LECTURE 12 FRICTION & SPRINGS Instructor: Kazumi Tolich
Lecture 12 2 Reading chapter 6-1 to 6-2 Friction n Static friction n Kinetic friction Springs
Origin of friction 3 The origin of friction is electromagnetic attraction force between molecules/atoms of one surface to these of another in close contact. The microscopic contacting surface area increases when the normal force increases due to the flattening of the tips. Polished steel surface
Static friction 4 Static friction is the frictional force that prevents surfaces in contact from sliding. The direction of the static friction is anti-parallel to the force trying to slide the object relative to the surface.
Static friction: 2 5 While the object is not sliding on a surface, the magnitude of the static friction equals the magnitude of the force trying to slide the object until it reaches the maximum value given by f s,max = µ s N µ s is the coefficient of static friction (dimensionless). N is the magnitude of the normal force by one surface on the other. f s FBD of the block N F mg
Clicker question: 1 & 2
Demo: 1 7 Four surface incline Demonstration of various materials with different coefficients of static friction
Example: 1 8 Hopping into your Porsche, you floor it and accelerate at a = 12 m/s 2 without spinning the tires. Determine the minimum coefficient of static friction between the tires and the road needed to make this possible.
Kinetic friction 9 Kinetic friction is the frictional force that opposes sliding motion. The direction of the kinetic friction is anti-parallel to the velocity of the sliding object relative to the surface. The magnitude of the kinetic friction is given by f k = µ k N µ k is the coefficient of kinetic friction (dimensionless). N is the magnitude of the normal force by one surface on the other. Kinetic friction is independent of the relative speed of the surfaces or the area of contact between the surfaces.
Demo: 2 10 Contact area and kinetic friction
Example: 2 11 A 0.11-kg hockey puck whose initial speed was 6.0 m/s slides on the ice for 15.0 m before it stops. a) What was the magnitude of the frictional force on the puck during the sliding? b) What was the coefficient of friction between the puck and the ice?
Static vs. kinetic frictions 12 For any given contacting surfaces, µ k is usually less than or equal to µ s. You have to push harder to get an object to begin sliding than to keep it sliding at constant speed. f s,max = µ s N f k = µ k N
Example: 3 13 A crate with a mass of m = 45 kg is placed on an inclined ramp. When the angle the ramp makes with the horizontal is increased to θ = 23, the crate begins to slide downward. a) What is the coefficient of static friction between the crate and the ramp? b) At what angle does the crate begin to slide if its mass is doubled?
Demo 3 14 Incline with Sliding Blocks (with Tacky Wax) Demonstration of various surfaces with different coefficients of static friction. Coefficient of static friction can be measured by the maximum angle without the block sliding. Max static friction: f s BR, max = µ s N BR N BR f s BR in x-dir: f s BR, max W BE sinθ = 0 in y-dir: N BR W BE cosθ = 0 +y +x θ µ s = tanθ θ W BE
Spring force 15 Force exerted by a compressed or stretched spring obey Hook s law. F x = kx - : the direction of force is opposite from the displacement of the end of the spring. This type force is called restoring force. k: force constant for stiffness of the spring x: the displacement of the end of the spring.
Demo: 4 16 Hook s Law
Example: 4 17 A backpack weighing w = 52.0 N rests on a table. A spring with a force constant of k = 150 N/m is attached to the backpack and pulled horizontally. If the spring is pulled until it stretches x = 2.00 cm and the pack remains at rest, what is the force of friction exerted on the backpack by the table?
Example: 5 18 A spring with a force constant of k = 120 N/m is used to push a 0.27-kg block of wood against a wall, as shown. Find the minimum compression of the spring needed to keep the block from falling, given that the coefficient of static friction between the block and the wall is µ s = 0.46.