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According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass $m$ that moves with an acceleration $a$ is equal to $ma$ . An object whose mass is $80$ grams has an acceleration of $20$ meters per seconds squared. What calculation will give us the sum of the forces that act on the object, in Newtons (which are $\text{kg} \times \text{m/s}^2$ )?

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Relate position, velocity, speed, and acceleration using derivatives

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Q. According to Newton's Second Law of Motion, the sum of the forces that act on an object with a mass

m

that moves with an acceleration

a

is equal to

ma

. An object whose mass is

80

grams has an acceleration of

20

meters per seconds squared. What calculation will give us the sum of the forces that act on the object, in Newtons (which are

\text{kg} \times \text{m/s}^2

)?

Convert to kilograms: Convert the mass from grams to kilograms, because the unit for mass in the formula $F=ma$ (Newton's Second Law) should be in kilograms (kg). $1$ gram $= 0.001$ kilograms $80$ grams $= 80 \times 0.001$ kg $80$ grams $= 0.08$ kg
Calculate force using formula: Use Newton's Second Law of Motion formula to calculate the force. $\newline$ Force $F = m \times a$ $\newline$ Given: $m = 0.08\,\text{kg}$ (from Step $1$ ), $a = 20\,\text{m/s}^2$ $\newline$ $F = 0.08\,\text{kg} \times 20\,\text{m/s}^2$ $\newline$ $F = 1.6\,\text{kg}\cdot\text{m/s}^2$
Determine total force: Since the unit of force is Newtons (N) and $1\,\text{N} = 1\,\text{kg}\cdot\text{m}/\text{s}^2$ , the force calculated in Step $2$ is already in the correct unit. $\newline$ Therefore, the sum of the forces acting on the object is $1.6\,\text{Newtons}$ .

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