# A steel

A steel hammer with a weight of 0.5 kg hits the nail at a speed of 3 m/s. How deep the nail penetrates the wood if the hammer acts on the nail with an average force of 50N.

Correct result:

x =  45 mm

#### Solution:

$m=0.5 \ \text{kg} \ \\ v=3 \ \text{m/s} \ \\ F=50 \ \text{N} \ \\ \ \\ E_{1}=1/2 \cdot \ m \cdot \ v^2=1/2 \cdot \ 0.5 \cdot \ 3^2=\dfrac{ 9 }{ 4 }=2.25 \ \text{J} \ \\ E_{1}=Fx \ \\ x_{1}=E_{1}/F=2.25/50=\dfrac{ 9 }{ 200 }=0.045 \ \text{m} \ \\ x=1000 \cdot \ x_{1}=1000 \cdot \ 0.045=45 \ \text{mm}$

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