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Laws Of Motion

Question
CBSEENPH11017043

a hammer weighing 1 kg moving with a speed of 20 m/s strikes the head of a nail driving it 10 cm into a wall. Neglecting the mass of the nail, calculate a) the acceleration during the impact, b) the time interval during impact, c) impulse. 

Solution

Here, 
m = 1 kg, u = 20 m/s 
s = 10 cm = 0.1 m 
v = 0, a = ?
a) As, 
v2 = u2 + 2as
therefore space 0 space equals space left parenthesis 20 right parenthesis squared space plus space 2. straight a. space left parenthesis 0.1 right parenthesis space

rightwards double arrow space straight a space equals negative fraction numerator 400 over denominator 2 space cross times 0.1 end fraction space equals space minus 2000 space straight m divided by straight s squared 
b) v = u + at 
therefore space 0 space equals space 20 space plus space left parenthesis negative 2000 right parenthesis straight t space

rightwards double arrow space straight t space equals space 20 over 2000
space space space space space space equals 1 over 100 equals 0.01 space sec 
c) Impulse = F. t
               = m (v-u)
               = 1 (0-20)
               = -20 N.s.