11.3 - Gravitational Acceleration and Free Fall

Gravitational Acceleration

• Gravitational force pulls objects towards the centre of Earth.
• Gravitational acceleration, $g$ is the acceleration of an object due to gravitational force.
• Near Earth’s surface, $g=10{\text{m s}}^{-2}$, directed towards the centre of Earth.
• Ignoring air resistance, a falling object’s velocity increases by $10{\text{m s}}^{-1}$ every second.
• An object moving upwards slows down because gravitational acceleration acts downwards.

Experiment 11.1: Determining Gravitational Acceleration

Aim: Determine gravitational acceleration, $g$, using a ticker timer.

Problem statement: What is the value of gravitational acceleration, $g$?

Hypothesis: Gravitational acceleration, $g$, is $10{\text{m s}}^{-2}$.

Variables:

• Manipulated: mass of the weight.
• Responding: gravitational acceleration, $g$.
• Constant: height from which the weight is released.

Materials and apparatus: ticker tape, cellophane tape, ticker timer, weights, G-clamp, $12\text{V}$ alternating current supply, bench, soft board, retort stand and clamp.

1. Clamp the ticker timer vertically to a retort stand placed on a bench; place a soft board below the falling weight.
2. Pass a $1\text{m}$ ticker tape through the ticker timer and attach a $50\text{g}$ weight to its end.
3. Switch on the ticker timer and release the weight.
4. From the tape, calculate $u=\frac{x_1}{0.02\text{s}}$ and $v=\frac{x_2}{0.02\text{s}}$ for two selected intervals separated by five ticks.
5. Use $t=5(0.02)=0.10\text{s}$ and calculate $g=\frac{v-u}{t}$; convert the result from ${\text{cm s}}^{-2}$ to ${\text{m s}}^{-2}$.
6. Repeat with $100\text{g}$, $150\text{g}$, $200\text{g}$ and $250\text{g}$ weights.

Conclusion: Near Earth’s surface, $g=10{\text{m s}}^{-2}$ and is the same for different masses.

Free Fall and Its Motion Graphs

• Free fall is the motion of a body influenced only by gravitational force.
• In free fall, no other force, including air resistance, acts on the object.
• Objects of different masses fall with the same gravitational acceleration in a vacuum.
• Objects released simultaneously from the same height in a vacuum reach the base at the same time.
• In air, an object is in non-free fall because air resistance acts against its motion.
• Size and shape affect air resistance; a feather or piece of paper falls more slowly than a compact object in air.

For an object released from rest:

• Initial velocity, $u=0{\text{m s}}^{-1}$.
• Its velocity-time graph is a straight line with a uniform positive gradient when downward is positive; gradient = $g$.
• Its displacement-time graph becomes progressively steeper because its velocity increases.

For an object thrown vertically upwards:

• Velocity decreases uniformly during ascent and becomes zero momentarily at maximum height.
• Its velocity-time graph has a uniform negative gradient.
• Its displacement-time graph becomes progressively less steep and reaches zero gradient at maximum displacement.

Experiment 11.2: Free Fall and Non-Free Fall

Aim: Study the time taken by an object in free fall and non-free fall.

Problem statement: Is the time taken by an object in free fall the same as that taken by an object in non-free fall to reach Earth’s surface?

Hypothesis: An object in free fall takes a shorter time to reach the surface than an object in non-free fall.

Variables:

• Manipulated: presence of air.
• Responding: time taken for the object to fall onto the rubber stopper.
• Constant: height of the object.

Material and apparatus: pieces of paper, transparent cylinder, rubber stopper and vacuum pump.

1. Set up the apparatus and insert pieces of paper into the transparent cylinder.
2. Seal its open end tightly with the rubber stopper and connect the cylinder to the vacuum pump.
3. Quickly invert the cylinder and record the time for the paper to reach the stopper when air is present.
4. Pump the air out and repeat the drop from the same height.

Observation: the paper falls faster in the vacuum than in air.

Conclusion: air resistance makes non-free-falling objects take longer; in a vacuum, only gravitational force acts.

• Galileo Galilei released two spheres of different masses simultaneously from the Leaning Tower of Pisa and found that they took almost the same time to reach the ground.

Activity 11.5: Parachute STEM Project

• Problem: food and medical supplies dropped during severe floods may be damaged because they strike the ground at high velocity.
• Principle: a parachute increases air resistance and reduces the velocity of the falling load.
• Design and build a parachute by investigating canopy size, canopy material, string length or number of strings.
• Keep the other factors constant and present the resulting design.