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Motion under gravity - Free fall, Displacement in second, Practice problems, FAQs
In the earlier classes, you would have come across the apple falling on famous scientist Sir Isaac Newton story. Every other person thought it was only natural, but he felt curious about the reason behind this. Rightly so! Why didn’t it go towards the sky! After much experimentation, he said gravity was responsible for making the apple fall. But what do we mean by gravity? It is the downward gravitational pull exerted by earth on all objects; we are standing or sitting but not floating in the air thanks to gravity.
Table of contents
- What is free fall?
- Motion under gravity
- Displacement traveled in second
- Equations of motion for a particle projected vertically upwards
- Practice problems
- FAQs
What is free fall?
We saw the case of an apple falling from a tree. The gravitational pull exerted by the earth acts downwards, and the acceleration due to it is called acceleration due to gravity(g). g carries a value of 9.8ms-2near the surface of the earth. Although its value changes on different points of the earth. The value of g does not depend upon the mass of the object undergoing freefall; but air resistance offered by air molecules plays an important role in accelerating a body. This is the reason a feather falls much slower in comparison to a coin. Air resistance makes the feather slow as compared to the coin, since air resistance on the feather is more. But if the coin and feather are released in vacuum where there is no air resistance, both would reach the ground at the same time.
Motion under gravity
A free fall motion is one dimensional motion. The necessary acceleration for motion is provided by earth.i.e . Applying equations of motion for this gives
Where
v-final velocity ; u-initial velocity a-acceleration; t-time ; s-displacement
On top of these 3 equations of motion, there is another equation of motion. Let’s see that.
Displacement traveled in the second
An object P traveling with initial velocity and constant acceleration undergoes displacement Sn in sec and Sn-1 in
Distance traveled by an object in the nth second
The displacement in seconds, from the second equation of motion can be written as
The displacement in seconds,
Equations of motion for a particle projected vertically upwards
When a stone is thrown upwards from the top of a tower of height with an initial velocity , taking upwards as positive. The acceleration . Applying second equation of motion,
Fig shows a stone thrown upwards
Applying first equation of motion
; at the highest point (when a stone is thrown upwards)
; indicates time of ascent.
If indicates total time of flight; then
For the above scenario, if denotes max height reached; then applying equation of motion
;
Note: g can be assumed constant only if displacement is much smaller than the radius of earth.
Practice problems
1) A ball is dropped from a balloon ascending upwards with a velocity of . If the balloon was at a height of 60 above the ground when the ball was dropped, find the time taken for the ball to hit the ground?(take
Soln) Taking upwards as positive,
;
Solving, we get
2)Particle is thrown with a velocity of from a building of height and particle is thrown vertically upwards from the ground with a velocity of . At what time do they meet?
Soln)Assuming the particles meet at a height above the ground
Taking upwards as positive,
For particle ;
For particle ;
3)A particle is thrown vertically upwards with a velocity of from the top of a tower. It reaches the ground in . Find the velocity with which it reaches the ground?
Soln)
Taking upwards as positive,
Applying first equation of motion;
at the top most point;
Remaining time
Let be the velocity with which it hits the ground;
4)A stone is dropped from a balloon upward going up with a uniform velocity of If the balloon was at a height of when the stone was dropped, the time after which the stone hits the ground is?(Take
Soln)
Given ;
;
FAQs
Q.A ball is thrown upwards. What is the correct expression for its acceleration?
Ans)
Q.Define motion under gravity?
Ans)When a body undergoes a motion such that the only force acting on it is gravitational force, it is said to be in motion under gravity.
- What is the value of acceleration due to gravity?
Ans)
Q.What is the third equation of motion in terms of ?
Ans)
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