– coefficient of kinetic friction a) Kinetic friction: fk – friction force N – normal force – coefficient of kinetic friction b) Static friction: - coefficient of static friction

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 C. Smaller than before. N F For the book not to fall down: mg This force is independent from the normal force. 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.

Example: Trying to move a trunk friction Fby you fS by floor fk by floor μsN Static friction Kinetic friction μkN Fby you

Example: Trying to move a trunk For “small” forces, the trunk does not move. So there must be a friction force fS = Fby you fS by floor Fby you Fby you fS by floor You increase the applied force, but the trunk still does not move: static friction is increasing too. You increase the applied force even more. Eventually, the trunk moves. Static friction cannot be larger than a certain value. Fby you And then friction becomes kinetic! fS by floor fk by floor

The maximum value that m2 can be before m1 starts to slide is ___. 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 Question 2: A box of weight 100 N is at rest on a floor where ms = 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 msN = 40 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction.

Example: Box on incline with friction (y) (x) f 1) Kinetic: 2) Static:

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, at low speed: , at high speed: (v – speed, k and D – coefficients)

This speed is called the terminal speed of the body. 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. v t Question: What is terminal speed of a 50 kg skydiver if the expression for the air resistance (air drag) is ? Use D=0.2 kg/m, and g = 10 m/s2.