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Question

A hammer of mass 0.5kg is to drive a nail of mass 50g into a piece of wood horizontally. If the hammer moves with a velocity of 4.4m/s and the resisting force of the wood is 100N. How far will the nail he driven into wood? Assuming the hammer doesn't rebound from the nail.

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Solution

Dear Student
  • Mass of nail: 𝑚=50 g = 0.05 kg
  • Mass of hammer: 𝑀=0.5kg
  • Velocity of hammer before striking nail: 𝑢 = 4.4ms−1
  • Velocities of hammer and nail after hammer strikes nail are the same: v
Muh + mun = M+mvv =Muh + mun M+m =0.5×4.4+m×00.5+0.05v =2.200.55 =4 m/s
a = F/m = 100 / 0.05 = 10000/5 = 2000v2 = u2 + 2as42 = 0 +2ass =162a =8a =82000 =1250s =0.004 m =0.4 cm m/s2
v2= u2 +2as42 =0+2ass =162×2000 = 1250 =0.004 m =0.4 cm

Regards


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