Question

Two electric force vectors act on a particle. Their x-components are 13.5 N and −7.40 N and their y-components are −12.0 N and −4.70 N, respectively. For the resultant electric force, find the following.
(a) the x-component N
(b) the y-component N
(c) the magnitude of the resultant electric force N
(d) the direction of the resultant electric force, measured counterclockwise from the positive x-axis ° counterclockwise from the +x-axis

Answer 1

Answer:

Explanation:

Given two vectors as follows

E₁ = 13.5 i -12 j

E₂ = -7.4 i - 4.7 j

Resultant E = E₁ + E₂

= 13.5 i -12 j -7.4 i - 4.7 j

E = 6.1 i - 16.7 j

a ) X component of resultant = 6.1 N

b ) y component of resultant = -16.7 N

Magnitude of resultant = √ ( 6.1² + 16.7² )

= 17.75 N

d ) If θ be the required angle

tanθ = 16.7 / 6.1 = 2.73

θ = 70° .

counterclockwise = 360 - 70 = 290°

Answer 2

By working with the vector forces, we will get:

• a) The x-component is 1.5 N
• b) The y-component is -12.2 N
• c) The magnitude is 12.9 N
• d) The direction is 277.01°.

How to find the resultant force?

Remember that we can directly add vector forces, so if our two forces are:

F₁ = <13.5 N, -7.5 N>

F₂ = < -12 N, -4.70 N>

Then the resultant force is:

F = F₁ + F₂ = <13.5 N + (-12 N), -7.5 N + ( -4.70 N) >

F = < 1.5 N, -12.2 N>

so we have:

a) The x-component is 1.5 N

b) The y-component is -12.2 N

c) The magnitude will be:

|F| = √( (1.5 N)^2 + (-12.2 N)^2) = 12.29 N

d) The direction of a vector <x, y> measured counterclockwise from the positive x-axis is given by:

θ = Atan(y/x)

Where Atan is the inverse tangent function, then here we have:

θ = Atan(-12.2 N/1.5 N) = 277.01°

If you want to learn more about vectors, you can read:

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