Falling with style: air resistance versus gravity Worksheet Answers This activity is an introduction to air resistance and the forces that act on falling objects. Experiment 1: slow the fall 1. Fold your sheet of paper in half with the short edges together and then cut along the crease so that you end up with two pieces of paper the same size. 2. Crumple one of the two halves into a ball. 3. Let go of the two halves at the same time and watch them fall. Do this several times. Make sure you drop them from the same height to make it a fair test! What happens? Do both pieces of paper fall at the same speed? If not, which one falls faster? The crumpled piece of paper will hit the floor first. Both pieces of paper weigh the same so what is happening to make them fall at different speeds? Both pieces of paper fall towards the floor due to the gravity. As they fall, they need to pass through the air. Pushing the air out of the way as the object falls takes some effort which is described as air resistance. The flat piece of paper has a larger surface area so encounters more air resistance, which slows its fall. Does it make any difference how you hold the flat piece of paper when you drop it? Try dropping it flat or from different edges. In theory holding the paper flat should give the maximum air resistance so it should fall slowest. Holding it on the edge should make it fall fastest as the surface area on the falling edge is smallest in this direction (in fact, it should fall even faster than the crumpled paper). In practice, in most cases it doesn t matter which way you drop it as the paper is flexible and small variations in how you drop it or air movement will result in the paper twisting and tumbling through the air. 1
Galileo s cannon balls and hammer & feather on moon In 1589, so the story goes, the Italian scientist Galileo Galilei took two cannon balls of different weight to the top of the Tower of Pisa and dropped them off the side. Both balls landed at the same time. This showed that the weight of an object does not change how fast it falls - heavy objects do not fall faster than light ones. However, when an object falls through air, the air being pushed out of the way by the falling object can slow the fall: this is called air resistance. The larger the area that the air resistance can act on then the slower the object will fall. This is the reason that feathers fall slowly and not because they are light weight. To prove the point, in 1971 during the Apollo 15 moon mission, David Scott dropped a hawk feather and a hammer at the same time in front of the cameras. As there is no air on the moon to get in the way, both feather and hammer hit the ground at the same time 1.2 seconds later. Resources are available on line to demonstrate this. The following link shows a clip from the BBC s Human Universe series presented by Brian Cox, with the feather hammer experiment being done in a vacuum chamber. http://thekidshouldseethis.com/post/the-hammer-feather-drop-in-the-worlds-biggest-vacuumchamber YouTube also hosts various versions of the original video clip from the Apollo 15 mission experiment, the link to a NASA version is here: https://youtu.be/zvfhztmk9zi (please note: the resolution on the Apollo clip quite low so it is not very easy to see the action). Experiment 2: steady the fall 1. Taking the flat piece of paper from experiment 1, fold it in half by putting the long edges together. Open it out so it forms a long V shape. 2. Holding the paper by the long edges, so the V is pointing down, drop your paper and observe how it falls. Do this several times, holding the paper in the same way and dropping it from the same height so that it is a fair test. 3. Make a note of where the paper lands each time and how it falls. What happens? Can you find a pattern in how the paper falls? The paper will fall in the same orientation as it is dropped; the bottom remains down, the front remains at the front. If it moves away from its vertical position then it will move in the direction of the fold it won t move to the side like the flat piece of paper might. Can you think why a V shape falls differently to a flat piece of paper? What would happen as the V shape starts to tip to one side? 2
The V shape of paper directs the air flow evenly to both sides as it falls. If it started to tip, the falling side would become more horizontal, meaning the area presented to the direction of the fall is larger, as shown in the diagram below. As a result there is more air resistance acting on the tipped side compared to the other side, the forces are unbalanced. This pushes the paper back up vertical. If the paper does move away from the vertical drop then it will move in the direction of the fold as that edge has least air resistance. View from end of the folded paper. Dark blue shape shows the paper upright: the paper has an equal horizontal area on both sides. Open shape shows the paper tipped over: the paper now projects more over the left than the right. The means that that more air resistance will act on the left hand side, pushing the paper back upright. Experiment 3: steady the fall part 2 1. Using the same piece of paper from experiment 2, open it out and then fold it in half the other direction by putting the short ends together. Open it out again. 2. You should now have ended up with the paper divided into four quarters by the crease. Holding the paper, gently adjust the folds so that the paper is bent up evenly in both directions. You should be able to spin it on its central point on the table once you have done this. 3. Holding the sheet flat with the centre pointing down, drop your paper and watch it fall. Do this several times and make a note of how and where it falls. 3
What happens? How does this compare to experiment 1 and 2? The paper falls vertically down to land directly below where it was released. Why do you think adding an extra fold makes it fall differently? What do you think is happening as it falls? Just as adding the first fold steadies the fall by preventing it falling to the side, by adding two folds you steady it in both directions. For extra fun, try dropping the paper with the centre point upwards. What happens and why? The paper will flip over and finish falling with the point down. In the starting position, with the tip up, the paper forms a cup like structure that directs the air inwards as it falls. This is unstable as the air has nowhere to go once it reaches the centre and so creates turbulence as the trapped air swirls around and spills out round the edge. All this turbulence rocks the paper causing it to flip over and fall in the more stable point down arrangement. A parachute is a similar arrangement to the point-up paper. However, the parachute canopy is prevented from flipping over by the weight of the person below (i.e. it has a low centre of gravity). It can still become unstable if air is trapped inside, leading to it to rock wildly. To prevent this, a small hole is normally located at the top of the parachute to allow the captured air to escape safely from the top without rocking the canopy. Experiment 4: directing the fall 1. Using the paper from experiment 3 chose one short edge to be the front - it doesn t matter which end. Add paper clips on the front edge of the paper, about 4-6 should work depending on their size. Position the paper clips evenly either side of the fold and as close to the central fold as possible. 2. With the front pointing forward, let go of the paper and watch the fall. Make a note of the landing point; do this several times. What happens? How does this compare to experiment 3? 4
The paper glides, travelling in the direction of the paperclips. This means it falls some distance away from the vertical starting point, unlike in experiment 3 where the paper falls vertically down. Why do you think adding weight to one edge makes it fall differently? What do you think is happening as it falls? The folds we put in the paper in experiments 2 and 3 have created an object that has a stable fall. The diagram below shows the main forces acting on the paper as it falls. As the paper falls, air resistance acts against it generating drag (a force) at right-angles to the surfaces. As the sum of all the drag is less than the gravity force, the paper falls down. However, if we look at these drag forces from the side, we can actually split the direction of the forces that are acting on each face of the paper in two components. See the diagram below. These component forces are calculated by doing a projection of the drag forces (in green) onto the vertical and horizontal axis, shown in blue and red respectively. In the situation shown below, the vertical forces add up, but the horizontal forces will cancel out, as they are pointed in opposite directions. It is worth noting at this point that the force slowing the falling paper is drag and not lift. Lift acts at right angles to the direction of air flow, whereas drag is a result of air resistance and acts in the same direction as the air flow. 5
When you add paperclip weight to one edge of the paper, you cause this edge to tip down as the paper falls. Here the forces acting on the paper are slightly different, as we have now changed the orientation of the paper. 6
The whole sheet is now angled. The horizontal forces on the face opposite to the paperclips increase due to the steeper angle of the paper. However, the face next the paper clips is almost flat, decreasing the horizontal force generated by this face. The horizontal forces now don t cancel each other out; there is an imbalance with an overall horizontal force pointing in the direction of the paperclips. The paper does not fall vertically, but slides towards the tipped down edge and the paper becomes a glider. Acknowledgements This worksheet was developed by Paul Lancelot and Juliet Jopson as part of the Marie Curie Initial Training Network AMEDEO. The project helped develop computer software tools needed by the European aerospace industry in order to design aircraft that are more environmentally-friendly. AMEDEO was funded from the European Union s Seventh Framework Programme for research, technological development and demonstration under grant agreement no 316394. Licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, please attribute to AMEDEO ITN, EU FP7 Grant no. 316394. 7