The 2.5-kg head of an ax exerts a force of 80 kN as it penetrates 18 mm into the truck of a tree. The speed of the ax head when it strikes the tree is
A) 1.2 m/s.
B) 3.4 m/s.
C) 34 m/s.
D) 107 m/s.

Question

Quizplus · Accepted Answer

The work done by the ax head as it penetrates the tree can be calculated using the formula $W = F \cdot d$, where $F$ is the force and $d$ is the distance. Here, $F = 80 \, \text{kN} = 80,000 \, \text{N}$ and $d = 18 \, \text{mm} = 0.018 \, \text{m}$. So, $W = 80,000 \, \text{N} \times 0.018 \, \text{m} = 1440 \, \text{J}$.The work done is equal to the kinetic energy the ax head had just before impact, which can be calculated using the formula $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity. Rearranging for $v$, we get $v = \sqrt{\frac{2KE}{m}}$.Substituting the given values, $m = 2.5 \, \text{kg}$ and $KE = 1440 \, \text{J}$, we get $v = \sqrt{\frac{2 \times 1440}{2.5}} = \sqrt{1152} \approx 34 \, \text{m/s}$.

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