Mr. Rogers AP Physics C Study Guide  --  Friction

Unit Plan Practice Test Study Guide

Mathematical models

The 3 Equations of Friction

Static friction (Fs): With static friction there is no sliding, the friction force is exactly equal to the parallel force.

Transition point: At the transition point, the equation shown at right can calculate the highest possible static friction and this is directly proportional to normal force, but only at the transition point. Otherwise, static friction is determined solely by the parallel force.

Dynamic friction (Fd): When sliding occurs, the friction force remains constant. Typically dynamic friction is lower than static but never higher. Dynamic or sliding friction is influenced only by the normal force.

Friction Force vs. Parallel Force

Note: there are three distinctly different equations. According to all three equations, contact area has no influence on friction.


Key Principles

Static vs. dynamic friction: Static friction is typically greater than dynamic friction.


Acceleration in Cars: Static friction is the force that makes a car accelerate.
Effect of Contact Area: There is none. According to our models of friction, increasing or decreasing the contact area has no influence on friction. The model does assume no deflection in the surfaces and no materials failures. For example, park a car in mud and the friction conditions are rapidly altered as the surface deflects beneath the tires.


Walking: Static friction is the force that propels a person forward when walking.
Tug of Wars: The team with the highest static friction force has the advantage in tug of wars. These contests are not won by pulling harder.
Effect of 4WD: Two wheel drive (2WD) cars have less traction than four wheel drive (4WD) because in 2WD only part of the car's normal force acts on the driven wheels. Hence, the friction force acting on the car is lower than 4WD where all the normal force acts on the driven wheels.  

Problem Solving Tips: Newton's Laws

FBD: When working problems with friction always draw a free body diagram. usually these problems will end up as F = ma or Newton's second law problems. (Remember static problems are simply a special case of F = ma problems in which a = 0.)


Direction of Friction Force: The 3 mathematical models for friction can calculate only the magnitude of the friction force. They are incapable of giving the correct sign indicating the direction of the friction force. You will have to judge the direction based on intuition and on the free body diagram.


Normal Force: Remember that the normal force is not always equal to the weight force (mg). This is especially true on slopes where the normal component of the weight force often is equal in magnitude to the normal force or when a pushing/pulling force is applied at an angle to the surface where sliding might occur


Air Foils: The normal force of a race car can be increased using air foils without increasing a vehicle's mass. In this situation the airfoil is designed to create a downward rather than upward lift force. This downward force increases normal force which increases the maximum possible static friction.  The effect: the race car will have a higher maximum acceleration and higher maximum speed in turns. Otherwise these parameters are fixed by the static COF and gravity field constant "g".


Minimum Stopping Distance: The minimum stopping distance of vehicles is independent of mass according to our model of friction. As mentioned earlier, the model assumes no deformation at surfaces and no material failures.


Pulling vs. pushing: Pulling an object using an upward angle will reduce the normal force and friction that opposes motion.

Pushing an object using a downward angle will increase both the normal force and the friction that opposes motion.

Pulling as described above will result in a higher acceleration than pushing assuming that everything else is equal.

Example Problems

Max Static Friction Problems

Sliding Friction Problems

Highest slope a 4WD Truck Can Climb
Angle = arctan ms

Note: mass is not a factor

Acceleration on a Slope
Highest Incline a Truck Can Rest On (Assume the brakes areapplied to all 4 wheels.)
Angle = arctan ms

Note: mass is not a factor

Sliding with Pushing vs. Pulling: (see above)
Maximum Speed of a 4WD Truck on a Circular Track
Note: (max centripetal acceleration) = msg
Where: ms = static COF between tires and road

Note: mass is not a factor

Sliding With Stacked Blocks: Block 1 sits atop block 2. A force F = 2.5 M1 g is applied to block 1. Find the acceleration of both blocks. COF conditions given. M2 = 1/2 M1.
Maximum Linear Acceleration of a 4WD Truck
Note: (max linear acceleration) = msg
Where: ms = static COF between tires and road

Note: mass is not a factor

Maximum Acceleration Without Losing Cargo
Note: (max acceleration) = msg
Where: ms = static COF between cargo and truck

Note: mass is not a factor

Minimum Stopping Distance
Note: (max stopping acceleration) = msg
Where: ms = static COF between tires and road

Note: mass is not a factor




Static Friction Static COF = ms
Dynamic Friction Dynamic COF = md Sliding Friction (same as dynamic)

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