Two forces of magnitude 80n and 60n are inclinde to each other at angle 90 calculate the resultant force and obtain it direction draw the system forces.
X = Hor. = 80 N.
Y = Ver. = 60 N.
tanA = Y/X = 60/80 = 0.75
A = 36.9o = Direction.
Resultant = X/cosA = 80/cos36.9 = 100 N.
Well, well, well, looks like we've got some forces getting cozy with each other! Let's see what kind of trouble they're causing.
To calculate the resultant force, we need to add up the two forces using some good old vector addition. Since they're inclined at a 90-degree angle, it means they are perpendicular to each other.
Now, when two forces are perpendicular, we can use the Pythagorean theorem to find the magnitude of the resultant force. In this case, it's sqrt(80^2 + 60^2). Crunching the numbers gives us approximately 100 Newtons. Voila!
But that's not all! We also need to find the direction of this shenanigans. To do that, we can use the concept of trigonometry. The angle between the resultant force and the 80 Newton force is the same as the angle between the 80 Newton force and the 60 Newton force (which is 90 degrees). So, we're dealing with a right-angled triangle!
Using some SOHCAHTOA magic, we can find the angle:
tan(theta) = (opposite/adjacent) = (60/80)
Taking the arctan of both sides will give us the angle, which is approximately 36.87 degrees.
So, the resultant force has a magnitude of 100 Newtons and is inclined at an angle of 36.87 degrees with the 80 Newton force.
Now, it's time to draw those forces! Just imagine two arrows—one representing the 80 Newton force and another representing the 60 Newton force—coming together at a right angle, forming a right-angled triangle. The resultant force arrow will complete the triangle, and it'll make you say, "Voila, a force triangle fortuitously!"
Remember, kids, physics can be fun, especially when you spice it up with some geometry and clownish humor!
To calculate the resultant force, we can use the concept of vector addition. The resultant force is the vector sum of the two given forces.
Step 1: Resolve the forces into their horizontal and vertical components.
The vertical component of a force can be found using the equation F_vertical = F * sin(θ), where F is the magnitude of the force and θ is the angle it makes with the horizontal.
The horizontal component of a force can be found using the equation F_horizontal = F * cos(θ).
For the 80 N force:
Vertical component: F_vertical_1 = 80 N * sin(90) = 80 N * 1 = 80 N
Horizontal component: F_horizontal_1 = 80 N * cos(90) = 80 N * 0 = 0
For the 60 N force:
Vertical component: F_vertical_2 = 60 N * sin(90) = 60 N * 1 = 60 N
Horizontal component: F_horizontal_2 = 60 N * cos(90) = 60 N * 0 = 0
Step 2: Add the horizontal and vertical components separately to find the resultant components.
Vertical component of the resultant: F_vertical_res = F_vertical_1 + F_vertical_2 = 80 N + 60 N = 140 N
Horizontal component of the resultant: F_horizontal_res = F_horizontal_1 + F_horizontal_2 = 0 + 0 = 0
Step 3: Find the magnitude and direction of the resultant force.
The magnitude of the resultant force can be found using the Pythagorean theorem:
Resultant magnitude = sqrt((F_horizontal_res)^2 + (F_vertical_res)^2)
Resultant magnitude = sqrt((0)^2 + (140 N)^2) = sqrt(0 + 19600 N^2) = sqrt(19600 N^2) = 140 N
The direction of the resultant force can be found using the inverse tangent function:
Resultant direction = arctan(F_vertical_res / F_horizontal_res)
Since F_horizontal_res = 0, the direction is perpendicular to the x-axis and parallel to the y-axis. In this case, the direction is 90 degrees.
Step 4: Draw the system of forces:
In this case, the forces are perpendicular to each other, so you can draw two arrows starting from the same point and forming a right angle between them. The 80 N force can be drawn vertically upwards, and the 60 N force can be drawn horizontally towards the right. The resultant force, with a magnitude of 140 N, can be drawn diagonally from the starting point with a direction of 90 degrees (upwards).
Please note that angles are usually measured counterclockwise from the positive x-axis, so 90 degrees is upwards in this case.
To calculate the resultant force, we can use the concept of vector addition. Since the forces are inclined at an angle of 90 degrees to each other, we can treat them as perpendicular forces.
Step 1: Calculate the horizontal and vertical components of each force.
- Force 1 (80 N):
- Horizontal component: 80 N * cos(90°) = 0 N (no horizontal component)
- Vertical component: 80 N * sin(90°) = 80 N
- Force 2 (60 N):
- Horizontal component: 60 N * cos(0°) = 60 N
- Vertical component: 60 N * sin(0°) = 0 N (no vertical component)
Step 2: Add up the horizontal and vertical components separately.
- Resultant horizontal component: 0 N + 60 N = 60 N
- Resultant vertical component: 80 N + 0 N = 80 N
Step 3: Calculate the magnitude and direction of the resultant force using Pythagoras' theorem and trigonometry.
- Magnitude of the resultant force (R): √(Resultant horizontal component² + Resultant vertical component²)
= √(60 N)² + (80 N)² = √(3600 N² + 6400 N²) = √(10000 N²) = 100 N
- Direction of the resultant force: tan^(-1)(Resultant vertical component / Resultant horizontal component)
= tan^(-1)(80 N / 60 N) = tan^(-1)(4/3) ≈ 53.13°
Step 4: Draw the system of forces.
- Draw a coordinate system.
- Draw a vector for each force.
- Place the vectors tip-to-tail, with the tail of the second force connected to the tip of the first force.
- The resultant force (R) is the vector from the tail of the first force to the tip of the second force.
- The direction of the resultant force is the angle made with the positive x-axis.
So, the resultant force is 100 N and its direction is approximately 53.13° with the positive x-axis.