Find out the resultant of two forces of 4N and 7N acting at an angle of 140°
7 along x axis
4 at 40 degrees above y axis
Fx = 7 - 4 cos 40
Fy = 4 sin 40
|F| = sqrt (Fx^2 + Fy^2)
angle above x axis = tan^-1 (Fy/Fx)
To find the resultant of two forces, we can use the method of vector addition.
Step 1: Resolve the forces into their horizontal and vertical components.
The 4N force can be split into a horizontal component and a vertical component using trigonometry. The angle between the force and the x-axis is (180° - 140°) = 40°.
Horizontal component of 4N force = 4N * cos(40°)
Vertical component of 4N force = 4N * sin(40°)
Similarly, for the 7N force:
Horizontal component of 7N force = 7N * cos(40°)
Vertical component of 7N force = 7N * sin(40°)
Step 2: Add the horizontal and vertical components separately.
Horizontal component of the resultant force = Sum of the horizontal components of the two forces
Vertical component of the resultant force = Sum of the vertical components of the two forces
Horizontal component of the resultant force = (4N * cos(40°)) + (7N * cos(40°))
Vertical component of the resultant force = (4N * sin(40°)) + (7N * sin(40°))
Step 3: Calculate the magnitude and direction of the resultant force.
Magnitude of the resultant force = √[(Horizontal component of the resultant force)^2 + (Vertical component of the resultant force)^2]
Direction of the resultant force = arctan(Vertical component of the resultant force / Horizontal component of the resultant force)
Magnitude of the resultant force = √[((4N * cos(40°)) + (7N * cos(40°)))^2 + ((4N * sin(40°)) + (7N * sin(40°)))^2]
Direction of the resultant force = arctan(((4N * sin(40°)) + (7N * sin(40°))) / ((4N * cos(40°)) + (7N * cos(40°))))
You can calculate the numerical values of the magnitude and direction using a calculator or mathematical software.
To find the resultant of two forces acting at an angle, we can use the concept of vector addition. We can break down each force into its horizontal and vertical components and then add them together to find the resultant force.
Step 1: Resolve the forces into their horizontal and vertical components.
- The first force of 4N can be resolved into a horizontal component and a vertical component.
- Horizontal component = 4N * cos(140°)
- Vertical component = 4N * sin(140°)
- The second force of 7N can also be resolved into a horizontal component and a vertical component.
- Horizontal component = 7N * cos(140°)
- Vertical component = 7N * sin(140°)
Step 2: Add the horizontal and vertical components of both forces.
- Horizontal component of the resultant force = (4N * cos(140°)) + (7N * cos(140°))
- Vertical component of the resultant force = (4N * sin(140°)) + (7N * sin(140°))
Step 3: Calculate the magnitude and direction of the resultant force using the Pythagorean theorem and trigonometry.
- Magnitude of the resultant force = √(horizontal component² + vertical component²)
- Direction of the resultant force = arctan(vertical component / horizontal component)
Simplifying the above calculations, the resultant of the two forces of 4N and 7N, acting at an angle of 140°, can be found by performing the following calculations:
- Horizontal component of the resultant force = (4N * cos(140°)) + (7N * cos(140°))
- Vertical component of the resultant force = (4N * sin(140°)) + (7N * sin(140°))
- Magnitude of the resultant force = √((horizontal component)² + (vertical component)²)
- Direction of the resultant force = arctan(vertical component / horizontal component)
Calculating these values will give you the magnitude and direction of the resultant force in this problem.