Question

Show that total energy is conserved for body fall freely under the effect of gravity.​

Answer 1

Answer:

Let us consider a body of mass m placed at A

h = AB = Height of body from ground

s = Distance if any point C from A

g = Acceleration due to gravity

v1 = Velocity of the body at C

v = Velocity of body at B

Velocity at point A = 0

(i) Mechanical energy at Point A

Potential energy at A = E (pA) = mgh

Kinetic energy at A = E (kA) = 0

Total mechanical energy at A (Ea) = E (pa) + E (kA)

= mgh + 0 = mgh -------- (i)

(ii) At point C

When body moves from A to C, it covers distance 's'. and v1 us velocity at C then from,

v^2 - u^2 = 2as

v1^2 - 0 = 2 gs

Kinetic energy at C = E (kC) = 1/2 mv^2

= 1/2 m (2gs)

= mgs

Potential energy at C = E (pC) = mg (h - s)

Total mechanical energy at C = E (C) =

E (C) = E (pC) + E (kC) = mg (h-s) + mgs = mgh ------ (ii)

(iii) At point B

v^2 = 2gh

Kinetic energy at B = E (kB) = 1/2 mv^2

= 1/2 m (2gh) = mgh

Potential energy at B = E (pB) = 0

Total mechanical energy = E (B) =

E (B) = E (kB) + E (pB) = mgh + 0 = mgh ----- (iii)

From (i) , (ii) and (iii)

E (A) = E (B) = E (C)

mgh = mgh = mgh

Total mechanical energy was same at all the three points. This proves that -

The total mechanical energy of the body throughout the free fall is conserved.

NOTE - We have neglected effect of AIR RESISTANCE on the motion of body.

                                                                 OR

Let a body of mass m fall freely under gravity from height h above ground.

Let A, B and C be the positions of body.

Let x be the distance fallen from A to B.

find in the attachment the picture for the calculations

From (i), (ii) and (iii) it is clear that sum of mechanical energy remains same at any point in the path of free fall of a body.

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Answer 2

Answer:

Explanation:Show that in case of a body falling freely under gravity, total mechanical energy remains conserved (neglect air resistance). Show that in case of a body falling freely under gravity, total mechanical energy remains conserved (neglect air resistance).