Newtonian mechanics

Free fall

Neglecting air resistance, an object falling near Earth has gravitational acceleration g ≈ 9.8 m/s², independent of its mass.

Drop two objects of different masses together in a vacuum: they fall alike. In air, drag can make a light or broad object fall more slowly.

v = gt, h = ½gt²

Definition: Quantities and model

These equations assume release from rest, downward chosen positive, and negligible air resistance. Near Earth’s surface g ≈ 9.8 m/s² (often rounded to 10 m/s²).

Use the simulation to observe motion and read quantitative values as time evolves.

Reading the model

Neglecting air resistance, an object falling near Earth has gravitational acceleration g ≈ 9.8 m/s², independent of its mass.

Example: Worked example

An object is dropped from rest for 2 s. With g = 9.8 m/s², h = ½×9.8×2² = 19.6 m and its downward velocity is 19.6 m/s.

Solution

An object is dropped from rest for 2 s. With g = 9.8 m/s², h = ½×9.8×2² = 19.6 m and its downward velocity is 19.6 m/s.

Near Earth, choose downward as positive: a released object has $v_0=0$ , $a=g$ , and $s= rac12gt^2$ . With $g≈10 m/s²$ , after 2 s it has fallen about 20 m and reaches 20 m/s. A sheet of paper falls more slowly than a marble in air because drag is large compared with its weight; in a vacuum tube they have the same fall acceleration.

Example: Fall time from a low balcony

An object is dropped from rest with no drag. How far does it fall in 1.5 s? Take g=10 m/s².

Solution

s=½gt²=½×10×1.5²=11.25 m.

Free-fall equations assume constant $g$ , a good approximation over heights small compared with Earth’s size. Fall time depends on initial height, while mass does not appear in the equation. In an experiment, repeating timing measurements helps reduce stopwatch error.

Quick check

Which quantity or statement is correct for this motion?

Which statement correctly describes the motion in this topic?

References

Young, Freedman (2019). University Physics
Halliday, Resnick, Walker (2014). Fundamentals of Physics