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

The value is
`\vec F_(n) = -5.67 i +14.82 j \ \ N`

Step-by-step 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`