Chapter 5 Notes: Force and Motion

5.1 Force

• A force is a vector representing a push or pull.

• Every force has an agent (specific identifiable cause).

• Objects cannot exert forces on themselves.

• Contact forces act through touching.

• Long-range forces act without physical contact (e.g., gravitational, electric, and magnetic forces).

• Net force is the vector sum of all forces acting on an object: $\vec{F}<em>{net} \equiv \sum</em>{i=1}^{N} \vec{F}<em>i = \vec{F}</em>1 + \vec{F}<em>2 + \cdots + \vec{F}</em>N$

5.2 A Short Catalog of Forces

• Gravity:

  • Earth exerts gravitational force on objects with mass.

  • Points vertically downward with magnitude $mg$.

  • Long-range force.

• Tension:

  • Force exerted by a string, rope, or wire when it pulls on an object.

  • Direction is along the string or rope.

• Spring Force:

  • Spring force, $\vec{F}_{Sp}$, is a push (when compressed) or a pull (when stretched), by a spring.

• Normal Force:

  • Exerted by a surface against an object, perpendicular to the surface.

  • Symbol: $n$.

  • Not always upward.

• Friction:

  • Parallel to the surface.

  • Kinetic friction ($f_k$): opposes motion when an object slides across a surface.

  • Static friction ($f_s$): prevents motion relative to the surface.

• Drag:

  • Resistive force of a fluid, opposite to the object’s motion relative to the fluid ($\vec{F}_{drag}$).

• Thrust:

  • Contact force exerted by exhaust gases on a jet or rocket, opposite to the direction of expelled gas ($\vec{F}_{thrust}$).

5.3 Identifying Forces

• Key Questions:

  1. Is Earth (or a planet-sized object) nearby? If yes, include gravitational force.

  2. What is touching the object of interest? Contact forces.

• Labeling Forces:

  • Type of force, object exerting the force, object on which the force is exerted.

  • Example: Tension exerted by a rope on a block is $\vec{T}_{rb}$.

5.4 What Do Forces Do? (Newton’s Laws of Motion)

• Newton’s First Law:

  • Object at rest stays at rest; object in motion stays in motion with constant velocity unless net force is non-zero.

  • Inertial reference frame: Newton’s first law is valid; accelerating frames are non-inertial.

• Newton’s Second Law:

  • $\vec{a} = \frac{\vec{F}_{net}}{m}$

  • $\vec{F}<em>{net} = \vec{F}</em>1 + \vec{F}<em>2 + \vec{F}</em>3 + \cdots$

• Newton’s Third Law:

  • For every action, there is an equal but opposite reaction.

  • $\vec{F}<em>{AB} = -\vec{F}</em>{BA}$

Force Unit and Inertia

• Inertia: Resistance to change in velocity.

• Inertial mass ($m$ in $F = ma$): Measure of resistance to change in motion.

• Equivalence principle: Inertial mass = gravitational mass.

• Force measured in Newtons: 1 N = 1 kg * m/s^2.

5.7 Free-Body Diagrams

• Represents object as a particle, showing all forces acting on it.