Free Fall & Measuring g

• In a vacuum a feather and a hammer land together. With no air, mass makes no difference to the acceleration.
• “Dropped” means $u = 0$. The equations then shorten to $v = gt$, $s = \tfrac{1}{2}gt^2$ and $v^2 = 2gs$.

vacuum

Free fall is SUVAT with $a = g = 9.81 \text{ m s}^{-2}$ and, if the object is dropped, $u = 0$. No new equations are needed.

• The syllabus asks you to describe an experiment that measures $g$ from a falling object. The standard set-up uses an electromagnet, a steel ball and an electronic timer.

1. An electromagnet holds a steel ball at a measured height $h$ above a trapdoor.
2. Switching the current off releases the ball and starts the timer at the same instant.
3. The ball hits the trapdoor, which stops the timer.
4. Record $h$ and $t$, then repeat for several heights.

electromagnetballtrapdoortimer

• The ball is dropped, so $h = \tfrac{1}{2}gt^2$. Plotting $h$ against $t^2$ (not against $t$) turns this into a straight line through the origin with gradient $g/2$.
• So $g = 2 \times \text{gradient}$. Using a graph of many readings, instead of one reading, reduces the effect of random error, the idea from lesson 1.5.