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Warm-up Rose is sliding down an ice covered hill inclined at an angle of 15° with the horizontal. If Rose and the sled have a combined mass of 54.0 kg, what is the force pulling them down the hill? (neglect friction) m = 54 kg g = 9.81 m/s² θ= 15° Sin θ = Fx/mg Fx = mg sin θ 15° Fn mg Fn Fx Fx Fx = (54 kg)(9.81 m/s²) sin 15° Fx = 137 N θ = 15° mg Friction There are two types of frictional forces in the physical world that affects us. - Static/Kinetic Friction - Air Resistance Air Resistance Is a resistance force that acts in the opposite direction of gravitational forces. Help!! Force of Gravity Force of Gravity SPLAT!! Air Resistance Air Resistance Can also be a horizontal force Fr (Air Resistance) mg Fx Static and Kinetic Friction Are forces that oppose motion between two surfaces that are touching each other. Fa Fr Fr (non-moving) = Static Friction (Fs) Fr (moving) = Kinetic Friction (Fk) Fk = ∑F The force of friction is proportional to the size and mass of an object that you are pushing across a surface. Fk Fk Fapplied Fapplied The amount of friction that occurs between an object and the surface can depend on the type of surface that the object is in contact with. Fk Fapplied Tile Floor Fk Fapplied Carpet The quantity that expresses the dependence of frictional forces on the particular surface the object is in contact with is called the coefficient of friction (µ). It is the ratio between the normal force and the force of friction between two surfaces. Coefficient of Kinetic Friction μk = Fk/Fn coefficient of kinetic friction μs = Fs,max/Fn coefficient of static friction Ff = μFn frictional force Practice problem While redecorating her apartment, Suzy slowly pushes an 82 kg cabinet across a wooden dining room floor, which resists the motion with a force of friction of 320 N. What is the coefficient of kinetic friction between the cabinet and the floor? Fn m = 82 kg g = 9.81 m/s² Fk = 320 N w = mg Fapplied mg w = (82 kg) (9.81 m/s²) w = 804 N w = Fn = 804 N μk = Fk/Fn μk = 320 N/804 N μk = 0.40 Practice Problem 2 A student moves a box of books by attaching a rope to the box by pulling with a force of 90 N at an angle 30° to the horizontal. The box of books has a mass of 20.0 kg and the coefficient of kinetic friction between the bottom of the box and the sidewalk is 0.50. What is the acceleration of the box? (Pg. 146) Step 1: Solve for Weight and X & Y components of applied force Fn Fk Fapplied = 90 N m = 20.0 kg g = 9.81 m/s² μk = 0.50 30° w = mg = 196 N mg 90 N 30° Fapp,y Fapp, x Fapp, y = (90N) (sin 30°) = 45.0 N Fapp, x = (90N) (cos 30°) = 77.9 N Step 2: Find the Kinetic Friction Fapp, y = 45.0 N μk = 0.50 Fapp, x = 77.9 N w = 196 N 90 N 30° Fapp, x Fapp,y ∑Fy = Fn + w + Fapp, y = 0 0 = Fn – 196 N + 45.0 N Fn = 196 N – 45 N = 151 N μk = Fk/Fn Fk = (μk)(Fn) = (0.50)(151 N) = 75.5 N Step 3: Solve for acceleration m = 20.0 kg 90 N 30° Fapp, x Fapp,y Fk = 75.5 N ∑F = ma a = ∑F/m Fapp, x = 77.9 N a = (Fapp, x – Fk) / m a = (77.9 N – 75.5 N) / 20.0 kg a = 0.12 m/s² to the right