Prediction
I expect to discover negative correlation between the size of the cones and the speed at which they fall. I would expect the differences in speed to be closely relative to the differences in the size of the cone but there may be some irregularities or offsets that would alter the shape of the graph.
Preliminary experiment
The purpose of the preliminary experiment was to help us determine whether or not the height at which the cone is dropped would affect the velocity at which the cones fell. We measured accurately the two heights at which we would be dropping the 6 cm diameter cone (from 4.48m and 2.72m) using a long piece of string and a meter ruler. The cone was dropped 3 times from both heights and averages were taken for greater accuracy.
The 6cm diameter cone fell at a greater velocity overall when falling 4.48m than falling 2.72m. This shows that a difference in height will make a difference in overall velocity. This is because, when the parachute was initially dropped, the weight was greater than the air resistance and so it’s velocity increased until the air resistance became equal and it’s terminal velocity was reached. Each parachute would take a small amount of time to reach its terminal velocity; therefore height makes a difference.
Results
Conclusion
I have found that, in general, the larger the parachute, the more time it took to reach the ground. This means that it’s velocity was lower so I used the equation: Velocity = to work out the average velocity at which the
parachutes were travelling. Also, using my graph, I could work out the percentage difference from one cone to the next.
We can tell from both the chart and the graph that there were anomalies in this experiment. These have occurred because of other factors affecting the experiment such as possible human error while using the stopwatch. When these anomalies are removed, we are left with more accurate averages of velocity.
This graph shows quite clearly the relationship between the size of the cone and the velocity at which it falls. The trend line (shown in red) indicates strong negative correlation, becoming stronger as the size of the cone increases. The large cones fall at a slower rate than the small cones because the difference between the weight and the air resistance is much greater for the larger cones. Even though the larger cones are heavier, the cone’s large cross sectional area means the air resistance is much greater, making them fall slowly.
Evaluation
This experiment has been successful; I have obtained a sufficient amount of useful data, which I have been able to use to draw conclusions. The experiment was performed with sufficient accuracy to obtain reliable evidence to support my conclusions. There were anomalies but because each cone was dropped three times, they were outlined and easy to remove, improving the accuracy of the experiment.
If more data was recorded, calculations could be made to find the acceleration of each cone and even the actual terminal velocity of each of the cones. It would then become possible to investigate the relationship between cone size and terminal velocity or acceleration.
Background Information
Air resistance is a force that acts against moving objects. Another name for air resistance is drag. Drag pushes against objects that are moving through the air. It is a kind of frictional force because it tries to slow objects down.
For a person jumping from an aircraft, the upward force of air resistance increases as the jumper falls freely and accelerates. The force continues to increase until it equals the downward pull of gravity. The jumper then continues to fall at a constant terminal velocity. On opening a parachute, there is a large increase in cross-sectional area, and the force of air resistance becomes larger than the weight, causing the parachutist to decelerate to a speed that is safe for landing.
If things need to go fast, they have to be streamlined, or aerodynamic. Aerodynamics is a branch of dynamics that studies the motion of gases and the movement of objects in gases, notably air. Aerodynamics study how all sorts of vehicles move through air, from aeroplanes to cars. Vehicles can be designed so that they move as efficiently as possible, with the minimum wastage of energy. This is known as “streamlining”. A car that is streamlined for example has sloping front and smooth sides.
Terminal velocity is the speed at which the force accelerating an object through a particular medium is balanced by the drag slowing it down. This terminal velocity depends on the nature of the medium, and the shape and size of the falling object.
Less compact shapes will fall slowly because air resistance slows them down. With more compact shapes, the drag force is much less in relation to its weight, so it is slowed down much less. A falling object will eventually reach a speed where the drag force exactly equals the objects weight. At this point, the object stops accelerating, and it is said to have reacted its terminal velocity.
The force of gravity acts between any two masses, making them attract to one another. Everything on Earth is pulled down to the Earth’s surface by gravity; and this force gives objects their weight. Like other forces, gravity is measured in Newtons. The gravitational force exerted by the Earth is about 9.81 Newtons on every kilogram of matter on its surface.