Free fall
Motion & Kinematics - OCR A-Level Physics
Key Definition
Free fall
Motion under the influence of gravity alone, with no other forces acting. The only acceleration is g = 9.81 $m s^{-2}$ directed downwards.
Motion under the influence of gravity alone, with no other forces acting. The only acceleration is g = 9.81 $m s^{-2}$ directed downwards.
- In free fallMotion under gravity alone, with no other forces acting. All objects in free fall near Earth's surface have the same acceleration, g = 9.81 m s⁻²., all objects accelerate at the same rate regardless of mass (in the absence of air resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohms (Ω).)
- g = 9.81 $m s^{-2}$ near the Earth's surface, directed vertically downwards
- When using SUVAT for vertical motion, choose a sign convention (e.g. $upwards = positive)$ and be consistent throughout
- An object thrown upwards decelerates at g; at the highest point v = 0; it then accelerates downwards at g
- The time to rise to the highest point equals the time to fall back to the launch height (ignoring air resistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential difference to current. Measured in ohms (Ω).)
Common Mistake
MEDIUM
Students often: Don't forget assign a negative sign to g when taking upward as positive, leading to wrong answers for objects thrown upwards.
Instead: If upward is positive, then a = -9.81 $m s^{-2}$ for all free-fall problems. If downward is positive, a = +9.81 $m s^{-2}$. State your convention clearly.
Instead: If upward is positive, then a = -9.81 $m s^{-2}$ for all free-fall problems. If downward is positive, a = +9.81 $m s^{-2}$. State your convention clearly.
Worked Example [3 marks]
A stone is dropped from rest from a bridge 45 m above a river. Calculate the time taken to reach the water and the speed on impact. Use g = 9.81 $m s^{-2}$.
Show Solution
1
Known
$s = 45 \text{ m}, u = 0, a = 9.81 \text{ m s}^{-2}. Use s = ut + \frac{1}{2}at^{2}: 45 = 0 + \frac{1}{2}(9.81)t^{2}$
[1]2
$t^{2} = \frac{2 \times 45}{9.81} = 9.174 \Rightarrow t = 3.03 \text{ s} \approx 3.0 \text{ s}$
[1]3
$Use v = u + at: v = 0 + 9.81 \times 3.03 = 29.7 \text{ m s}^{-1} \approx 30 \text{ m s}^{-1}$
[1]Answer
Time = 3.0 s; speed on impact = 30 $m s^{-1}$
- To measure g experimentally: use an electromagnet and trapdoor timerAn apparatus for measuring free-fall time: an electromagnet releases a ball and a trapdoor at the bottom stops a timer on impact. to drop a steel ball from a known height h, measure fall time t, then $g = 2s / t^{2}$
- Plot s against $t^{2}$; the gradient = g/2, giving a more reliable value than a single measurement
- Alternative: use light gatesDevices that detect when an object passes through, used to measure speed and acceleration by timing intervals. to measure velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹. at two points with known separation, then use $v^{2}$ = $u^{2}$ + 2as
Examiner Tips and Tricks
- In practical questions about measuring g, always describe the graph you would plot.
- Plotting s against \(t^{2}\) gives a straight line through the origin with gradient g/2.
- This is far more reliable than a single measurement.