determine the vertical force required if the horizontal force is 30N and the resultant vector is 80N (also determine the angle of the resultant vector).
To determine the vertical force required and the angle of the resultant vector, we need to use vector addition.
First, let's draw a vector diagram to represent the given information.
Start by drawing a horizontal line representing the 30N horizontal force. Then, draw a line from the end of the horizontal force vector to represent the 80N resultant vector. The angle between the horizontal force and the resultant vector is the angle we want to find.
Next, let's break down the resultant vector into its horizontal and vertical components.
We can use trigonometry to find the values of the horizontal and vertical components. Since we know the angle between the horizontal force and the resultant vector, we can use the sine and cosine functions.
Let's assume the angle between the horizontal force and the resultant vector is θ.
The horizontal component (F_x) can be found using cosine:
F_x = R * cos(θ)
where R is the magnitude of the resultant vector, which is 80N in this case.
Similarly, the vertical component (F_y) can be found using sine:
F_y = R * sin(θ)
Now, let's calculate the values:
F_x = 80N * cos(θ)
F_y = 80N * sin(θ)
To find the angle θ, we can use the inverse tangent function:
θ = tan^(-1)(F_y / F_x)
Now, substitute the values we have:
θ = tan^(-1)((80N * sin(θ)) / (80N * cos(θ)))
Simplifying further, we can cancel out the 80N:
θ = tan^(-1)(sin(θ) / cos(θ))
Now, we can solve for the angle by using a scientific calculator or a trigonometric table.
Once we have the angle θ, we can calculate the vertical force (F_y) using the given horizontal force (30N) and the angle.
F_y = F_x * tan(θ)
Substituting the values:
F_y = 30N * tan(θ)
By using this process, we can determine the vertical force required and the angle of the resultant vector.