Question

Two forces F1 and F2 are applied at the same point of an object. F1 has a magnitude of 20 N and is directed at an angle of 120 degrees with respect to the positive x axis. F2 has a magnitude of 5 N and is directed at an angle of -30 degrees with respect to the positive x axis. Determine net force acting on the object in i, j, k unit notation.

Answer 1

Answer:

The value is  $\vec F_{n} = -5.67 i +14.82 j \ \ N$

Explanation:

From the question we are told that

   The magnitude of the first force is  $F_1 = 20 \ N$

    The angle which it makes with the x-axis is  $\theta_1 = 120 ^o$

    The magnitude of the second force is  $F_2 = 5 \ N$

     The angle which it make with x-axis is  $\theta_2 = -30 ^o$

Generally the x-component of the first force is  

       $F__{1x}} = 20 cos (120 )$'

=>     $F__{1x}} = -10 \ N$

Generally the y-component of the first force is  

       $F__{1y}} = 20 sin (120 )$

=>     $F__{1y}} = 17.32 \ N$

Generally the vector representation of the first force is mathematically represented as

       $\vec F_1 = [ -10 i + 17.32 j \ ] \ N$

Generally the x-component of the second force is  

       $F__{2x}} = 20 cos (-30 )$

=>     $F__{2x}} = 4.33 \ N$

Generally the y-component of the second force is  

       $F__{2y}} = 20 sin (-30 )$

=>     $F__{2y}} = -2.5 \ N$

Generally the vector representation of the first force is mathematically represented as

       $\vec F_2 = [ 4.33 i - 2.5 j \ ] \ N$

Generally the net force acting that point is mathematically represented as

       $\vec F_{n} = -10 i + 17.32 j + 4.33 i - 2.5 j$

=>    $\vec F_{n} = -5.67 i +14.82 j \ \ N$