Assume that a muscle is having a force of 300N is pulling at an angle of 75 degrees. What are the components of the force both the trigonometric method and graphic method.
To determine the components of a force, you need to resolve it into its horizontal and vertical components. This can be done using trigonometric calculations or by graphical representation. I will explain both methods below.
Trigonometric Method:
1. Identify the force vector and the given angle. In this case, the force is 300N, and the angle is 75 degrees.
2. Define an x-axis and a y-axis. The x-axis is horizontal, and the y-axis is vertical.
3. Determine the horizontal component of the force (Fx) using the cosine function:
Fx = Force * cos(angle)
= 300N * cos(75 degrees)
≈ 75.72N (rounded to two decimal places)
4. Determine the vertical component of the force (Fy) using the sine function:
Fy = Force * sin(angle)
= 300N * sin(75 degrees)
≈ 287.28N (rounded to two decimal places)
So, the horizontal component (Fx) is approximately 75.72N, and the vertical component (Fy) is approximately 287.28N.
Graphic Method:
1. Draw a coordinate system on a piece of paper or a graphing tool. Place your force vector originating from the origin.
2. Measure the length of the force vector using a ruler or scale.
3. Draw a line perpendicular to the force vector starting from the tip of the vector. This line represents the vertical component.
4. Measure the length of the vertical line using a ruler or scale.
5. Draw a line parallel to the force vector starting from the tip of the vertical line. This line represents the horizontal component.
6. Measure the length of the horizontal line using a ruler or scale.
The length of the vertical line represents the vertical component of the force (Fy), and the length of the horizontal line represents the horizontal component of the force (Fx).
Using either method, you can determine the components of a force when given the force magnitude and the angle.