When a ball is dropped from a height, it accelerates downwards under the influence of gravity. The ball gains speed as it falls. The force causing this acceleration and increase in speed is the gravitational force.
When objects fall towards the Earth, they accelerate downwards. This means their velocity or speed increases as they fall. What causes objects to accelerate downwards when dropped? The answer lies in understanding the forces acting on a falling object.
There are four fundamental forces in nature – gravitation, electromagnetism, strong nuclear and weak nuclear forces. Of these, the gravitational force is responsible for causing objects to accelerate downwards when dropped from a height.
The gravitational force is an attractive force between all objects that possess mass. The Earth’s large mass exerts an attractive gravitational pull on all objects towards its center. When we drop an object like a ball, this gravitational force accelerates it downwards.
As the ball falls under gravity, its speed increases until it hits the ground. The acceleration and increase in speed depends directly on the gravitational force. A larger gravitational force causes a larger acceleration and increase in speed.
Understanding the gravitational force helps explain the motion of objects when dropped. It reveals why a ball gains speed when dropped from a height. The rest of this article will further analyze this concept in detail.
The Gravitational Force
Gravity or the gravitational force is one of the four fundamental interactions in nature. It is an attractive force that acts between all objects possessing mass.
The gravitational force between two objects depends on:
- Their masses – heavier objects exert a greater force
- The distance between them – gravitational force decreases with increasing separation
For two objects with masses m1 and m2 separated by a distance r, the gravitational force (F) between them is given by Newton’s law of gravitation:
F = Gm1m2/r2
Where G is the universal gravitational constant.
The Earth has a very large mass (5.97 x 1024 kg). Therefore, it exerts a significant gravitational force on all objects. The gravitational acceleration on Earth is denoted by g and has a value of 9.8 m/s2. This acceleration is independent of an object’s mass.
Gravitational Force and Falling Objects
When an object is dropped from a height near the Earth’s surface, the main force acting on it is gravity. Newton’s second law applies a relationship between mass, acceleration and force:
F = ma
Where F is the net force, m is the mass and a is the acceleration.
As the gravitational force acts downward, the object accelerates downwards. The acceleration equals g or 9.8 m/s2 independent of mass. Objects fall with the same acceleration on Earth.
However, the gravitational force does depend on an object’s mass. Newton’s second law gives:
Fgravity = mg
Where Fgravity is weight or the gravitational force. Since g is constant, heavier objects experience a larger gravitational force or weight.
However, the key point is that when dropped, all objects fall with the same acceleration g due to gravity. Gravity acts as the force causing a falling object to accelerate downwards.
Falling Objects Gain Speed
Now that we know gravity causes a dropped object to accelerate downwards at g, we can analyze how this results in a gain in speed.
By definition, acceleration is the rate of change of velocity. Velocity is speed in a given direction. As gravity causes a downward acceleration g, the object’s vertical velocity or speed increases as it falls.
Using equations of motion, the increase in vertical velocity v with time t can be calculated as:
v = gt
Where v is vertical velocity, g is gravitational acceleration (9.8 m/s2) and t is time.
This shows that as time passes while the object falls, its vertical velocity or speed increases linearly. The increase is proportional to the gravitational acceleration g.
After 1 second of falling, velocity increases by 9.8 m/s. After 2 seconds, it increases by 19.6 m/s and so on. The velocity-time graph for a freely falling object shows this linear increase:
| Time t (s) | Velocity v (m/s) |
|---|---|
| 0 | 0 |
| 1 | 9.8 |
| 2 | 19.6 |
| 3 | 29.4 |
| 4 | 39.2 |
| 5 | 49.0 |
This table and graph show how velocity increases linearly with time as the object accelerates under gravity. The gravitational force is responsible for this downward acceleration g, which results in the gain in speed.
Factors Affecting Speed Gain
We can summarize the factors that determine the increase in speed of a falling object:
- Gravitational acceleration (g) – greater on larger planets like Jupiter. On the moon g is 1.6 m/s2.
- Time (t) – speed increases with time of fall.
- Height (h) – falling from greater heights allows the object more time to accelerate and gain speed.
- Air resistance – reduces acceleration and speed gain, especially for light objects.
- Mass (m) – does not affect acceleration or speed gain unless considering air resistance.
Gravity causes the downward acceleration g. Time and height influence the time available for the acceleration to increase speed. Air resistance opposes motion for light objects. Mass does not change the acceleration on Earth.
For a given height and object, gravity provides the impetus for downward acceleration and the resultant increase in velocity.
Effect of Height
Height influences the time of fall and therefore, the speed gained. An object dropped from a greater height has more time to accelerate under gravity and gains greater speed.
Velocity after falling height h is given by:
v = sqrt(2gh)
Where v is final velocity, g is gravitational acceleration and h is height.
This shows that final velocity increases with the square root of height h. Doubling the height quadruples the final velocity. The following table illustrates this:
| Height h (m) | Time t (s) | Final velocity v (m/s) |
|---|---|---|
| 10 | 1.4 | 14 |
| 20 | 2.0 | 20 |
| 40 | 2.8 | 28 |
This shows how doubling the height from 10 m to 20 m increases the final velocity from 14 m/s to 20 m/s. Thus, greater heights allow for larger speed gains.
Effect of Mass
Mass does not affect the acceleration due to gravity or the speed gain, provided air resistance is negligible. All objects on Earth fall with the same acceleration g.
However, mass does determine the gravitational force as per Newton’s law of gravitation. The gravitational force is proportional to the object’s mass. Therefore, heavier objects experience a larger gravitational force, even though they do not accelerate faster.
For example, a 1 kg ball and a 5 kg ball dropped from the same height hit the ground at the same time. But the gravitational force on the 5 kg ball is larger. The accelerations and velocity gains are identical.
When air resistance becomes significant, such as for light objects like feathers, the downward acceleration is reduced. This decreases the speed gain compared to heavier objects.
Applications
Understanding gravity and free fall motion has many useful applications:
Sports Science
The motion of balls in sports like tennis, cricket and basketball involves parabolic trajectories influenced by gravity. Sports scientists study free fall motion to understand ball trajectories.
For example, the height and speed of a basketball shot determines the time of flight and accuracy. This depends on the velocity gain caused by gravity during the upwards and downwards motion.
Skydiving
Skydivers experience prolonged free fall before opening their parachutes. The speed gain during the free fall depends directly on the gravitational force. Terminal velocity is when air resistance equals the gravitational force.
Understanding gravitational acceleration allows skydivers to estimate their velocity for safe parachute opening.
Piloting Aircraft
Pilots must account for gravity when estimating descent rates and pitch angles. The trajectory of an aircraft under gravity depends on its vertical speed. Knowledge of free fall motion assists pilots in smooth landings.
Space Exploration
NASA uses gravity assists to propel spacecraft on interplanetary trajectories. By harnessing a planet’s gravitational force, spacecraft can gain speed. Gravitational acceleration provides an effective means of space travel.
Conclusion
When an object is dropped from a height, the dominant force acting on it is gravity. Gravity causes a downward acceleration g, leading to a gain in vertical velocity and speed as the object falls.
The gravitational force depends on mass, while the acceleration g is independent of mass. Heavier objects experience larger gravitational forces. Time, height and air resistance also impact the speed gain during free fall.
Understanding gravitational motion helps predict trajectories in sports, skydiving and space travel. Gravity acts as the force that causes a ball dropped from a height to accelerate downwards and gain speed.