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Download Kinetic Friction
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Kinetic Friction Sliding Sliding objects also have a frictional force exerted on them. This frictional force is kinetic friction. An approximate formula: F fr m k FN mk is the coefficient of kinetic friction Continuing Motion FN mg cosq • Fgx = mg sinq. • Block increases or decreases speed depending on which is greater. F fr m k mg cos q mg sin q q mg cos q Ffr = mkFN = mkmg cosq Compare to the downslope component of gravity If equal there is constant velocity. Fg mg mg sin q m k mg cosq m k tan q Static vs. Kinetic Static and kinetic friction are similar. Static and kinetic friction are different. • Force in opposite direction to motion • Static friction is an inequality up to a maximum • Proportional to normal force • Coefficient of friction is typically greater for static friction at the same surface • Coefficient of friction depends on materials • Wood on wood (0.4 vs. 0.2) Drag Kinetic friction is a constant force. • If there is a net force an object would accelerate forever Air resistance causes a friction called drag. • At low velocity drag is proportional to velocity, Fd = -bv • At higher velocity drag goes as velocity squared, Fd = -cv2 Because it depends on velocity the force increases as an object speeds up. Terminal Velocity An object may fall through the air at constant velocity. By the law of inertia the net force is zero. The force of drag must balance the force of gravity. Fd = cv2 Fg = -mg Fd Fg 0 This velocity is called the terminal velocity. cvt2 - mg 0 vt mg c Downhill Skiing CBS Sports has invited you to be the special science commentator for the Winter Olympics downhill ski race. You observe the following: • • • • The downhill course is 2.5 km long with a drop of 800 m A downhill skier needs at least 3° of slope to move forward The speed gun clocks the skier at a maximum of 130 km/h An average skier is about 90 kg What is the coefficient of kinetic friction and drag coefficient for a skier? Force Diagram FN = mg cosq At constant velocity the forces must all balance. Friction doesn’t act in the direction of the normal force. The normal force cancels the component of gravity. Fd = -cv2 Ffr = -mkFN Fg = -mg q Fgy = -mg cosq FN mg cosq Minimum Sliding FN = mg cosq Ffr = -mkFN Fgx = mg sinq When the skier is sliding to a halt we can neglect drag. Kinetic friction balances the component of gravity pulling forward. Fgx F fr 0 q 3° mg sin q m k mg cosq m k tan q 0.052 Downhill Run FN = mg cosq Fgx = mg sinq • sinq = 800 m / 2500 m q = 19° Fd = -cv2 Ffr = -mkFN The slope of the downhill course is Drag force balances the force of gravity and kinetic friction. Fgx F fr Fd 0 q 19° mg sin q - m k mg cos q - cv 2 0 mg sin q - m k mg cos q v2 c 0.19 kg/m c
