Solved problem: Acceleration from forces

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Statement

difficulty

The following forces act on a body:

${\vec{F}}_{a} = \vec{i} + \vec{j} N; {\vec{F}}_{b} = \vec{j} + \vec{k} N; {\vec{F}}_{c} = \vec{i} + \vec{k} N$

What is the acceleration of the body if its mass is 2kg?

Solution

Data

Mass of the body: m = 2 kg

Forces: ${\vec{F}}_{a} = \vec{i} + \vec{j} N; {\vec{F}}_{b} = \vec{j} + \vec{k} N; {\vec{F}}_{c} = \vec{i} + \vec{k} N$

Resolution

To resolve this exercise we simply use the fundamental equation of dynamics (Newton´s second law). We must have into account the vector notation:

$\sum \vec{F} = m \cdot \vec{a} \Rightarrow \vec{a} = \frac{\sum \vec{F}}{m} = \frac{{\vec{F}}_{a} + {\vec{F}}_{b} + {\vec{F}}_{c}}{m} = \frac{\vec{i} + \vec{j} + \vec{j} + \vec{k} + \vec{i} + \vec{k}}{2} = \vec{i} + \vec{j} + \vec{k} m / s^{2}$

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

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\sum_{} \vec{F} = m \cdot \vec{a}

Newton´s Second Law

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Acceleration from forces

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