Match each mechanical scenario to its corresponding missing value (net force, mass, or acc… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each mechanical scenario to its corresponding missing value (net force, mass, or acceleration) using Newton's Second Law ( $F = ma$ ).

A $10 \text{ kg}$ gear assembly accelerating at $3 \text{ m/s}^2$ requires a net force of... $30 \text{ N}$
A mechanism experiencing $100 \text{ N}$ of net force and accelerating at $5 \text{ m/s}^2$ has a mass of... $20 \text{ kg}$
A $25 \text{ kg}$ engine block pushed with a net force of $50 \text{ N}$ experiences an acceleration of... $2 \text{ m/s}^2$
A $200 \text{ kg}$ payload accelerating at $4 \text{ m/s}^2$ requires a net force of... $800 \text{ N}$

Match the scenarios by calculating the missing variable:

10 \text{ kg}

3 \text{ m/s}^2

matches

30 \text{ N}

;

100 \text{ N}

5 \text{ m/s}^2

matches

20 \text{ kg}

;

25 \text{ kg}

50 \text{ N}

matches

2 \text{ m/s}^2

;

200 \text{ kg}

4 \text{ m/s}^2

matches

800 \text{ N}

The correct matches are found by identifying the two known variables in Newton's Second Law (

F = ma

) for each scenario and algebraically solving for the third unknown variable.

Calculate the net force for the gear assembly.

F = 10 \text{ kg} \times 3 \text{ m/s}^2 = 30 \text{ N}

Applying the direct formula

F = ma

to find the required force.

Calculate the mass of the mechanism.

m = \frac{100 \text{ N}}{5 \text{ m/s}^2} = 20 \text{ kg}

Rearranging the formula to

m = \frac{F}{a}

to solve for mass.

Calculate the acceleration of the engine block.

a = \frac{50 \text{ N}}{25 \text{ kg}} = 2 \text{ m/s}^2

Rearranging the formula to

a = \frac{F}{m}

to solve for acceleration.

Calculate the net force for the payload.

F = 200 \text{ kg} \times 4 \text{ m/s}^2 = 800 \text{ N}

Applying the direct formula

F = ma

to find the required force.

Newton's Second Law (

F = ma

)

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