4. Friction a) Kinetic friction: f k k N fk – friction force N – normal force k – coefficient of kinetic friction b) Static friction: f s f s max s N s - coefficient of static friction k s 1 Example: When you push a book against a wall, the static friction between the wall and the book can prevent it from falling. If you press harder, the friction force will be: fS A. Larger than before B. The same N F C. Smaller than before. For the book not to fall down: f s mg mg This force is independent from the normal force. f s f s max s N Pushing harder (increasing F) increases N and therefore fS,MAX increases, but not the actual value of fS that we had, which needs to continue to be exactly mg. 2 Example: Trying to move a trunk friction Fby you ffSk by by floor floor μsN μkN Fby you Static friction Kinetic friction 3 Example: Trying to move a trunk For “small” forces, the trunk does not move. So there must Fby you be a friction force fS = Fby you fS by floor You increase the applied force, but the trunk still does not move: static friction is increasing too. Fby you fS by floor You increase the applied force even more. Eventually, the trunk moves. Static friction cannot be larger than a certain value. And then friction becomes kinetic! Fby you fSk by by floor floor 4 Question 1: Mass m1 sits at rest on a horizontal surface. A string connects m1 over a pulley to a hanging mass m2. The coefficient of static friction between m1 and the horizontal surface is 0.25. The maximum value that m2 can be before m1 starts to slide is ___. A) m1/4 B) m1/2 C) m1 D) 2 m1 E) 4 m1 m2 g s m1 g m2 s m1 Question 2: A box of weight 100 N is at rest on a floor where s = 0.4. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? m T The static friction force has a maximum of sN = 40 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction. 5 Example: Box on incline with friction N f m g cos mg m gsin y (y) N m g cos 0 (x) m gsin f m a 1) Kinetic: f k k N k m g cos m gsin k m g cos m a a g (sin k cos ) x 2) Static: f s s N s m g cos m g sin f s 0 m g sin s m g cos t an s s t an critical 6 5. Fluid resistance and terminal speed • The force of fluid resistance is in the opposite direction of the object’s velocity and will cause the object to slow down if no other force opposes it. • The faster an object goes, the larger the force of fluid resistance. • There is no simple equation for the force of air resistance, however, f kv , at high speed: f Dv 2 • at low speed: • (v – speed, k and D – coefficients) 7 v • As a body falls through the air, the force of air resistance opposite to the downward force of gravity, so the net force decreases. • This continues as the body gains speed until the force of air resistance acting upward equals the weight acting downward: f=mg. • At this point, the net force is zero, so the speed stays constant from then on. • This speed is called the terminal speed of the body. t Question: What is terminal speed of a 50 kg skydiver if the expression for the air resistance (air drag) is f Dv 2 ? Use D=0.2 kg/m, and g = 10 m/s2. Dv2 mg v mg D 50 kg 10 m / s 2 0.2kg / m 50 m / s 8