Solved problem: Massive force

Development
Formulas

Statement

difficulty

If the following forces act on a body: ${\vec{F}}_{1} = - 10 \cdot \vec{i} + 10 \cdot \vec{j} ⋮ {\vec{F}}_{2} = 4 \cdot \vec{i} - 3 \cdot \vec{j} ⋮ {\vec{F}}_{3} = 5 \cdot \vec{i} - \vec{j} ⋮ {\vec{F}}_{4} = \vec{i} - \vec{j}$

Find out a force whose effect is equal to exert the 4 forces proposed.

Solution

In that case, what we are asked for is to calculate the resultant force of a system of forces applied on the body. By definition:

$\sum_{} \vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} \Rightarrow \sum_{} \vec{F} = ({\vec{F}}_{1 x} + {\vec{F}}_{2 x} + {\vec{F}}_{3 x} + {\vec{F}}_{4 x}) \cdot \vec{i} + ({\vec{F}}_{1 y} + {\vec{F}}_{2 y} + {\vec{F}}_{3 y} + {\vec{F}}_{4 y}) \cdot \vec{j} \Rightarrow \sum_{} \vec{F} = (- 10 + 4 + 5 + 1) \cdot \vec{i} + (10 - 3 - 1 - 1) \cdot \vec{j} \Rightarrow \sum_{} \vec{F} = 5 \cdot \vec{j}$

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.

Formulas

Related sections

\sum_{} \vec{F} = \vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}} + . . . + \vec{F_{n}}

Resultant Force of a System of Forces

Statement

Solution

Formulas worksheet

Site

Contact form

Follow us

Massive force

Ayúdanos a mantenernos en órbita

¿Nuestros contenidos te están resultando de utilidad?

Statement

Solution

Formulas worksheet