describe the force board experiment to show how to obtain the resultant of two non-parallel coplanar force acting at a point.four forces of magnitude 10N, 5N, 4N, AND 6N acts on an oblect in the direction north. West, east and south respectively.find the magnitude and direction of their resultant
Determine the magnitude and direction of the resultant of these force vectors having 20newton at20degrees north east,30newtons at 40degrees north west,40newtons at 45degrees south west and 10newtons at 70degrees south east
All angles are measured CCW from the +X-axis.
Fr = 20N[20o] + 30[140o[] + 40[225o] + 10[290o].
X = 20*Cos20 + 30*Cos140 + 40*Cos225 + 10*Cos290 = -29.05 N.
Y = 20*sin20 + 30*sin140 + 40*sin225 + 10*sin290 = -11.56 N.
Fr = sqrt(X^2 + Y^2 = 31.3 N.
TanA = Y/X.
A = 21.7o S. of W. = 201.7o CCW = Direction.
Ah, the force board experiment! Alright, picture this: you've got an object chillin' on a force board, minding its own business. Now, you've got four forces acting on it, each with their own style.
First up, we've got 10N of force heading north. It's like the object is saying, "Time to go on an adventure!"
Next, we've got 5N of force pushing to the west. The object might think, "Okay, let's lean to one side and see where this takes us."
Then, we've got 4N of force pulling us to the east. The object is like, "Whoa, hold on a second! Make up your minds! Am I going west or east?!"
Lastly, we've got 6N of force pushing the object down south. Our poor object is thinking, "Alright, enough is enough! I'm ready to head south and just relax."
Now, to find the magnitude and direction of their resultant, we need to do a little math. We'll be using some good ol' trigonometry. Hang on tight!
First, let's break down the forces into their x and y-components.
The 10N north force has no east or west component, only a north component of 10N.
The 5N west force has a west component of 5N and no north or south component.
The 4N east force has an east component of 4N and no north or south component.
Finally, the 6N south force has no east or west component, only a south component of 6N.
Now, we add up all the x-components and all the y-components separately.
Summing up the x-components, we've got -5N (5N to the left due to the west force and 4N to the right due to the east force).
For the y-components, we've got a net force of 16N (10N up due to the north force and 6N down due to the south force).
Now, using the Pythagorean theorem, we can find the magnitude of the resultant force:
Resultant force = √((-5N)^2 + (16N)^2)
Calculating that out, we get:
Resultant force ≈ √(25N^2 + 256N^2) ≈ √281N^2 ≈ 16.76N (rounded to two decimal places)
So, the magnitude of the resultant force is approximately 16.76N.
Now, to find the direction, we can use some more trigonometry! The angle θ can be found using the formula:
θ = tan^(-1)(y-component / x-component)
Plugging in the values, we get:
θ = tan^(-1)(16N / -5N)
Calculating that out, we find:
θ ≈ -72.59°
Since the force is acting towards the west (negative x-direction) and pointing upwards (positive y-direction), we can say that the direction of the resultant force is approximately -72.59° from the positive x-axis (westwards and upwards).
So, to sum it up, the magnitude of the resultant force is approximately 16.76N, and its direction is approximately -72.59° from the positive x-axis (westwards and upwards).
To obtain the resultant of two non-parallel coplanar forces acting at a point, you can use a force board experiment. Here's how you can conduct the experiment:
1. Set up the force board: Start by positioning a force board on a horizontal surface. A force board consists of a flat board with three or more strings attached to it at different angles. The point where the strings are attached is the point of force application.
2. Attach the forces: Attach the four forces to the strings on the force board. Each force should be attached to correspond with the given direction (North, West, East, South). Ensure that the strings are aligned with the respective directions.
3. Measure the forces: Use a force sensor or a spring balance to measure the magnitudes of the forces. Attach the force sensor to each string separately and record the measurements. In this case, the four forces have magnitudes of 10N, 5N, 4N, and 6N.
4. Analyze the forces: To find the resultant of the forces, use vector addition. Add the forces using their respective magnitudes and directions. You can do this either graphically or mathematically.
- Graphical method: Draw each force vector to scale on a piece of paper or graph paper. Arrange the vectors head-to-tail, aligning their directions. The resultant vector is the vector from the tail of the first vector to the head of the last vector. Measure the magnitude of the resultant using a ruler and its direction using a protractor or compass.
- Mathematical method: Use the magnitude and direction angles of each vector to calculate the horizontal and vertical components of each force. Add the horizontal components together separately, and do the same with the vertical components. Use these resultant horizontal and vertical components to calculate the magnitude and direction of the resultant force using a trigonometric function such as the Pythagorean theorem or trigonometric ratios.
In this case, since the four forces are aligned with the north, west, east, and south directions, the magnitudes of the forces are 10N, 5N, 4N, and 6N, respectively. To find the magnitude and direction of their resultant, follow the steps described above to analyze the forces using either the graphical or mathematical method.
X = hor = 4 + (-5) = -1N.
Y = ver = 10 + (-6)
R = sqrt(x^2+y^2) = sqrt(1+16) = 4.12
tanA = Y / X = 4 / -1 = -4,
A = -76 deg, CW = 180-76 = 104 deg =
Direction.