physic form 4

Part 1: Suppose that the air resistance is negligible

As Fanny starts to fall, before the string stretches, she is under free fall in which her gravitational potential energy is converted to kinetic energy. So mechanical energy is conserved in this period.

When the string starts to stretches, it gains elastic potential energy which comes from Fanny's original kinetic energy and the gravitational potential energy as she continues to fall before coming to momentarily at rest.

So the mechanical energy is totally conserved in ths situation.

Part 2: So to speak, Fanny can only fall 8 m further at most when the string starts to stretches.

At the moment when the string starts to stretch, her nstantaneous velocity is:

mv2/2 = mgh where h = 12 m (the height fallen by her)

v2 = 240

v = 15.5 m/s

So applying v2 - u2 = 2as with v = 0, u = 15.5 and s = 8:

-240 = 16a

a = -15 m/s2 (the negative sign means her acc. is upward)

So the net force on her should be 50 x 15 = 750 N

In additional to her weight, the min. average decelerating force on her is 750 + 500 = 1250 N

Mechanical energy is conserved because Fanny is under free fall before the elastic string is exteded.

Let F be the average retarding force. Use the formula:
work done = change of energy
(F - 50g) x (20 - 12) = 50g x 12
where g is the acceleration due to gravity, taken to be 10 m/s2
hence, (F - 500) x 8 = 6000
F = 1250 N