Vertical Motion under Gravity

1
Vertical Motion under Gravity
The object moves along a vertical line.
The only force acting on the object is the
attraction due to earth.
Air resistance is neglected.
The change in the height of the object is small
compared to the radius of earth.
2
Vertical Motion under Gravity
Vertical
(passing through the centre of earth)
It is an attraction acting on the object by
earth. It always directs towards the centre of
earth.
Horizontal
3
Vertical Motion under Gravity
According to Newtons Second Law of Motion, the
acceleration points in the same direction as the
force.
Vertical
Therefore the acceleration always points
vertically downward
Horizontal
4
Vertical Motion under Gravity
Vertical

• It always points vertically downward.
• If the change in height is small, its magnitude
  is constant and is equal to g.
• Near to the surface of the earth, a good
  approximation of g is 9.8 m s-2.

5
Vertical Motion under Gravity
Vertical
If the object moves up, the acceleration and the
velocity points in different directions. The
object slows down.
Object moving up
6
Vertical Motion under Gravity
Vertical
Object at its maximum height
Velocity 0
Even when the object is instantaneously at rest,
the gravitational attraction still exists and so
does the acceleration due to gravity.
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Vertical Motion under Gravity
Vertical
If the object moves down, the acceleration and
the velocity points in the same direction. The
object speeds up.
Object moving down
8
Vertical Motion under Gravity
Two heavy metal spheres of different masses are
to be released from rest at the roof of the tower.
9
Vertical Motion under Gravity
Objects of different masses have the same
acceleration due to gravity.
The motions of the objects are identical. They
reach the ground at the same time.
10
An object is projected with speed u vertically
upward
displacement (upward positive)
x ut 0.5(- g)t2
time
0
T
2T
11
An object is projected with speed u vertically
upward
velocity (upward positive)
u
v u (- g)t
time
0
T
2T
-u
12
An object is projected with speed u vertically
upward
acceleration (upward positive)
a - g
time
0
T
2T
-g