A sledgehammer head with a weight of 19.6 \text{ N} on Earth strikes a metal spike with a … — Armed Services Vocational Aptitude Battery (ASVAB)

A sledgehammer head with a weight of $19.6 \text{ N}$ on Earth strikes a metal spike with a downward velocity of $4 \text{ m/s}$ . The impact brings the hammer head to a complete stop in $20 \text{ ms}$ (milliseconds). What is the average impact force exerted on the spike? (Assume $g = 9.8 \text{ m/s}^2$ )

A
$0.4 \text{ N}$
B
$3,920 \text{ N}$
$400 \text{ N}$ Answer
D
$0.16 \text{ N}$

Answer

The correct answer is

400 \text{ N}

The force is found by first converting weight to mass (

19.6 / 9.8 = 2 \text{ kg}

) and time to seconds (

20 \text{ ms} = 0.02 \text{ s}

). The change in momentum is

2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg} \cdot \text{m/s}

. Dividing this change by the impact duration (

0.02 \text{ s}

) gives an average impact force of

400 \text{ N}

Step-by-Step Solution

Calculate the mass of the sledgehammer head.

m = \frac{W}{g} = \frac{19.6 \text{ N}}{9.8 \text{ m/s}^2} = 2 \text{ kg}

Momentum equations require mass, not weight.

Convert the impact time to standard SI units (seconds).

t = 20 \text{ ms} = 0.02 \text{ s}

Standard units must be used to calculate force in Newtons.

Calculate the change in momentum (impulse).

\Delta p = m \times \Delta v = 2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg} \cdot \text{m/s}

Impulse is equal to the change in momentum.

Calculate the average impact force.

F = \frac{\Delta p}{\Delta t} = \frac{8 \text{ kg} \cdot \text{m/s}}{0.02 \text{ s}} = 400 \text{ N}

Force is the rate of change of momentum.

Key Concept

Impulse and Momentum

Question

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Step-by-Step Solution

Key Concept

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