Surface Forces Surface Forces

October 4, 2015

I Two components of contact force between objects: 1. tangential k, like friction These 2 types of surface force are referred to as 2. and normal ⊥ friction Force – a sideways force that resists the direction of intended travel Normal Force – the outward force that we have already studied

I Types of friction Onset of Friction

There are also 2 types of friction:

static friction fs, which adjusts to applied force

kinetic friction fk, which has ﬁxed relation to F~ N

Applied Force

kinetic friction Friction Coeﬃcients

I kinetic friction is a simple function of normal force

fk = µkN fk is the kinetic friction force (lower case) µk is a fraction dependent on materials N is the magnitude of normal force ~f is opposite direction of intended travel Solution: Solution: 7.4 N 0.245

Solution:

2 I Fnet =(10 kg)(2.0 m/s ) = 20 N.

I For a frictionless incline: m m g sin θ = (10 kg) (9.8 ) sin 37◦ s2 = 59 N .

I ∴ frictional force is 39 N.

Active Learning Exercise Active Learning Exercise

Problem: Kinetic Friction Problem: Kinetic Friction A person is pushing a 2.0 kg box along a floor with a force of 10 N A 25.0 kg box rests on a horizontal surface. A at an angle of 30◦ below the horizontal force of 75.0 N is required to set the horizontal. (The box is moving.) box in motion. Once the box is in motion, a The coefficient of kinetic friction horizontal force of 60.0 N is required to keep the between the box and the floor is box in motion at constant speed. What is the 0.30. What is the force of friction? coefficient of kinetic friction?

Active Learning Exercise static friction

Problem: Review Problem I static friction is a function of applied force A 10 kg block, released from rest ◦ on a 37 inclined plane, slides I down the plane – gaining speed at a rate of 2.0 m/s2. The frictional ~ force on the block is what? fs = min Fapplied, µsN

≤ µsN

µs is the static coeﬃcient of friction, which is (always?) greater than µk ~f is opposite direction of intended travel Solution: 32.3 N

Friction Coeﬃcients Counterintuition(?!)

Friction does NOT depend on the following:

1. velocity of motion

2. surface area of contact

I That is strange and counterintuitive!

Active Learning Exercise 6.4 – Best Physics Lecture Ever Problem: Static Friction Apollo 15 moon walk, Commander David Scott (1971): www.youtube.com/watch?v=5C5 dOEyAfk A block of mass m1 = 1.00 kg sits on another block with mass m2 = 10.0 kg. The bottom block slides without friction on the surface beneath it, but there is friction between the blocks, with µs = 0.300 and µk = 0.200. What is the greatest horizontal force Fmax that can be applied to the lower block without causing the upper block to slip? Drag Force Active Learning Exercise The subject of drag force is good review of Problem: Drag Force F.B.D.’s. There is one equation: A 86 kg object falls from rest. The drag force is 2 Drag Equation Fdrag = (0.27kg/m)v . What is its terminal speed?

Fdrag ~ 1 2 |D| = CρAv x 2 86 kg |D~ | magnitude of ρ air density the drag force A cross section C drag coeﬃcient v airspeed. mg v y

Some terminal velocities Acceleration in a circle

I We previously deﬁned the acceleration

v2 a = directed inward centripetal r for motion (1) in a circle, and (2) at uniform speed.

I Let’s apply that knowledge to two problems: 1. Motion on a ﬂat track. 2. Motion on a banked track. Solution:

ANS: µs = .90

Active Learning Exercise Active Learning Exercise Now we analyze the problem on a banked track Problem: Static Coefficient of friction for Problem: Banked Track Tires What is the free body diagram for this system? A race car moves through a turn at a constant speed of 29 m/s. The road is dry and flat (no banking) and the radius of the turn is 95 m. What minimum coefficient of static friction µs is required for a safe turn?

Label θ in your force diagram.

Summary of Eqns. – Ch.6 Dissipative Forces

I The force that opposes relative motion: f ≤ µN .

I Can be classifed as kinetic or static (µk or µs).

I Kinetic case: fk is equal to µkN.

I Static case: fs matches applied force up to µsN.

I Related Concept: Drag Force 1 D = Cρ Av2 2 air