Express fx and fy in terms of the length of the

Ответ:

sherry59Sherry59

17.01.2022

Fx, Fy = F cos θ, F sin θ

Further explanation

This is a fundamental problem with vector components.

A vector quantity is some quantities that have the magnitude and a direction. For example, all forces or momentums are vectors. Whereas, a scalar quantity only has magnitude. For example, all forms of energy are scalars.

The list below shows some recognized methods to represent a vector. i.e., a force.

$\boxed{ \ \textit{\textbf{F}}, \vec{F}, \bar{F} \ }$

It is possible to split one vector into two vectors. This process is called resolving and the vectors that we get are called the components of the original vector.

Vector problems can always be solved by using the mathematics of trigonometry, i.e., the functions of sine or cosine. This is particularly appropriate when resolving.

By using the cartesian coordinate system, see the attachment on how to calculate the values of either these components.

Horizontal component: $\boxed{ \ F_x = \textit{\textbf{F}}\ cos \ \theta \ }$ Vertical component: $\boxed{ \ F_y = \textit{\textbf{F}} \ sin \ \theta \ }$

Here, the angle between the vector F and the horizontal axis we call θ (theta).

As a reminder:

$\boxed{cos \ \theta = \frac{adjacent}{hypotenuse}} \rightarrow cos \ \theta = \frac{F_x}{F} \rightarrow \boxed{F_x = F cos \ \theta}$ $\boxed{sin \ \theta = \frac{opposite}{hypotenuse}} \rightarrow sin \ \theta = \frac{F_y}{F} \rightarrow \boxed{F_y = F sin \ \theta}$ Learn moreFinding the acceleration between two vectors linkA correct representation of 0.000025 in scientific notation link The theoretical density of platinum which has the FCC crystal structure link

Keywords: express Fx and Fy, in terms of the length of the vector F, and the angle θ, with the components, separated by a comma, resolving, split, horizontal, vertical, angle, theta, sine, cosine, trigonometry, cartesian coordinate system

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Ответ:

astultz309459

17.01.2022

Mathematics

The components of the vector F are $\fbox{\begin\\F\cos\theta\end{minispace}}$ and $\fbox{\begin\\F\sin\theta\end{minispace}}$ .

Further Explanation:

A physical quantity can be defined as the physical property that can be measured and have some value in numbers.

For example- mass, amount of substance, length, time, electric current, temperature, force, light intensity, density, velocity, speed etc.

A quantity is said as a vector if it has some magnitude and direction in order to give the details regarding the quantity.

For example- Force, velocity, current density, electric field, magnetic field, displacement, acceleration, momentum etc.

A quantity is said as a scalar if it has only the magnitude in order to give the details regarding the quantity.

For example- speed, distance, current, volume, density, mass, energy, time, temperature etc.

Given:

The resultant vector is .

The horizontal component is ${\vec F_x}$ .

The vertical component is ${\vec F_y}$ .

Concept:

Let a vector have some length and making an angle $\theta$ with horizontal axis.

The triangle rule of resultant vector state that when two vector is denoted by the two sides of the triangle and the magnitude and the direction is taken in the same direction then the third side of the triangle denoted by resultant vector with some magnitude and direction.

The diagram is drawn as shown in the Figure 1.

The vertical component is along y-axis and the vertical component of the vector $\vec F$ is expressed as: