Using Newton's Second Law (F = ma), match each mechanical scenario with its correct missin… — Armed Services Vocational Aptitude Battery (ASVAB)

Using Newton's Second Law ( $F = ma$ ), match each mechanical scenario with its correct missing value (force, mass, or acceleration).

Net force required to accelerate a $15 \text{ kg}$ tool box at $3 \text{ m/s}^2$ $45 \text{ N}$
Mass of a component that accelerates at $4 \text{ m/s}^2$ when a $150 \text{ N}$ push is opposed by $30 \text{ N}$ of friction $30 \text{ kg}$
Acceleration of a $250 \text{ kg}$ engine block pushed with $1,200 \text{ N}$ of forward force against $200 \text{ N}$ of friction $4 \text{ m/s}^2$
The new acceleration of a moving object if the net force acting on it is tripled (assuming mass is constant) from an initial state that produced $2 \text{ m/s}^2$ $6 \text{ m/s}^2$

Cevap

The matches are calculated by rearranging

F = ma

to solve for the missing variable, factoring in net force where applicable, and applying direct proportionality.

Newton's Second Law states that net force equals mass times acceleration (

F = ma

). By determining the net force and algebraically rearranging the formula, or by applying proportional reasoning rules, each scenario can be correctly matched to its missing value.

Adım Adım Çözüm

Calculate the net force where opposing forces are present.

Subtract friction from the applied force to find the true net force acting on the object.

Newton's Second Law only applies to the net force, not just the applied force.

Apply Newton's Second Law (

F = ma

) or its rearranged forms.

Use

F = ma

for force,

m = \frac{F}{a}

for mass, and

a = \frac{F}{m}

for acceleration.

These equations isolate the missing variable for the first three scenarios.

Apply proportional reasoning for the final scenario.

Recognize that tripling the force triples the acceleration.

Since

a = \frac{F}{m}

, acceleration and force are directly proportional when mass is constant.

Anahtar Kavram

Newton's Second Law

Tahmini Süre:1m 30s

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