Static Friction : fs
Object 'stuck together' Static friction provides force to oppose motion that other forces would have created Maximum static friction budget: \( f_{s,max} = \mu_s F_N \) Actual static friction present: \( f_s \leq f_{s,max} \)

Kinetic Friction : fk
Object sliding along another object direction opposite to object's motion magnitude: \( f_k = \mu_k F_N \)

Book notation : same symbol for both types

Actual Mechanism Complicated...
microscopically rough surfaces 'stiction' (molecular bonds)

 

Example: Two Sheets of Glass
Two sheets of smooth glass are in contact as shown in the figure. How much force (applied horizontally) is required to cause the top sheet (which has a mass of 10 kg to start moving? Once it starts moving, what will it's acceleration be? Glass on glass: μs=0.94 μk=0.40

 

Example: Moving an Object Across the Floor

A 100 kg crate is sitting on the floor. The coefficients of friction between the crate and the floor are μs=0.8 and μk=0.6 If we pull horizontally, how much force would be needed to cause the crate to start moving? What happens if we pull on the crate with a 650 N force 30o ABOVE the horizontal? (Note: this is LESS force than we needed in the first part.) What happens if instead we push on the crate with a 1200 N force 30o BELOW the horizontal? (Note: this is MORE force than we needed in the first part.)

 

Object on Incline : Static Case
An object of some mass M is placed on an incline that makes an angle of θ relative to the horizontal.   As we increase the angle, eventually the object will start sliding down the incline. At what angle does that happen?

 

Object on Incline : Kinetic Case
An object of some mass M is sliding down an incline that makes an angle of θ relative to the horizontal. What does the acceleration ultimately depend on? At what angle will the object slide down the incline at a constant speed? (I.e. where a=0.)

 

Stopping Distance (horizontal surface)
An object of some mass M is initially moving at vo to the right on a flat, horizontal surface. The coefficient of kinetic friction between the object and the surface is μk How far will the object move before coming to a stop?

 

Jurassic Park 2 : Connected Objects with Friction
At one point in the movie, a dinosaur has pushed a trailer of mass 2000 kg over the edge of a cliff. It hangs there, connected by a cable to another trailer of mass 4000 kg which remains on the ground as shown in the figure. Let the coefficients of friction here (between the ground and the 4000 kg object) be: μs=0.8 μk=0.6
Verify that the present situation is stable (i.e. static friction is providing enough force to keep the trailers from sliding over the edge). The dinosaur is not happy with that and decides to push horizontally on the trailer. How much force does the dinosaur need to provide to overcome static friction and cause the trailers to start to move? If the dinosaur continues to push with the same amount of force, determine the acceleration present, and the tension in the connecting cable.