Friction Kinetic friction: fk- friction force N - normal force - coefficient of kinetic friction Static friction: - coefficient of static friction

fS,book,wall Fbook,hand Nbook,wall Wbook,Earth 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: A. Larger than before B. The same C. Smaller than before. fS,book,wall Fbook,hand Nbook,wall Wbook,Earth For the book not to fall down, fS = W Pushing harder (increasing Fbook,hand) increases Nbook,wall and therefore fS,MAX increases, but not the actual value of fS that we had, which needs to continue to be exactly W.

Example: A 49 kg rock climber is climbing a “chimney” between two rock slabs. The coefficient of static friction between her shoes and the rock is 1.2; between her back and the rock it is 0.80. She has reduced her push against the rock until her back and her shoes are on the verge of slipping. What is her push against the rock? N fS back fS feet w fs back fs feet N N y W x If the climber dos not slip or move up, the value of the sum of frictional forces is fixed:

Answer B

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

Example: Box on incline with friction 1)Static: 2) Kinetic

mgsinθ – F = m ax = 0 F = mg sinθ N – mgcosθ = m ay = 0 N = mg cosθ Example: A hand keeps a 20-kg box from sliding down a frictionless incline. The plane of the incline makes an angle θ = 30° with the horizontal. What is the magnitude of the force exerted by hand? mgsinθ – F = m ax = 0 N – mgcosθ = m ay = 0 F = mg sinθ N = mg cosθ x y F = (20 kg)(9.8 m/s2)sin(30°) = 98 N N FB,hand mgsinθ Directions: Draw the free-body diagram Choose axes (draw them!) Use Newton’s 2nd law in the x and y-directions. θ mgcosθ θ mg

Centripetal force F = ma

Example: A stone of mass m sits at the bottom of a bucket. A string is attached to the bucket and the whole thing is made to move in circles. What is the minimum speed that the bucket needs to have at the highest point of the trajectory in order to keep the stone inside the bucket? F = ma

Examples (centripetal force) F = ma (1) mg N (2) N mg (3) N mg

Example: Little Jacob (15 kg) sits on the edge of a merry-go-round of radius 1.0 m while big sister makes it turn… faster and faster. How fast can the system go before Jacob takes off if the coefficient of static friction between Jacob’s pants and the merry-go-round is 0.5? N fs Static friction provides the needed radial acceleration: mg Maximum speed  Maximum static friction:

Example: A car of mass m with constant speed v drives through a curve of radius R. What is the minimum value of the coefficient of static friction between the tires and the road for the car not to slip? fs