Question

An object of mass 5 kg and at rest falls to the ground from a height of 10.0m. If the object penetrates the ground to a depth of 50 mm after impact estimate the average retarding force.

Answer 1

Let velocity of object at ground = v

by kinematics law,

v^2 - u^2 = 2*a*S

here,

u = initial velocity of object = 0

a = g = 9.81 m/sec^2

S = height = 10.0 m

So, v^2 = 2*9.81*10 = 196.2

v = 14 m/sec.

It goes 50 mm depth,

Let average retarding force = F

So, F = m*a

here, m = mass of object = 5 kg

a = de-acceleration = ??

For finding value of a,

by kinematics equation,

v^2 - u^2 = 2*a*S

here,

u = initial velocity of object = 14 m/sec

final velocity = v = 0

a = ??

S = height = 50 mm = 0.05 m

So, a = - (14^2)/(2*0.05)

a = -1960 m/sec^2

So, retarding force(F) = 5*1960

F = 9800 N

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