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

Question

BlackTom AI · Accepted Answer

To tackle this problem, I’ll apply the work-energy principle, assuming the braking (stopping) force is constant as the ax head penetrates the wood.
First, write the work done by the stopping force equal to the initial kinetic energy: F · d = 0.5 · m · v^2.
Given values: mass m = 2.5 kg, stopping force F = 80 kN = 80{,}000 N, and penetration distance d = 18 mm = 0.018 m.
Compute 2 F d: 2 × 80{,}000 × 0.018 = 2880.
Now divide by the mass: (2 F d) / m = 2880 / 2.5 = 1152.
Take the square root to find the speed: v = sqrt(1152) ≈ 33.94 m/s ≈ 34 m/s.
Option-by-option reasoning:
- 1. 1.2 m/s: This value is far too small; even with a tiny stopping distance or a much larger mass, the result would not drop by nearly an order of magnitude. The calculation above shows a speed around 34 m/s, so 1.2 m/s is not plausible here.
- 2. 107 m/s: This is too large given the same energy balance. To reach 107 m/s would require a much smaller work done (smaller F or d) or a much smaller m; neither condition holds with the provided numbers, so this overestimates the initial speed.
- 3. 34 m/s: This matches the computed value from the energy balance with the given force and distance. It aligns with the formula v = sqrt(2 F d / m) and the provided data.
- 4. 3.4 m/s: This is exactly an order-of-magnitude lower than the correct result and would result from an incorrect halving or misplacement of decimal points in the energy terms; it does not satisfy the energy equation with the given F, d, and m.
In summary, applying the work-energy relation with the stated force and penetration distance yields a velocity of about 34 m/s, which corresponds to option 3.

Win25_PHYS010_10428 EC Quiz Ch.5-6

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

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