an object of mass 40 kg is raised to a height of 5m above the ground if the object is allowed to fall find its kinetic energy when it is Halfway down
Answers
(A)
MASS (M) = 40 KG
HEIGHT (H)= 5 M
WE KNOW, POTENTIAL ENERGY (U) = MGH G = ACCELERATION DUE TO GRAVITY = 9.8ms^-2
OR U = 40 X 9.8 X 5 = 1960 J
(B)
NOW ,
IF THE OBJECT IS AT HALF-WAY DOWN,
THE POTENTIAL ENERGY OF THE OBJECT = KINETIC ENERGY/2
=1960 / 2 = 980 J.
Due to the law of conservation of energy. the object has an equal amount of potential and kinetic energy. Hence, half way down, the kinetic energy of the object will be 980 J.
Given:
Mass (m) = 40 kg
Acceleration due to gravity (g)= 10m/s²
Height (h)= 5m
Potential energy= m × g× h
P.E= 40 × 10 × 5 = 2000J
Potential energy = 2000J ( 2000 joules)
At a height of 5 metre object has a potential energy of 2000 J.
When this object is allowed to fall and it is Half way down its height above the ground will be half of 5 m= 5/2= 2.5m.
P.E at Half way down= m× g×h
P.E= 40× 10 × 2.5= 1000J
[h= 2.5 m]
Potential Energy at Half way down= 1000 joules.
According to law of conservation of energy:
Total potential energy= potential energy at Half way down+ kinetic energy at Half way of a down
2000 = 1000 + K.E at Half way down
K.E at Half way down= 2000- 1000= 1000J
Kinetic energy at half way down= 1000 joules.
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