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.
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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