An object of mass 1000 g falls from a height of 30m on the sand below. If it penetrates 4cm into the sand, what opposing force is exerted on it by the sand? Neglect air friction. (f = 7350 N) 


Given:

Mas of the object = m = 1000 g = 1 kg
Height = h = 30 m
Depth penetrated = d = 4 cm = 0.04 m
Value of g = 9.81 m s⁻²

To Find:

Opposing force on the object = F = ?


Solution:

In the downward motion, the object losses P.E. and gains K.E.. If there is no air resistance then

Gain in K.E. = Loss in P.E 

K.E. = mgh 

K.E. = 1 kg ｘ 9.81 m s⁻² ï½˜ 30 m

K.E. = 294.3 J

K.E = 294 J = W

This is the total energy of the object just before hitting the sand and it will be responsible to do work done by penetrating the object into the sand at a 4 cm depth. so, Work done by opposing (friction) force is equal to lose in K.E. through a distance d in sand, (K.E = W = 294 J ) 

Work done is given by formula as

W = Fd

or

F = `\frac {W}{d}`

by putting values 

F = `\frac {294 J }{0.04 m}`

F = 7,350 N -----------Ans

Thus the friction force is 7,350 N


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