1. Further Mathematics Support Programme

2. the Further Mathematics Support Programme www.furthermaths.org.uk June 2010 Mechanics Misconceptions Sue de Pomerai the Further Mathematics Support Programme

3. Miconceptions

4. http://nagty.lboro.ac.uk/pages/resources.html When I got to the top of the building I rigged up a beam and a pulley and hoisted up a couple of barrels of bricks. When I had finished there were a lot of bricks left over so I hoisted the barrel to the top again and secured the line at the bottom. I filled the barrel with bricks and climbed down. I cast off the line but unfortunately the barrel of bricks was heavier than I was and before I knew what was happening the barrel started down jerking me off my feet. I hung on. Halfway up I met barrel coming down …….

8. the Further Mathematics Support Programme www.furthermaths.org.uk June 2010 Practical approaches to mechanics

9. Why do practicals? Mechanics is all about modelling the real world, so some insight (‘feel’) about how the real world behaves is vital. Every Mechanics lessons should have a practical element to this – this can be a full-scale experiment, a short practical or a thought-experiment. This ensures that the theory is linked with experiences of interacting with the physical world. Practicals are fun!

10. Why short easy practicals? We don’t have much time! We teach maths, not science - we are more interested in the modelling than the experiments themselves. Accurate experiments and measurements are not necessary to get a ‘feel’ for a mechanical situation, sufficient to justify the modelling.

11. The experiments The experiments require little specialised apparatus. They are quick and easy to carry out. The questions accompanying the experiments are key to their use.

12. Newton’s laws rephrased N1: No change in momentum  No net force N2: A net resultant force in a direction  change of momentum in a direction N3: Forces are subjective (I push down with 3N on you means you push up with 3N on me) N1 covers two situations: a stationary object and one with a constant velocity.

13. Short easy practicals Forces on stationary objects (N1 stationary, N3)  Stand up and feel the forces on your feet. What forces are on you?  Lift one foot off the floor. What happens to the forces?  Push down on a table whilst stood up. What happens to the forces?  Stand with one foot in contact with the floor and one on scales or both feet on the scales and pushing down on a table. What is your maximum/minimum “weight” on the scales? How can you make a set of scales show more than your weight? (Push up on the ceiling standing or jump to give an acceleration).

14. Short easy practicals Net resultant force (N2)  Two people push against each other. Who moves?  As above but one on wheels/ice/socks on lino.  Drop an object. Drop an object whilst walking fast and observe its vertical motion.

15. Short easy practicals Looking at the force due to the same object in different places (N3)  Two people pull either side of a bungee cord. Compare the extension to 2 people pulling on one side with it fixed to a door/wall. How can we get the same extension? (4 people – 2 each end).  Attach 2 tables with a bungee cord. Pull the first table using another bungee cord. Which one will stretch more?

16. Short easy practicals Forces on objects with constant velocity (N1 not stationary)  Drop a ball whilst walking fast and observe its horizontal motion.  Stand up and imagine you are on a train. What would happen when it accelerates/decelerates/turns? Compare this to when it is not turning/accelerating.

17. Dropping a heavy and a light ball simultaneously Before you do the experiment, try to predict which ball will hit the ground first and why. What forces are acting on the balls when they are falling? Can you explain what actually happens?

18. Sliding a graphical calculator on a desk Try to slide it button side up And button side down What do you notice? Can you explain? How could this be modelled mathematically?

19. Sliding fingers together under a ruler What do you think will happen? Try it out – were you right? Try starting your fingers at different positions on the ruler Can you explain? Can you suggest how to model this Rest a ruler on two fingers, then slide your fingers together

20. Playing catch When the ball is in the air, what path does it follow? What forces are acting on the ball when it is in the air? How can you throw the ball so that it goes further? angle projectiles projectiles component

21. Hanging a mass between two masses suspended over pulleys Set up the apparatus as shown Vary the masses to see what happens. Can you predict the angles from the masses, or vice versa? (as shown in the photo, where the masses are hidden)

22. Stretching a rubber band between masses suspended from pulleys Measure the length of the unstretched rubber band Set up the apparatus as shown in (1), with equal weights suspended from strings attached to each end of the band and then passed over pulleys Measure the length of the stretched rubber band Now change the set up by tying the strong off at one end and transferring all of the weight to hang from the pulley at the other end, as in (2) Measure the length of the stretched rubber band again ? What do you notice? Can you explain? ? (1) (2)

23. Closing a door by pushing at different distances from the hinge What do you think will happen? Try it out – were you right? Can you explain? Can you suggest how to model this mathematically?