10.1 Observe and Find a Pattern Friction Can Be Rough Observe the following experiment: Rest a brick on a rough surface. Tie a string around the brick and attach a large spring scale to it. Pull the scale slowly, pulling harder and harder. Notice what happens to the scale reading while the shoe does not move. Notice the reading right before the brick starts moving and right after, keeping it moving but not accelerating. a) Explain a time when you have experienced this phenomenon before. b) Draw a force diagram for the brick (the system) for the following situations. 1. The shoe sits on the table with no scale pulling it. 2. The spring pulls on the brick, which does not start moving. 3. The spring pulls harder, but the shoe still does not move. 4. The spring pulls on the brick, and the shoe is just about to start moving. 5. The spring pulls the brick at a slow, constant velocity. c) Describe in words how the magnitude of the horizontal forces change as you pull harder and harder. d) What object is exerting this resistive force for the scenarios given above? e) Compare the magnitude of the resistive force just before the shoe starts moving to the magnitude when it is moving at a constant velocity. What do you observe? f) Summarize your findings for the resistive force exerted on an object at rest and the resistive force exerted on the same object moving at a constant velocity. g) Give a name to each of the two different resistive forces. h) Physicists use the term friction to describe the resistive force you observed and the terms static and kinetic to describe the two different friction forces. Rename your resistive forces using these terms. i) Which friction force changed during your experiment? Which friction force did not change during your experiment?
Did You Know? The friction force is a resistive force exerted by the surface on an object. There are two kinds of friction forces you observed in the experiments above. The static friction force is variable. As you saw, once the maximum static friction force is overcome, the object will start to move. The kinetic friction force is the resistive force exerted on a moving object. 10.2 Observe and Find a Pattern Instead of the shoe in the previous activity, you have rectangular blocks with different surface areas and different types of surfaces on which the block slides horizontally. A B C The force that the string exerts on the block (as measured by the spring scale reading) when the block just starts to slide is recorded in the table that follows. This force is equal in magnitude to the maximum static friction force (as we discovered in the previous activity). a) Consider scenarios A and B. Which scenario, if any, do you think will give a larger spring scale reading? a. A b. B c. They will give the same reading b) Consider scenarios A and C (the surface in C is rougher than the surface in A). Which scenario, if any, do you think will give a larger spring scale reading? a. A b. C c. They will give the same reading Examine the data in the table that follows. Quality of Maximum Mass of the block Surface area surfaces static friction force 1 kg 0.1 m 2 Medium smooth 3.1 N 1 kg 0.2 m 2 Medium smooth 3.0 N 1 kg 0.3 m 2 Medium smooth 3.1 N 1 kg 0.1 m 2 A little rougher 4.2 N 1 kg 0.1 m 2 Even rougher 5.1 N 1 kg 0.1 m 2 Roughest 7.0 N c) Now decide how the maximum static friction force that the surface exerts on the block depends on the surface area of the block and on the roughness of the two surfaces. d) How does this change your original thinking?
10.3 Observe and Find a Pattern Take a textbook and drag it with your pinky finger. Repeat but this time, have your neighbor push down lightly on the book. Repeat 3 more times with your neighbor pushing down successively harder. a) Draw a force diagram for each case. b) What can you say about the maximum static friction force as you push down harder and harder? 10.4 Observe and Find a Pattern A spring scale pulls a 1 kg block over a medium smooth surface. The reading of the scale can be used to determine the magnitude of the maximum static friction force in this instance, the force when the block starts to slide. In some experiments, a compressible spring also pushes vertically down on the block (see the second block). Spring pushes down 1 kg 1 kg Extra downward force exerted on the 1-kg block Normal force exerted by the board on the block 0 N 10 N 3 N 5 N 15 N 4.5 N 10 N 20 N 6 N 20 N 30 N 9 N Maximum static friction force a) Use the data in the table to draw a graph of the maximum static friction force versus the normal force the surface exerts on the block. b) Express mathematically a relationship between the normal force and the maximum static friction force. Find the slope and write this relationship as an equation. 10.5 Reason a) Consider the previous activity. Why would we consider the normal force exerted on the object rather than the force of the Earth exerted on the object? b) A person is holding a book against a vertical wall, pushing on it horizontally. The book is at rest. Draw a force diagram for the book. Check if all forces balance. c) Which force prevents the book from falling down? d) Why, if you do not push on the book hard enough, does the book start falling? Draw a force diagram to support your reasoning.
Did You Know? Normal force: When two objects touch each other, they exert a normal force on each other. The force of the one object on the other object points perpendicular to the surface of contact. Often one symbol N is used to denote this force (do not confuse with the Newton, N). There is no equation for calculating the normal force. Its magnitude must be determined for each situation by some other method. Static friction force: When two objects touch each other, they exert a friction force on each other. The friction force of the one object on the other object points parallel to the surfaces of contact. If the objects are not moving with respect to each other, the friction force that they exert on each other is static. The static friction force between two surfaces opposes the tendency of one surface to move across the other and provides flexible resistance (as much as is needed) to prevent motion up to some maximum value. This maximum static friction force depends on the relative roughness of the surfaces (on the coefficient of static friction µ s between the surfaces) and on the magnitude of the normal force N between the surfaces. The magnitude of the static friction force is always less than or equal to the product of these two quantities: fs = µsn Kinetic friction force: The kinetic friction force between two surfaces is exerted parallel to the surfaces and opposes the motion of one surface relative to the other surface. The kinetic friction force depends on the relative roughness of the surfaces (on the coefficient of kinetic friction µ k ) and on the magnitude of the normal force N between the surfaces: fk = µkn 10.6 Reason a) Compare the surfaces of sandpaper and paper. What do you observe? b) Sketch what these two surfaces might look like at a microscopic level. c) Observer the difference between the images of paper and aluminum taken from a microscope. d) Think about what might happen on the microscopic level when two surfaces slide across each other. What if you increase the normal force? Use this new observation to explain what causes friction.
10.7 Reason Homework Think about what happens what happens on a gym floor when you have dirt or dust on the bottom of your sneakers. Or what happens when the gym floor is wet. Use your new understanding of friction to explain why this happens. 10.8 Observe and Represent Imagine that you could watch yourself walk in slow motion. Analyze your steps in terms of the force of friction that the floor exerts on your foot and in terms of Newton s Second and Third Laws. In order to do this, break the step into two parts: (1) when you put the foot down to finish up the previous step, and (2) when you are pushing off the floor to start a new step. Draw force diagrams to represent your reasoning. 10.9 Evaluate Eugenia says that the force of friction is something that we should reduce in order to make the cars go faster. What friction force could she mean? Do you agree or disagree with her opinion? If you agree, how would you argue for it? If you disagree, how would you argue against it? 10.10 Represent and Reason Some students are trying to move a heavy desk across the room. Diana pushes it across the floor (in the positive direction) at the same time that Omar and Jeff pull on it (in the negative direction). Omar pulls on the desk, exerting an (-150) N force, and Jeff pulls exerting a (-125) N force. There is also a (-200) N friction force exerted by the floor on the desk. The net force exerted on the desk is +27 N. a) Make a sketch of the situation. b) Draw a force diagram for the desk. Draw a motion diagram. c) Write a net force statement that describes the force diagram you drew. d) How hard is Diana pushing? e) Is the desk moving with a constant velocity or is it speeding up? How do you know? f) What would happen if, after a few seconds, the boys stopped pulling?