Friction, Forces, and Newton's Laws: Study Notes

Friction, Inclines, and Systems

Introduction to Forces and Free-Body Diagrams

Understanding the forces acting on objects is fundamental in physics. A free-body diagram is a visual tool used to represent all the forces acting on a single object, simplifying the analysis of its motion.

• Forces are interactions that can cause an object to accelerate. Common forces include gravity, normal force, friction, tension, and applied forces.

• Free-body diagrams help in systematically identifying and representing these forces as vectors.

Steps to Draw a Free-Body Diagram:

1. Identify all forces acting on the object.

2. Draw a coordinate system (axes), aligning with the problem's context (e.g., parallel to an incline).

3. Represent the object as a dot at the origin (particle model).

4. Draw and label vectors for each force, indicating their direction and type.

5. Draw and label the net force vector beside the diagram (not on the particle).

Example: For a skier being towed at constant speed up a slope, the free-body diagram includes gravity (downward), normal force (perpendicular to slope), friction (opposing motion), and the towing force (up the slope). If the speed is constant, the net force is zero, indicating equilibrium.

Friction: Static and Kinetic

Friction is a force that opposes the relative motion or attempted motion between two surfaces in contact. It arises due to microscopic irregularities on surfaces.

• Acts parallel to the contact surfaces and opposite to the direction of motion or impending motion.

• Depends on the nature and roughness of the surfaces.

Static Friction

Static friction prevents an object from starting to move. It adjusts to match the applied force up to a maximum value.

• Applies only when there is no relative motion between surfaces.

• Direction: Opposes the direction in which the object would move if friction were absent.

• Maximum static friction force is given by:

$f_{s,\text{max}} = \mu_s F_N$

• Where $\mu_s$ is the coefficient of static friction (dimensionless), and $F_N$ is the normal force.

• Typical values: Rubber on concrete ($\mu_s \approx 0.8$), ice on ice ($\mu_s \approx 0.003$).

Example: A woman pushes a box that does not move. The static friction force equals her push, up to the maximum value. If she pushes harder than $f_{s,\text{max}}$, the box will start to move.

Kinetic Friction

Kinetic friction acts when an object is sliding over a surface. It has a constant magnitude and always opposes the direction of motion.

• Applies only when there is relative motion between surfaces.

• Magnitude is given by:

$f_k = \mu_k F_N$

• Where $\mu_k$ is the coefficient of kinetic friction (typically less than $\mu_s$).

• Kinetic friction does not depend on the speed of sliding.

Example: Sliding a block along a bench top, the frictional force opposing the motion is $f_k$.

Forces in Free Fall: Weight, Drag, and Terminal Speed

Weight Force

The weight of an object is the gravitational force acting on it. It always acts vertically downward.

Calculated by:

$w = mg$

• Where $m$ is mass (kg), $g$ is acceleration due to gravity ($9.8\ \text{m/s}^2$).

Example: A 2 kg object has a weight of $w = 2 \times 9.8 = 19.6\ \text{N}$ downward.

Drag Force

Drag is a resistive force experienced by objects moving through a fluid (such as air or water). It increases with speed and depends on several factors:

• Density of the fluid ($\rho$)

• Speed of the object ($v$)

• Cross-sectional area facing the fluid ($A$)

• Shape of the object (streamlining reduces drag)

At low speeds, drag is often negligible, but at higher speeds, it becomes significant.

Terminal Speed

Terminal speed is the constant speed reached by a falling object when the upward drag force equals the downward weight, resulting in zero net force and zero acceleration.

• At terminal speed: $D = w$ and $a = 0$

• More massive objects (with the same shape and area) have higher terminal speeds.

• Terminal speed varies with shape and area, not just mass.

Table: Approximate Terminal Speeds for Various Objects

Object	Terminal Speed (m/s)
Fluffy feather	0.4
Sheet of paper	0.5
Snowflake	1
Parachutist	7
Sky diver (spread eagle)	58
Large rock	200
Peregrine falcon	90

Additional info: The drag force at high speeds can be modeled as $D = \frac{1}{2} C_d \rho A v^2$, where $C_d$ is the drag coefficient.

Newton's Third Law of Motion

Action-Reaction Pairs

Newton's Third Law of Motion states: For every action, there is an equal and opposite reaction. More precisely, if object A exerts a force on object B, then object B exerts a force of equal magnitude and opposite direction on object A, simultaneously.

• Forces always occur in pairs (interaction pairs).

• Each force in the pair acts on a different object.

• The effects of the forces depend on the masses of the objects (see Newton's Second Law).

Examples of Action-Reaction Pairs:

Action	Reaction
Tire pushes on road	Road pushes on tire
Rocket pushes on gas	Gas pushes on rocket
Man pulls on spring	Spring pulls on man
Earth pulls on ball	Ball pulls on Earth

Application: When a hammer strikes a nail, the nail exerts an equal and opposite force on the hammer. The resulting accelerations depend on the masses involved (Newton's Second Law: $a = F/m$).

Additional info: Although the forces are equal in magnitude, the resulting accelerations can be very different due to differences in mass (e.g., the Earth and a falling object).