Motion of objects under the influence of gravitational force of the earth
We know that an object experiences acceleration during free fall. This acceleration experienced by an object is independent of its mass . This means that all objects hollow or solid, big or small, should fall at same rate. According to a story, Galileo dropped different objects from the top of the Leaning tower of Pisa in Italy to prove the same.
As g is constant near the earth, all the equations for the uniformly accelerated motion of objects become valid with acceleration a replaced by g, the equations are:-
v = u + at Changes to v = u + gt
s = ut + 1/2at2 Changes to h = ut + 1/2gt2
v2 = u2 + 2as Changes to v2 = u2 = 2gh
where u and v are the initial and final velocities and s is the distance covered in time, t.
In applying these equations, we will take acceleration, a to be positive when it is in the direction of the velocity, that is, in the direction of motion. The acceleration, a will be taken as negative when it opposes the motion.
Example:- A car falls off a ledge and drops to the ground in 0.5 s. Let g = 10 m s-2.
- What is its speed on striking the ground?
- What is its average speed during the 0.5 s?
- How high is the ledge from the ground?
Sol:- Time (t) = 0.5 s = 1/2 s
Initial velocity (u) = 0 m s-1
Acceleration due to gravity (g) = 10 m s-2
Acceleration of the car (a) = + 10 m s-2 (downward)
- Speed v = u + at
v = 10 m s-2 × 0.5 s
v = 5 m s-1
2. Average speed = u + v/ 2
= (0 m s-1 + 5 m s-1)/ 2
= 2.5 m s-1
3. Distance = ut + 1/2at2
= 0 × 0.5 + 1/2 × 10 m s-2 × (0.5 s)2
= 1/2 × 10 × 0.25
= 1.25 m
