Acceleration Due to Gravity – A Level Mathematics B (MEI) OCR Revision

Understanding Acceleration Due to Gravity

Acceleration due to gravity is a specific case of acceleration, occurring when an object is falling freely under the effect of gravity.
It is symbolised by the letter g, and near the surface of the Earth, its approximate value is 9.8 m/s².
The acceleration due to gravity is directed downwards, towards the centre of the Earth, regardless of the initial direction of movement.
Acceleration due to gravity is a constant. This means that, in the absence of other forces (like air resistance), all objects near the surface of the earth fall towards the centre with the same acceleration.
This is why, famously, Galileo demonstrated that heavy and light objects fall at the same rate.

The equations of motion, established by Sir Isaac Newton, are useful tools for working with acceleration due to gravity.
Typically, when it comes to free-falling objects under gravity, the initial velocity (u) is often 0 (unless an initial upward or downward velocity is given), the acceleration (a) is -9.8 m/s² on Earth’s surface (negative indicating downward), and time (t) is whatever the context of the problem provides.
Finally, the change in vertical position (s) can be calculated using the equation: s = ut + 0.5at².

Note, however, that while the gravitational pull from the earth is constant, the actual acceleration due to gravity can vary with certain factors.
Altitude: The higher from the Earth’s surface an object is, the lesser the acceleration due to gravity it experiences. This is because gravity decreases with distance from the Earth’s centre.
Latitude: Earth is not a perfect sphere but an oblate spheroid, bulging at the equator, thus objects at the poles are closer to the centre and experience a slightly higher gravitational pull.
These factors only cause significant changes at extremely high altitudes or precise measurements; for most A Level problems you would likely use the approximation of 9.8 m/s².

Realistically, the acceleration of a falling object isn’t constant because of air resistance.
Air resistance is a force that acts against the motion of an object through air, and it increases as the object’s speed increases.
When taking into account air resistance, the object will initially accelerate due to gravity, but as its speed increases the air resistance will increase until it is equal to the weight of the object. At this point, the object will stop accelerating and continue to fall at a constant speed known as the terminal velocity.
For illustrative purposes and simplicity, when tackling exam problems, air resistance is often neglected thereby assuming objects move in a vacuum, unless stated otherwise.

Acceleration due to gravity has numerous real-life applications and plays a crucial role in physics and engineering.
From predicting the trajectory of projectiles, to calculating the orbital paths in space missions, understanding the principles of acceleration due to gravity is paramount.
It also plays a significant role in designing safety equipment like airbags and roller coasters, where an understanding of how gravity affects motion is essential.