Newton's Second Law of Motion in terms of acceleration

Newton's Second Law of Motion in Terms of Acceleration

1. Understanding Newton's Second Law

• If a net force $(\vec{F}_{\text{net}})$ acts on an object, it will accelerate in the direction of the net force.
• The acceleration is:
  • Directly proportional to the net force.
  • Inversely proportional to the mass of the object.
• Formula:

where: $\vec{F}_{\text{net}} = m\vec{a}$

• $\vec{F}_{\text{net}} =$ net force $(N)$
• $m$ = mass $(kg)$
• $\vec{a}$ = acceleration $(m/s²)$

2. Effects of a Net Force

If $\vec{F}_{\text{net}} \neq 0$, the object will:

• Start moving if initially at rest.
• Stop moving if force opposes motion.
• Speed up (accelerate) or slow down (decelerate).
• Change direction.

3. Graphical Representations

• Acceleration vs. Force $(\vec{a} \propto \vec{F}_{\text{net}})$ → Straight-line graph through the origin.
• Acceleration vs. Mass $(\vec{a} \propto \frac{1}{m})$ → Hyperbolic graph (as mass increases, acceleration decreases).

5. Key Takeaways

• Larger force = greater acceleration.
• Larger mass = smaller acceleration.
• Always resolve forces into components when dealing with inclined planes.