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SPH3U1 Date: _____________ FRICTION WHAT CAUSES FRICTION? We believe that intermolecular forces between two surfaces form microscopic welds that must be broken for an object to move. As the object moves, these microscopic welds form and break continuously. WHAT DETERMINES THE STRENGTH OF THE FORCE OF FRICTION? materials in contact normal force FORCE OF FRICTION Ff μFn COEFFICIENT OF FRICTION The coefficient of friction is a number that indicates the ratio of the magnitude of the force of friction (Ff) between two surfaces to the magnitude of the normal force (Fn - force perpendicular to these surfaces). Ff - force of friction (N) μ - coefficient of friction Fn - normal force (N) 2 TYPES OF FRICTIONAL FORCES: 1. Friction can be STATIC, when the object is NOT moving 2. Friction can be KINETIC, when the object is moving An object at rest experiences more friction. The force needed to start the motion of an object initially at rest is greater than the force needed to keep it going at a constant velocity. Static friction is usually slightly greater than the kinetic friction. 2 TYPES OF COEFFICIENT OF FRICTION: 1. coefficient of static friction us 2. coefficient of kinetic friction uk HOW TO SOLVE PROBLEMS THAT INVOLVE FRICTION 1. Write down your GIVENS 2. Draw a Free Body Diagram (FBD) – include all forces acting on the object 3. Select positive direction (based on applied forces) 4. Solve for Fn using Fnet ma (usually Fnety 0 ) 5. Solve for Ff μFn 6. Solve for a using Fnet ma Determining the coefficients of friction for various surfaces can be done only experimentally. See Table 1 on page 170. EXAMPLE 1 A 3.0kg block of wood sits on a horizontal wooden floor. The largest horizontal force that can be applied to the block before it will start moving is 14.7N. Once the block starts moving, it only takes 8.8N to keep it moving at a constant velocity. a) Calculate the coefficient of static friction for the block of wood and the floor. b) Determine the coefficient of kinetic friction. STATIC FRICTION PROBLEMS EXAMPLE 2 Two sleds are tied together with a rope. The coefficient of static friction between each sled and the snow is 0.22. A small child is sitting on sled 1 (total mass of 27 kg) and a larger child sits on sled 2 (total mass of 38 kg). An adult pulls on the sleds. a) What is the greatest horizontal force that the adult can exert on sled 1 without moving either sled? (ans: 140N[fwd]) b) Calculate the magnitude of the tension in the rope between sleds 1 and 2 when the adult exerts this greatest horizontal force. (ans: 82N) EXAMPLE 3 A 4.0 kg block of wood sits on a table. A string is tied to the wood, running over a pulley and down to a hanging object. The greatest mass that can be hung from the string without moving the block of wood is 1.8 kg. Calculate the coefficient of static friction between the block of wood and the table. EXAMPLE 4 The coefficient of static friction between a person’s shoe and the ground is 0.70. Determine the maximum acceleration of the 62.0kg person, if he starts running on a horizontal surface from rest. (ans: 6.9m/s2 [fwd]) KINETIC FRICTION PROBLEMS EXAMPLE 5 The following forces are applied on a box: 18N [down], 22 N [right], 70 N [left], 13 N [up]. The box has a mass of 14kg and =0.12. a) Draw a Free Body Diagram. (add Fg, Fn and Ff) b) Calculate the force of friction acting on the box. c) Calculate the acceleration of the box. EXAMPLE 6 Two sleds tied together are pulled across an icy surface with an applied force of 150 N [E]. The mass of sled 1 is 18.0 kg and the mass of sled 2 is 12.0 kg. The coefficient of kinetic friction for each sled is 0.20. a) Calculate the acceleration of the sleds. (ans: 3.0m/s2[E]) b) Determine the magnitude of the tension in the rope between the sleds. (ans: 60N) EXAMPLE 7 The truck’s brakes are applied so hard that the truck starts to skid on a dry asphalt road. If the truck and its contents have a mass of 4.2 x103 kg, determine the force of kinetic friction on the truck. (ans: 2.7x104N) EXAMPLE 8 A 0.17kg hockey puck has a velocity of 19 m/s [F] when it suddenly hits a rough patch of ice that is 5.1m across. Assume that the coefficient of kinetic friction between the puck and the rough ice is 0.47. a) Draw a Free Body Diagram. b) Calculate the kinetic friction acting on the puck. c) Determine the puck’s acceleration on rough ice. d) Calculate the puck’s velocity as it leaves the rough ice and returns to smooth ice. (ans: 18m/s) EXAMPLE 9 A string is tied to a 3.2 kg object on a table and a 1.5 kg object hanging over a pulley. The coefficient of kinetic friction between the 3.2 kg object and the table is 0.30. a) Calculate the acceleration of each object. b) Determine the magnitude of the tension in the string. c) How far will the objects move in 1.2 s if the initial velocity of the 3.2 kg object is 1.3 m/s [right]? (ans: 2.4m) HOMEFUN 4.2 and 4.3 read pg 168-171 questions pg 172 #1-7 read pg 173-177 questions pg 178 #1-10 EXAMPLE 10 A lawnmower (12kg) is being pushed by a horizontal force of 150.0N and a downward force of 40.0N. a) If the kinetic coefficient of friction between the wheels and the grass is 0.90, find the force of friction acting on the lawnmower. (ans: 142N[bwd]) b) Determine the lawnmower acceleration. (ans: 0.68m/s2 [bwd]) EXAMPLE 11 Two people are pushing on a crate of mass 50.0 kg. One person pushes left with a force of 80.0N, the other person pushes right with a force of 50.0N. The coefficient of friction is 0.30. Find the acceleration of the crate. The answer is tricky!! EXAMPLE 12 Your physics teacher is erasing the board with an eraser that has a mass of 0.50 kg block. She slides the eraser up the chalkboard with an applied force of 6.0N upward and 2.0N towards the board. If the coefficient of kinetic friction is 0.40, calculate the acceleration of the block. (ans: 0.60m/s2 [up]) TRY THIS!!! A hockey puck of mass 0.30kg is sliding along ice at 6.0 m/s (assume frictionless). It encounters a rough patch of ice with a coefficient of kinetic friction of 0.10. a) How long will it take for the puck to stop? (ans: 6.1s) b) How far will it travel? (ans: 18m) motion equation