How far does a car travel from a ramp?
Introduction
This research tries to find out the relationship between the distance s car travels, and the angle of the ramp, and the relationship between the distance a car travels and the length of the ramp.
It is useful to know the answer to our questions, because then you know whether it is better to make a bridge high or low. If you make the bridge too steep, a cyclist might fall really hard trying to ride down the bridge.
Research questions
What is the relationship between the distance the car travels, and the angle of the ramp?
What is the relationship between the distance the car travels and the length of the board?
Expectations
We thought of these questions and all wrote down our answers. All our answers were almost the same, but together we made our final expectations. These are:
• We think that when we let the car travel from a bigger height (so with a bigger angle), the car will go faster then if we would let it go from a smaller height. This is because of the gravitational potential energy. As the object gets higher, the GPE increases. So if we would put the car on top of a 10 meter high object, the gravitational potential energy is bigger then if the car is on an 8 meter high object. This energy will turn into kinetic energy, which makes the car move, and this energy will also be bigger, so the car will move faster.
We expect that the speed relates to the square of the height. This means that if the speed doubles, the height has to quadruple, and in order for the speed to quadruple, you have to have a height of 16x as high!
We expect this because of the formulas: g x h x m = GPE and
½ x m x s² = KE
Because GPE gets converted to KE: g x h = ½ x s² Change the formula around: 2 x g x h = s Because the gravity remains constant, the height will affect the speed. Because the speed is squared, it relates to the square. • We think that if the ramp is longer, the speed the car travels will be bigger and thus the distance the car travels will be larger, because of the acceleration. Because the long board is longer, the car will have more time to accelerate. It will go faster and faster until the ramp ends. Method To find out the answer of these two questions, we used: • A ramp of 50 cm • A ramp of 35 cm • A toy car • A rope of 190 cm • A stopwatch • A ruler
Our original plan was to measure how far the car would go from the moment it left the ramp, but our toy car kept going in a curve, so we couldn’t measure it accurately. We thought of the following method: We attached the rope onto the toy car, and let the car go from the ramp. We measured the time that it took to travel 190 cm. We did this with several heights of the ramp. We used: 20 cm, 15 cm, and 10 cm. We kept the mass of the car and the length of the board constant, and of course the gravity. For the other experiment, we had a long board and a short board. We let the car go from 10 cm high, and let it go from the short and the long board. We measured the time of these two distances, and calculated the average speed. We kept the height constant, the mass of the car, and gravity, to keep the experiment fair. Results Time taken to travel 1.90 m
Measurement Long board (50 cm.) Short board (35 cm.) 1 2.12 2.94
2 2.04 2.81
3 2.43 2.46
Average
Time 2.20 2.74
Speed 0.86 m/s 0.69 m/s
From this graph you can deduct that if the length of the board is increased 1.43 times (50cm / 35 cm), the speed increases 1.25 times (0.86 /0.69). Time taken to travel 1.90 cm
Measurement 5 cm 10 cm 15 cm 20 cm
1 2.89 2.12 1.84 1.40
2 2.68 2.04 1.60 1.58
3 3.39 2.43 1.68 1.66
Average
Time 2.99 2.20 1.71 1.55
Speed 0.64 0.86 1.11 1.22
The points in this graph are the measurements and the line is the average. You can clearly see a relationship between the height (and thus angle) of the board, and the time it takes to travel 1.90 m and thus the speed. When you increase the height, the time shortens. When we quadruple the height, the time halves and the speed doubles. Conclusion The height of the board affects the speed of the car. If you double the height of the board, the speed of the car quadruples. This is what we expected because we used formula 2 x g x h = s. The reason why the measurements are not completely accurate is because some of the energy is lost due to friction. The length of the board affects the speed of the car. When the length of the board is increased 1.43 times, the speed increases 1.25 times.
Because GPE gets converted to KE: g x h = ½ x s² Change the formula around: 2 x g x h = s Because the gravity remains constant, the height will affect the speed. Because the speed is squared, it relates to the square. • We think that if the ramp is longer, the speed the car travels will be bigger and thus the distance the car travels will be larger, because of the acceleration. Because the long board is longer, the car will have more time to accelerate. It will go faster and faster until the ramp ends. Method To find out the answer of these two questions, we used: • A ramp of 50 cm • A ramp of 35 cm • A toy car • A rope of 190 cm • A stopwatch • A ruler
Our original plan was to measure how far the car would go from the moment it left the ramp, but our toy car kept going in a curve, so we couldn’t measure it accurately. We thought of the following method: We attached the rope onto the toy car, and let the car go from the ramp. We measured the time that it took to travel 190 cm. We did this with several heights of the ramp. We used: 20 cm, 15 cm, and 10 cm. We kept the mass of the car and the length of the board constant, and of course the gravity. For the other experiment, we had a long board and a short board. We let the car go from 10 cm high, and let it go from the short and the long board. We measured the time of these two distances, and calculated the average speed. We kept the height constant, the mass of the car, and gravity, to keep the experiment fair. Results Time taken to travel 1.90 m
Measurement Long board (50 cm.) Short board (35 cm.) 1 2.12 2.94
2 2.04 2.81
3 2.43 2.46
Average
Time 2.20 2.74
Speed 0.86 m/s 0.69 m/s
From this graph you can deduct that if the length of the board is increased 1.43 times (50cm / 35 cm), the speed increases 1.25 times (0.86 /0.69). Time taken to travel 1.90 cm
Measurement 5 cm 10 cm 15 cm 20 cm
1 2.89 2.12 1.84 1.40
2 2.68 2.04 1.60 1.58
3 3.39 2.43 1.68 1.66
Time 2.99 2.20 1.71 1.55
Speed 0.64 0.86 1.11 1.22
The points in this graph are the measurements and the line is the average. You can clearly see a relationship between the height (and thus angle) of the board, and the time it takes to travel 1.90 m and thus the speed. When you increase the height, the time shortens. When we quadruple the height, the time halves and the speed doubles. Conclusion The height of the board affects the speed of the car. If you double the height of the board, the speed of the car quadruples. This is what we expected because we used formula 2 x g x h = s. The reason why the measurements are not completely accurate is because some of the energy is lost due to friction. The length of the board affects the speed of the car. When the length of the board is increased 1.43 times, the speed increases 1.25 times.
REACTIES
:name
:name
:comment
1 seconde geleden