if an object increases its speed, since kinetic energy is proportional, it must also increase along side the speed of the object. - As the velocity of the vehicle increases, so does the stopping distance. In ‘Results’, we calculated frictional force as 0.850N/s opposite to the direction of travel. This frictional force remains constant. So if initial velocity increases and the frictional force stays constant, the constant frictional force will require more distance to completely stop the vehicle’s movement as the initial velocity increases. - As the kinetic energy of the vehicle increases, so does the stopping distance. The energy that an object possess(whilst in motion) is only slowed down by a constant frictional force. Therefore if the energy(KE) increases and the frictional force remains constant, the frictional force will require a larger distance to reduce the energy of the body to zero. Validity: In the experiment we changed the velocity by moving the vehicle higher up the ramp so the acceleration will have more time to increase the velocity of the vehicle. Secondly, we measured Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? the stopping distance of the vehicle, using rulers and disregarding results in which the car did not travel in a straight line. Therefore because the experimental method addresses the two key areas, it can be said that this experiment is valid. Accuracy and Reliability: This accuracy of the experiment could be better. The car’s wheel is flawed in its movement. The wheels occasionally touch the body of the vehicle and significantly affect its velocity, and thus the velocity we calculated is not the velocity of the car in practice. The uncertainty mentioned in ‘Analysis’ would have affected the distance travelled, thus making the results somewhat inaccurate. The reliability of the experiment was well controlled. Through the use of meter rulers to measure all results and the distance up the ramp and the calculation of weight using an electronic scale to get the most accurate result possible. The experiment was also done 3 times for reliability. However as mentioned above, the velocity of the vehicle is unreliable as the use of theoretical results is not representative of the velocity the car was travelling at. Problems encountered and Actions Taken: Before this experiment, the wooden plank and the ground had a small gap, which meant the car would hit the ground, lose velocity and then roll off. To negate this issue, the use of a cardboard piece attached to the plank to completely get rid of the gap, was added later on so that the results could be accurate. Also before, the stopping distance was recorded regardless of whether it travels in a straight line or not. This means that the car would roll left and right occasionally and the place it ended up, was actually more than the distance from that place and the end of the ramp. So to negate this issue, all results in which the car did not travel in a straight line were disregarded, to allow for more accurate results. Improvements to the Experimental Method: The main improvement that could be made is the inclusion of a data logger with a motion sensor, to detect the velocity of the vehicle. This would allow for the practical results to be incredibly accurate and reliable, rather than using a kinematic formula to calculate velocity. Secondly, the use of a car, which does not have its wheels touch the car body, will allow for the velocity of the vehicle to remain as unchanged as possible. Finally, perhaps the use of a track, in which the car can only travel forward, would mean that time would not be wasted with results that cannot be used because the vehicle did not travel forward. Paul Parackal Year 11 How does initial velocity affect stopping distance of a vehicle? Conclusion: To conclude, this experiment was successful in proving the hypothesis. The results showed a clear correlation between kinetic energy and velocity and velocity and stopping distance. Thus this meant that the hypothesis, which concluded that stopping distance increased due to an increased velocity and since an increased velocity increases the kinetic energy, the constant frictional force required more distance to completely stop a vehicle’s energy (KE) and therefore the movement.