## Statement

difficulty

A 35 kg body at rest is subjected to the following forces for 3 minutes:

If N is the measure given, calculate:

1. Resultant force

2. Impulse

3. Linear momentum variation

Velocity aquired by the body during these 3 minutes. La velocidad que ha adquirido el cuerpo in these 3 minutes.

## Solution

Data

• Mass of the body: m=35 kg
• Performance time of the forces: t = 3 minutes = 3·60 s = 180 s
• Forces:
• Rest part ( ${\stackrel{\to }{v}}_{i}=0$ )

Resolution

We start calculating the resultant force. For that we simply have to sum the forces provided.

Now we can calculate the impulse requested multiplying the resultant force obtained by the interval of time during the forces are acting:

As we know, because the impulse-momentum theorem, the previous value coincides with the variation of linear momentum requested. We find the velocity requested turning to the definition of that linear momentum:

## 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
${\sum }_{}\stackrel{\to }{F}=\stackrel{\to }{{F}_{1}}+\stackrel{\to }{{F}_{2}}+\stackrel{\to }{{F}_{3}}+...+\stackrel{\to }{{F}_{n}}$
$\stackrel{\to }{p}=m·\stackrel{\to }{v}$