Free Fall – the motion of an object where the only force acting on it is its weight.
The weight acting on an object can be calculated using the following equation:
Where W is the weight, m is the mass of the object and g is the acceleration of the object caused by gravity.
The value of g on Earth is approximately 9.81ms-2 (3s.f.). Any object in free fall on Earth experiences this acceleration, which remains constant and acts vertically downwards.
The Acceleration due to Free Fall
The acceleration of an object in free fall does NOT depend on the mass of the object.
To prove that the acceleration of an object in free fall is the same for all objects regardless of mass Galileo preformed an experiment. He, or one of his students, dropped two balls of different mass from the top of the Leaning Tower of Pisa.
Both balls hit the ground at virtually the same time (the slight difference was due to factors like air resistance), hence proving that all objects in free fall have the same acceleration.
This means that if we neglect air resistance two objects of different masses will fall at the same speed when dropped.
Dropping and Throwing
When an object is dropped it has zero initial velocity. It is then in free fall, with constant acceleration, until it reaches the ground.
Dropped objects aren’t the only objects to experience the acceleration due to gravity. If an object is thrown downwards, giving it an initial velocity, it still experiences the acceleration due to gravity, g.
The same applies to objects thrown upwards, they still have constant acceleration vertically downwards throughout their journey. Just before the object begins to fall once it has reached its maximum height the velocity is 0 ms-1 but it’s acceleration is still equal to g. This motion can be represented with a velocity-time graph:
- The object moving upwards is taken as the positive direction, hence the positive velocity on the graph
- The object slows down until it reaches it’s maximum height at 0 ms-1
- After reaching it’s maximum height the object falls back down to Earth (the velocity is negative)
- As the acceleration is constant the gradient of the graph is constant and equal to g
IMPORTANT: the final velocity of an object is NOT zero. It is the moment just before it hits the ground, as when it has hit the ground it is no longer in free fall.
Points to Note for Answering Questions
As the acceleration of free fall is constant, many questions use SUVAT equations to get to the answer.
Air resistance generally means that most objects falling aren’t actually in free fall. In physics questions, however, we quite often assume that there is no air resistance to make the calculations easier.
As acceleration is a vector quantity it is important to define direction. This can be done by giving the values positive or negative signs. Generally the upwards direction is given positive values and the downwards direction is given negative values.
However, if you are answering a question you can define these directions yourself, you just need to be consistent. You could do this by drawing a diagram and putting a little arrow with a positive sign in the direction you are defining as positive.
Worked Examples
In all of the questions below it is assumed that g = 9.81ms-2 and the upwards direction is positive.
These questions all require knowledge of SUVAT equations.
Example 1
A rock is dropped from the top of a cliff and hits the ground 5s later. Calculate the height of the cliff and the final velocity of the rock. Ignore the effects of air resistance.
Example 2
A student drops a book out of a window. The book hit’s the ground with a speed of 5ms-1. How high is the window? Ignore the effects of air resistance.
Example 3
A tennis ball is dropped from a height of 15m. 0.5s later another tennis ball is thrown to the floor from the same height with an initial velocity of v ms-1. The balls hit the floor at the same time. What is the initial velocity of the second ball? Ignore the effects of air resistance.
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