Free fall motion is all about objects moving under gravity's influence alone. It's a key concept in physics, showing how things fall without air resistance or other forces getting in the way.
The math behind free fall is surprisingly simple. A few equations describe how objects move, speed up, and change position over time. Understanding these basics helps solve all sorts of falling object problems.
Free Fall Motion
Concept of free fall
- Objects move solely under gravity's influence without air resistance or other forces
- Acceleration remains constant at Earth's surface ($9.8 , m/s^2$) always pointing downward
- Motion characteristics independent of mass, velocity increases over time, projectiles follow parabolic paths
Equations for free fall motion
- Kinematic equations describe motion: $v = v_0 + gt$, $y = y_0 + v_0t + \frac{1}{2}gt^2$, $v^2 = v_0^2 + 2g(y - y_0)$
- Variables represent final velocity $(v)$, initial velocity $(v_0)$, final position $(y)$, initial position $(y_0)$, time $(t)$
- Upward direction considered positive, downward negative for consistent problem-solving
Graphical analysis of free fall
- Position-time graphs show parabolic shape, concave downward, vertex at maximum height
- Velocity-time graphs display linear relationship, negative slope $-g$, y-intercept as initial velocity
- Acceleration-time graphs appear as horizontal line at $-g$, indicating constant acceleration
- Graph relationships: position-time slope equals velocity, velocity-time area equals displacement, velocity-time slope equals acceleration
Vertical motion problems
- Objects thrown upward: positive initial velocity, reach maximum height when velocity becomes zero
- Maximum height calculations: time to reach $t_{max} = \frac{v_0}{g}$, height $h_{max} = \frac{v_0^2}{2g}$
- Dropped objects: zero initial velocity, time to ground $t = \sqrt{\frac{2h}{g}}$, final velocity $v = \sqrt{2gh}$
- Vertical motion symmetry: upward time equals downward time, launch speed matches impact speed (ignoring air resistance)
- Problem-solving approach: identify knowns/unknowns, select appropriate equations, solve, verify units and reasonableness