Forces and motion 3: Friction

Transcription

1 Forces and motion 3: Friction University of York

2 Friction The questions in this set probe pupils understanding of friction. Friction is the name of the interaction between two surfaces when they move (or if an applied force tries to make them move) relative to one another. It acts along the line of contact. A key point to grasp about the friction force between two given objects is that its size depends on the external applied force which causes it. For a given object on a given surface, the friction force will increase in size to match the applied force that is trying to make the object slide over the surface up to a certain limit. If that limit is exceeded, the object will move. Once it begins moving, the friction force is almost constant, regardless of its speed. In fact, the situation is more complicated than this: the applied force needed to start an object moving is slightly bigger than the force needed to keep it moving. That is, the starting friction force is greater than the moving friction force. In an introductory exploration of friction, at Key Stage 3 level, however, it is better to avoid this point, as even a simplified understanding of friction, as a force whose size matches the applied force up to a limit, is quite challenging for pupils to grasp. Once they have grasped this securely, the difference between starting friction and moving friction could be explored but this is not likely to be until after Key Stage 3. An understanding of the difference between starting and moving friction is not required to answer any of these questions. The idea of friction is first introduced in the National Curriculum at Key Stage 2, where pupils should be taught that friction is a force that slows moving objects and may prevent objects from starting to move (Sc4/2c). This is then developed at Key Stage 3 into an understanding of how frictional forces affect motion (statement Sc4/2d). The basic idea of friction is introduced in the QCA Scheme of work for Key Stages 1&2 in Unit 4E, Friction. It is then developed in the QCA Scheme of work for Key Stage 3, in Unit 7K, Forces and their effects and Unit 9K, Speeding up. Questions to probe understanding of friction inevitably bring in ideas about the relationship of forces and motion for example, knowing that when an object moves at a steady speed, the forces on it add to zero (the total force is zero). These ideas are probed by diagnostic questions in the set The link between force and motion. Several questions in the set Identifying forces also probe understanding of when a friction force arises. A selection of questions from these packs could, therefore, be used along with those in this pack when teaching about friction. Questions 1-2 These look at when there is, and is not, a friction force on an object. Some pupils may think friction switches off when the object moves. Others may think friction only depends on the choice of surfaces, and so is present all the time. The situation of a slope is not used in any of the subsequent questions because an analysis of the forces acting involves vector ideas and is too difficult for Key Stage 3 (or 4). 134 University of York 2003

3 Questions 3-5 These probe understanding of friction as a responsive force, whose size depends on the applied force, up to a limit and is independent of speed, once an object is moving. The two-tier structure of these questions helps to show the reasoning behind the pupil s choice of response. Four situations are considered: object not moving, with a small applied force; object not moving with a larger applied force; object moving at steady speed with an even larger applied force; object moving at an increasing speed with a still larger applied force. The question becomes very complex if all four situations are included. So each of these questions compares two situations. Q3 considers a smaller and larger force, both of which are insufficient to make an object move. Q4 then compares the situation where a small force does not cause motion, but a larger one makes the object move at a steady speed. Q5 then considers two situations in which the object is moving: at steady speed, and with increasing speed. These questions are intentionally asked in a qualitative form, to probe understanding without the distraction of numerical values. They require students also to understand the relationship between force and motion (in particular, to appreciate that, when an object moves at a steady speed, the resultant force on it is zero). Question 6 Although this question looks very similar to Q4, it has one crucial difference. In Q4, it is stated that the applied force is bigger in the second situation: the furniture remover pushes harder. In Q6 nothing is said about the sizes of the forces, just about the motion (or lack of it). In fact, there are two possible correct answers here. It is possible that the box in Figure 1 is just on the point of beginning to move. If so, then the friction force is almost at the limit of starting friction in which case, the friction force is smaller when it begins to move, and option 1 is the right answer. But it is also possible that the push in Figure 1 is nowhere near the limit of starting friction, so that the friction force in Figure 1 is much less than the moving friction force making option 2 the right answer. The second part of this question is therefore essential, in order to probe the reasoning leading to the answer chosen. Questions 7-10 These questions, in contrast to Q3-6, do use numerical values, though they do not involve any calculations. Like earlier questions in this set, they require students also to understand the relationship between force and motion. Q10(a) probes the quite common misconception that the friction force on an object is directly related to its weight. All of these, particularly Q7, would be suitable for small-group discussion. Q8 is the only question in this set that uses a wheeled vehicle (a trolley) largely to introduce a little variety. In fact the forces on wheeled vehicles are very complicated and it would not be wise to go into this in any depth. If you want more questions to practise these ideas, questions similar to Q3-7 could be written for the situation in which an object is dragged across a level surface. University of York

4 Questions Students may have the idea that friction always opposes motion. In fact it opposes relative motion of one thing past another and this is sometimes essential to enable an object to move at all. We could not walk if there were no friction, and bicycles and cars could not move. Q11 looks at the direction of the friction force in a situation where friction is necessary for an object (a crate on the back of a lorry) to move. The situations in Q12-13 are similar. These are quite challenging questions. 136 University of York 2003

5 1 (a) A box is sitting on a level floor. It is not moving. box not moving Is there a friction force acting on the box? Tick ONE box () yes no (b) A furniture remover is pushing the box. But it is not moving. box not moving Is there a friction force acting on the box? Tick ONE box () yes no (c) The furniture remover is now pushing the box harder. It is moving along at a steady speed. moving at a steady speed Is there a friction force acting on the box? Tick ONE box () yes no University of York

6 (d) The furniture remover pushes even harder. The box moves along, getting faster as it goes. moving along, getting faster Is there a friction force acting on the box? Tick ONE box () yes no 138 University of York 2003

7 2 A box is sitting on a wooden plank. One end of the plank can be raised to make a slope. (a) At first, the plank is level. The box is not moving. box not moving Is there a friction force on the box? Tick ONE box () yes no (b) One end of the plank is then raised to make a gentle slope. The box is still not moving. box not moving Is there a friction force on the box? Tick ONE box () yes no (c) The slope is then made steeper. The box slides slowly, at a steady speed. moving at a steady speed Is there a friction force on the box? Tick ONE box () yes no University of York

8 (d) The slope is now made even steeper still. The box slides down, getting faster and faster as it goes. slides down, getting faster Is there a friction force on the box now? Tick ONE box () yes no 140 University of York 2003

9 3 A furniture remover is pushing on a box. It is not moving. box not moving Figure 1 still not moving He pushes harder. But the box still does not move. Figure 2 (a) How does the size of the friction force in these two situations compare? Tick ONE box () The friction force on the box is bigger in Figure 1. The friction force on the box is bigger in Figure 2. The friction force on the box is the same size in both figures. (b) How would you explain your answer? Tick ONE box () The total force on the box is zero each time. It is the same box and the same surface. When the pushing force is small, the box grips the surface better. University of York

10 4 A furniture remover is pushing on a box. It is not moving. box not moving Figure 1 He pushes harder. Now the box is moving along at a steady speed. moving at a steady speed Figure 2 (a) How does the size of the friction force in these two situations compare? Tick ONE box () The friction force on the box is bigger in Figure 1. The friction force on the box is bigger in Figure 2. The friction force on the box is the same size in both figures. (b) How would you explain your answer? Tick ONE box () The total force on the box is zero each time. It is the same box and the same surface. In this situation, the friction force is big enough to stop the box moving. 142 University of York 2003

11 5 Mai Lin is pushing a box. The box is moving along at a steady speed. moving at a steady speed Figure 1 She pushes harder. The box moves along, getting faster as it goes. getting faster Figure 2 (a) How does the size of the friction force in these two situations compare? Tick ONE box () The friction force on the box is bigger in Figure 1. The friction force on the box is bigger in Figure 2. The friction force on the box is the same size in both figures. (b) How would you explain your answer? Tick ONE box () The total force on the box is zero each time. When the box is moving, the friction force on it does not depend on the speed. As the box moves faster, it grips the surface less and so the friction force on it is smaller. As the box moves faster, it rubs harder on the surface so the friction force on it is bigger. University of York

12 6 Mai Lin is pushing on a box. It is not moving. box not moving Figure 1 Whitney pushes the same box. It moves along at a steady speed. moving at a steady speed Figure 2 (a) How does the size of the friction force in these two situations compare? Tick ONE box () The friction force on the box is bigger in Figure 1. The friction force on the box is bigger in Figure 2. The friction force on the box is the same size in both figures. It is not possible to say from this information. (b) Explain your answer: 144 University of York 2003

13 7 Mohammed tries to push a box across a level floor. (a) He pushes with a force of 50N. The box does not move. What is the size of the friction force acting on the box? Tick ONE box () 50N less than 50N more than 50N 50N The box does not move. (b) Mohammed pushes harder, with a force of 100N. The box still does not move. What size is the friction force acting on the box now? Tick ONE box () more than 100N 100N 50N less than 50N between 50N and 100N 100N The box does not move (c) After taking a rest, he pushes harder still, with a force of 150N. Now the box moves slowly, at a steady speed. What size is the friction force acting on the box now? Tick ONE box () more than 150N 150N just a little bit less than 150N quite a lot less than 150N 150N moves at a steady speed University of York

14 (d) After another rest, Mohammed pushes the box even harder still, with a force of 200N. How does the box move?? 200N Tick ONE box () The box moves at a steady speed, faster than in part (c). The box accelerates, getting faster and faster. (e) When Mohammed pushes with a force of 200N, what size is the friction force acting on the box now? Tick ONE box () more than 200N 200N 150N less than 150N just a little bit less than 200N 200N (f) Mohammed stops pushing and the box sits on the level floor. What size is the friction force acting on the box now? Tick ONE box () 200N 150N 100N 50N zero another value (please write here): 146 University of York 2003

15 8 A shopper pushes a trolley across a level floor. She pushes with a force of 40N. The trolley moves slowly, at a steady speed. moves at a steady speed (a) What is the size of the friction force on the trolley? Tick ONE box () more than 40N exactly equal to 40N a little bit less than 40N a lot less than 40N (b) She now pushes harder, exerting a force of 60N on the trolley. What will happen? Tick ONE box () The trolley will continue to move across the floor at the same speed as before. The trolley will move across the floor at a faster steady speed. The speed of the trolley will keep increasing, as long as she keeps pushing with 60N. The speed of the trolley will increase at first, then it will settle down at a constant speed which is bigger than before. University of York

16 9 Mai Lin pushes a box across a level floor. The box moves slowly, at a steady speed. box moves at a steady speed (a) While the box is moving at a steady speed, the horizontal force exerted by the Mai Lin on the box is: Tick ONE box () equal to the weight of the box greater than the weight of the box exactly equal to the friction force on the box a tiny bit bigger than the friction force on the box a lot bigger than the friction force on the box (b) Mai Lin then doubles the horizontal force that she exerts on the box. How does the box move now? Tick ONE box () With a constant speed that is double the speed in part (a). With a constant speed that is bigger than the speed in part (a), but not necessarily double. With a continuously increasing speed. With an increasing speed at first, then settling down at a higher constant speed. 148 University of York 2003

17 10 Tom pushes a sled across some level ice. The sled moves slowly, at a steady speed. sled moves at a steady speed ice (a) While the sled is moving at a steady speed, the horizontal force exerted by Tom on the sled is: Tick ONE box () equal to the weight of the sled greater than the weight of the sled exactly equal to the friction force on the sled a tiny bit bigger than the friction force on the sled a lot bigger than the friction force on the sled (b) Tom then doubles the horizontal force that he exerts on the sled. How does the sled move now? Tick ONE box () With a constant speed that is double the speed in part (a). With a constant speed that is bigger than the speed in part (a), but not necessarily double. With a continuously increasing speed. With an increasing speed at first, then settling down at a higher constant speed. University of York

18 (c) Tom suddenly stops applying a horizontal force to the sled. How does the sled move now? Tick ONE box () It immediately comes to a sudden stop. It keeps on moving at a steady speed for a while and then slows to a stop. Its speed immediately starts to get less, and keeps on slowing until it stops. It continues at a constant speed. Its speed keeps increasing for a while and then it gradually slows down until it stops. 150 University of York 2003

19 11 A truck is travelling along a level road. It is carrying a large crate. The crate does not slide around on the truck because of the friction between the bottom of the crate and the floor of the truck. (a) The truck is starting up from rest and is gaining speed. Which of the following best describes the friction force acting on the crate? Tick ONE box () There is a friction force on the crate in the forward direction. There is a friction force on the crate in the backward direction. There is no friction force on the crate. (b) The truck is travelling at a steady speed. Which of the following best describes the friction force acting on the crate? Tick ONE box () There is a friction force on the crate in the forward direction. There is a friction force on the crate in the backward direction. There is no friction force on the crate. (c) The truck is slowing down. Which of the following best describes the friction force acting on the crate? Tick ONE box () There is a friction force on the crate in the forward direction. There is a friction force on the crate in the backward direction. There is no friction force on the crate. University of York

20 12 A large wooden block is sitting on a table, with a second smaller wooden block on top of it. blocks pulled along by a string The two blocks are pulled across the table, by a string attached to the bottom block. The top block does not slide on the bottom block. Both move together. (a) Which of the diagrams below best shows the friction force acting on the top block, while the speed of the blocks is increasing? (Circle one letter A, B or C to indicate your answer.) no friction force A B C (b) Which of the diagrams below best shows the friction forces acting on the bottom block, while the speed of the blocks is increasing? (Circle one letter D, E, F, G, H, I to indicate your answer.) D E F G H I 152 University of York 2003

21 (c) Which of the diagrams below best shows the friction forces acting on the top block, while the blocks are moving at a steady speed? (Circle one letter A, B or C to indicate your answer.) no friction force A B C (d) Which of the diagrams below best shows the friction forces acting on the bottom block, while the blocks are moving at a steady speed? (Circle one letter D, E, F, G, H, I to indicate your answer.) D E F G H I University of York

22 13 A large wooden block is sitting on a table, with a second smaller wooden block on top of it. blocks pulled along by a string The two blocks are pulled across the table, by a string attached to the top block. The top block does not slide on the bottom block. Both move together. (a) Which of the diagrams below best shows the friction force acting on the top block, while the speed of the blocks is increasing? (Circle one letter A, B or C to indicate your answer.) no friction force A B C (b) Which of the diagrams below best shows the friction forces acting on the bottom block, while the speed of the blocks is increasing? (Circle one letter D, E, F, G, H, I to indicate your answer.) D E F G H I 154 University of York 2003

23 (c) Which of the diagrams below best shows the friction forces acting on the top block, while the blocks are moving at a steady speed? (Circle one letter A, B or C to indicate your answer.) no friction force A B C (d) Which of the diagrams below best shows the friction forces acting on the bottom block, while the blocks are moving at a steady speed? (Circle one letter D, E, F, G, H, I to indicate your answer.) D E F G H I University of York

24 Answers and discussion Friction In the discussion below, answer options are referred to by number (1, 2, 3 ), in the order in which they appear in the question. 1 (a) no (b) yes (c) yes (d) yes Some students may think that there is only a friction force when the box is being pushed but is not moving ( yes to (b) only). 2 (a) no (b) yes (c) yes (d) yes This is similar to Q1. The reasoning involved is more difficult, though, as this is a two-dimensional situation. When the box is sitting on a sloping surface, a component of the gravity force on the box acts down the slope. This tends to make the box slip and friction forces then arise from the interaction between the box and the surface of the slope. 3 (a) 2 (b) 1 Here the reasoning really goes from (b) to (a). In both cases, the box is not moving, so the total force acting on it is zero. Friction matches the force exerted by the workman. Answer patterns 3/2 and 1/3 indicate other (incorrect) ways of thinking about this situation, which might be worth following up. 4 (a) 2 (b) 1 Again, the reasoning goes from (b) to (a) the total force is zero in both cases. This requires an understanding of Newton s First Law of motion. Answer patterns 3/2 and 1/3 indicate other (incorrect) ways of thinking about this situation, which might be worth following up. 5 (a) 3 (b) 2 6 For a student who has not been taught that there is a difference between starting friction and moving friction (see Notes at the start of this question pack), the correct answer is: (a) 2 (b) The force exerted by Whitney in Figure 2 is bigger. In both cases, the resultant (or total) force on the box is zero. So the friction force must also be bigger in Figure University of York 2003

25 However, if a student knows that the maximum value of starting friction is bigger than moving friction, then the best answer is: (a) 4 (b) In both cases, the friction force is equal to the force applied by the person pushing. But it is not possible to say for certain whether this applied force is bigger in Figure 1 or Figure 2. It is probable that Mai Lin is applying a smaller force in Figure 1. But if the box in Figure 1 is just on the point of moving, then Mai Lin might be applying a larger force in Figure 1 because the starting friction force will be at (or close to) its maximum value, which is bigger than the value of the moving friction force. 7 (a) 2 (50N) (b) 2 (100N) (c) 2 (150N) (d) 2 (e) 4 (150N) (f) 5 (zero) This question is probing understanding that the friction force matches the applied force up to a limit. If the applied force is bigger than this, the friction force stays at its maximum value. 8 (a) 2 (b) 3 Part (b) also tests understanding of Newton s first and second laws of motion. 9 (a) 3 (b) 3 Part (b) also tests understanding of Newton s first and second laws of motion. 10 (a) 3 (b) 3 (c) 3 Parts (a) and (b) of this question are very similar to Q9. Parts (b) and (c) also test understanding of Newton s first and second laws of motion. 11 (a) 1 (b) 3 (c) 2 The key here is to think about the motion of the crate. In (a), the crate is accelerating to the right. The only horizontal force on the crate is the force exerted by the floor of the truck (friction). So this must be towards the right. In (b), the crate is moving at a steady speed, so the resultant force on it is zero. In (c), the crate is getting slower. So the resultant force on it is in the direction opposite to its motion. Again the only horizontal force is the friction force, so this must act towards the left. If, however, air resistance were to be considered (and some pupils may feel that it should be), there would also be a drag force acting on the crate in the backward direction. For (a) and (c), the direction of the friction force on the crate would University of York

26 not be changed, but for (b) there would need to be a friction force acting on the crate in the forwards direction to counter the drag force due to the air resistance. 12 (a) B (b) D As in Q11, start from the motion of the top block. It is accelerating to the right. The only horizontal force on the top block is the friction force from its interaction with the lower block. So this must be towards the right. The other force of this interaction pair acts on the lower block and must be on the opposite direction, towards the left. There is also a friction interaction between the lower block and the table. The friction force on the lower block is towards the left. (c) C (d) H When the blocks are moving at a steady speed, the resultant force on the top block is zero. The friction forces between the lower block and the table are the same as before, though. 13 (a) A (b) F The applied force tends to make the top block move to the right over the lower block. So the friction force on the top block is towards the left. The other force of this interaction pair acts on the lower block towards the right. There is also a friction interaction between the lower block and the table. The friction force on the lower block is towards the left. (c) A (d) F When the blocks are moving at a steady speed, the resultant force on the top block is zero. So the friction force on the top block must be equal to the force exerted by the string. The bottom block is also moving at a steady speed, so the resultant force acting on it is also zero. The friction force exerted by the top block on the bottom one is equal in size and opposite in direction to that on the top block (they are an interaction pair). This is then balanced by the friction force exerted by the table on the lower block so that the resultant is zero. 158 University of York 2003

27 Acknowledgements Some of the questions in this pack are based on probes used by science education researchers to explore learners understanding of key ideas about forces and motion. These have been modified, often quite substantially, to improve their clarity or to make them easier to use in class. Others are new questions, written for EPSE Project 1: Using Diagnostic Assessment to Enhance Teaching and Learning in Science. Questions which are knowingly based on previous probes are listed below, with an indication of the original source. If precursors of any questions in this pack are not acknowledged below, we would be grateful to have this pointed out, so that it can be rectified in any subsequent publication. Q2 Based on a question in: Stead, K. & Osborne, R. (1980). Learning in Science Project Working Paper No. 19. University of Waikato: LISP Project. Q9-10 Based on questions in the revised version of the Force Concept Inventory (FCI) (Halloun, I., Hake, R., Mosca, E. & Hestenes, D. 1995), reproduced in: Mazur, E. (1997). Peer Instruction (pp ). Upper Saddle River NJ: Prentice Hall. Q12-13 The situation used in these questions is similar to (though not exactly the same as) that used in probes by H. Caldas (1994), discussed in: Viennot, L. (2003). Teaching Physics (pp ). Dordrecht: Kluwer Academic Publishers. University of York

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