3.12:
Free-falling Bodies: Example
Recall that when an object falls towards the ground and is only influenced by gravity, it is said to be in free-fall. Under the earth's gravity, an object falls with constant acceleration, known as acceleration due to gravity.
The kinematic equations for constant acceleration are used to solve the problems of freely falling bodies.
For example, a stone is freely dropped from the top of a cliff into a river. What will be its position and velocity after 5 seconds?
The known quantities are the initial position, the initial velocity, the acceleration due to gravity, and time.
Considering the vertical coordinate of the y-axis, the cliff top is the origin, and the upward direction is negative. The unknown quantities are the position and velocity of the stone after 5 seconds.
Substituting the known values in the kinematic equations gives 122.5 meters as the distance traveled and 49 meters per second as the velocity of the stone.
3.12:
Free-falling Bodies: Example
An object falling without any air resistance under the influence of gravitational force is said to be in free-fall. For free-falling bodies, the acceleration due to gravity is constant, irrespective of their mass. Free-fall is experienced not only by objects falling downward, but also by all objects whose motion is influenced by gravitational force alone. The dynamics of free-fall motion can be calculated using kinematic equations of motion, since free-fall acceleration is constant.
The acceleration experienced by all objects in free-fall is constant; therefore, any two objects dropped from the same height and location on the Earth will fall to the ground at the same speed, provided that the air resistance is neglected. Similarly, if two objects are dropped in succession, then the time required for them to reach the ground will be the same. However, the velocity of the object dropped first will always be greater than the velocity of the object dropped later.
Some real-life examples of free-fall include:
- Skydiving and bungee jumping
- A meteoroid accelerating toward the Earth's center
- A spacecraft in the Earth's orbit
- The projectile motion of an object in 2-dimensional space
This text is adapted from Openstax, University Physics Volume 1, Section 3.5: Free-fall.