Friction forces, Grade 11 physics When the surface of one object slides over the surface of another, each body exerts a frictional force on the other. For example if a book slides across a table, the table exerts a frictional force onto the book and the book exerts a frictional force onto the table (Newton’s Third Law). Frictional forces act parallel to the surfaces. A force is not always big enough to make an object move, for example a small applied force might not be able to move a heavy crate. The frictional force opposing the motion of the crate is equal to the applied force but acting in the opposite direction. This frictional force is called static friction. When we increase the applied force (push harder), the frictional force will also increase until the applied force overcomes it. This frictional force can vary from zero (when no other forces are present and the object is stationary) to a maximum that depends on the surfaces. When the applied force is greater than the frictional force and the crate will move. The frictional force will now decrease to a new constant value which is also dependent on the surfaces. This is called kinetic friction. In both cases the maximum frictional force is related to the normal force and can be calculated as follows: For static friction: F$_{f }$≤ µ$_{s }$N Where µ$_{s}$ = the coefficient of static friction and N = normal force For kinetic friction: F$_{f}$ = µ$_{k}$ N Where µ$_{k}$ = the coefficient of kinetic friction and N = normal force Remember that static friction is present when the object is not moving and kinetic friction while the object is moving. For example when you drive at constant velocity in a car on a tar road you have to keep the accelerator pushed in slightly to overcome the kinetic friction between the tar road and the wheels of the car. The higher the value for the coefficient of friction, the more ’sticky’ the surface is and the lower the value, the more ’slippery’ the surface is. The frictional force (F$_{f}$ ) acts in the horizontal direction and can be calculated in a similar way to the normal for as long as there is no movement. If we use the same example as in figure 12.12 and we choose to the right as positive, F$_{f}$ + F$_{x}$ = 0 F$_{f}$+ (+8) = 0 F$_{f}$ = −8 F$_{f}$ = 8 N to the left Worked Example 1: Forces on a slope Question: A 50 kg crate is placed on a slope that makes an angle of 30◦ with the horizontal. The box does not slide down the slope. Calculate the magnitude and direction of the frictional force and the normal force present in this situation Hướng dẫn Step 1 : Draw a force diagram Draw a force diagram and fill in all the details on the diagram. This makes it easier to understand the problem. Step 2 : Calculate the normal force The normal force acts perpendicular to the surface (and not vertically upwards). It’s magnitude is equal to the component of the weight perpendicular to the slope. Therefore: N = F$_{g}$cos 30◦ N = 490 cos 30◦ N = 224 N perpendicular to the surface Step 3 : Calculate the frictional force The frictional force acts parallel to the surface and up the slope. It’s magnitude is equal to the component of the weight parallel to the slope. Therefore: F$_{f }$= F$_{g}$ sin 30◦ F$_{f}$= 490 sin 30◦ F$_{f}$ = 245 N up the slope We often think about friction in a negative way but very often friction is useful without us realizing it. If there was no friction and you tried to prop a ladder up against a wall, it would simply slide to the ground. Rock climbers use friction to maintain their grip on cliffs. The brakes of cars would be useless if it wasn’t for friction! Worked Example 2: Coefficients of friction Question: A block of wood weighing 32 N is placed on a rough slope and a rope is tied to it. The tension in the rope can be increased to 8 N before the block starts to slide. A force of 4 N will keep the block moving at constant speed once it has been set in motion. Determine the coefficients of static and kinetic friction. Hướng dẫn Step 1 : Analyse the question and determine what is asked The weight of the block is given (32 N) and two situations are identified: One where the block is not moving (applied force is 8 N), and one where the block is moving (applied force is 4 N). We are asked to find the coefficient for static friction µ$_{s}$ and kinetic friction µ$_{k}$. Step 2 : Find the coefficient of static friction F$_{f}$ = µ$_{s}$N 8 = µ$_{s}$(32) µ$_{s}$ = 0,25 Note that the coefficient of friction does not have a unit as it shows a ratio. The value for the coefficient of friction friction can have any value up to a maximum of 0,25. When a force less than 8 N is applied, the coefficient of friction will be less than 0,25. Step 3 : Find the coefficient of kinetic friction The coefficient of kinetic friction is sometimes also called the coefficient of dynamic friction. Here we look at when the block is moving: F$_{f}$ = µ$_{k}$ N 4 = µ$_{k}$(32) µ$_{k}$ = 0,125 Exercise Friction forces, Grade 11 physics E - 1. A 12 kg box is placed on a rough surface. A force of 20 N applied at an angle of 30◦ to the horizontal cannot move the box. Calculate the magnitude and direction of the normal and friction forces. E - 2. A 100 kg crate is placed on a slope that makes an angle of 45◦ with the horizontal. The box does not slide down the slope. Calculate the magnitude and acceleration of the frictional force and the normal force present in this situation. E - 3. What force T at an angle of 30◦ above the horizontal, is required to drag a block weighing 20 N to the right at constant speed, if the coefficient of kinetic friction between the block and the surface is 0,20? E - 4. A block weighing 20 N rests on a horizontal surface. The coefficient of static friction between the block and the surface is 0,40 and the coefficient of dynamic friction is 0,20. 4.1 What is the magnitude of the frictional force exerted on the block while the block is at rest? 4.2 What will the magnitude of the frictional force be if a horizontal force of 5 N is exerted on the block? 4.3 What is the minimum force required to start the block moving? 4.4 What is the minimum force required to keep the block in motion once it has been started? 4.5 If the horizontal force is 10 N, determine the frictional force. E - 5. A stationary block of mass 3kg is on top of a plane inclined at 35◦ to the horizontal. 5.1 Draw a force diagram (not to scale). Include the weight of the block as well as the components of the weight that are perpendicular and parallel to the inclined plane. 5.2 Determine the values of the weight’s perpendicular and parallel components. 5.3 There exists a frictional force between the block and plane. Determine this force (magnitude and direction). E - 6. A lady injured her back when she slipped and fell in a supermarket. She holds the owner of the supermarket accountable for her medical expenses. The owner claims that the floor covering was not wet and meets the accepted standards. He therefore cannot accept responsibility. The matter eventually ends up in court. Before passing judgement, the judge approaches you, a science student, to determine whether the coefficient of static friction of the floor is a minimum of 0,5 as required. He provides you with a tile from the floor, as well as one of the shoes the lady was wearing on the day of the incident. 6.1 Write down an expression for the coefficient of static friction. 6.2 Plan an investigation that you will perform to assist the judge in his judgement. Follow the steps outlined below to ensure that your plan meets the requirements. i/ Formulate an investigation question. ii/ Apparatus: List all the other apparatus, except the tile and the shoe, that you will need. iii/ A stepwise method: How will you perform the investigation? Include a relevant, labelled free body-diagram. iv/ Results: What will you record? v/ Conclusion: How will you interpret the results to draw a conclusion? Xem thêm: Physics 11.II Force, Momentum, Impulse High School Students Studying the Sciences Physics