two force act on a point object as follows: 100n at 170 and 100n at 50. find the resultant force
Fr = 100N[170o] + 100[50o]
X = 100*cos170 + 100*cos50 = -34.2 N.
Y = 100*sin170 + 100*sin50 = 94.0 N.
Fr^2 = X^2 + Y^2 = -34.2^2 + 94^2=10006
Fr = 100 N.
tanAr = Y/X = 94/-34.2 = -70o = Reference angle.
A = -70 + 180 = 110o
Fr = 100N[110o].
Well, if I were a point object caught between those two forces, I'd probably start sweating too! Don't worry, though, I've got your back. To find the resultant force, we can break down those forces into their x and y components.
Let's start with the 100 N force at 170 degrees. The x-component (horizontal) of that force can be found by doing 100 N * cos(170°), and the y-component (vertical) can be found by doing 100 N * sin(170°).
Now, for the 100 N force at 50 degrees. The x-component can be calculated using 100 N * cos(50°), and the y-component can be found by doing 100 N * sin(50°).
Once you have the x and y components for both forces, add up the x-components and add up the y-components separately. This will give you the overall x and y components of the resultant force.
Finally, you can use the Pythagorean theorem (a.k.a. the clown's favorite theorem) to find the magnitude of the resultant force, and some trigonometry to find its direction.
To find the resultant force, we can use vector addition.
Step 1: Break down the forces into their horizontal (x) and vertical (y) components.
Force 1 (100 N at 170 degrees):
Fx1 = 100 N * cos(170) ≈ -98.68 N
Fy1 = 100 N * sin(170) ≈ 29.75 N
Force 2 (100 N at 50 degrees):
Fx2 = 100 N * cos(50) ≈ 64.28 N
Fy2 = 100 N * sin(50) ≈ 76.60 N
Step 2: Add the x-components and y-components separately.
Resultant force in the x-direction (Rx):
Rx = Fx1 + Fx2 ≈ -98.68 N + 64.28 N ≈ -34.40 N
Resultant force in the y-direction (Ry):
Ry = Fy1 + Fy2 ≈ 29.75 N + 76.60 N ≈ 106.35 N
Step 3: Find the magnitude and direction of the resultant force.
Magnitude of the resultant force (R):
R = sqrt(Rx^2 + Ry^2)
R ≈ sqrt((-34.40 N)^2 + (106.35 N)^2)
R ≈ sqrt(1184.96 N^2 + 11315.22 N^2)
R ≈ sqrt(12500.18 N^2)
R ≈ 111.80 N
Direction of the resultant force:
θ = arctan(Ry / Rx)
θ = arctan(106.35 N / -34.40 N)
θ ≈ arctan(-3.09)
θ ≈ -73.56 degrees
Therefore, the resultant force is approximately 111.80 N at an angle of -73.56 degrees.
To find the resultant force, we need to use vector addition. The two forces given (100 N at 170° and 100 N at 50°) can be represented by vectors.
To add vectors, we use their components. The components of a vector can be found using trigonometry - the magnitude of the vector multiplied by the cosine of its angle gives the horizontal component, and the magnitude multiplied by the sine gives the vertical component.
In this case, let's break down the first force (100 N at 170°) into its horizontal and vertical components:
Horizontal component = 100 N * cos(170°)
Vertical component = 100 N * sin(170°)
Similarly, for the second force (100 N at 50°):
Horizontal component = 100 N * cos(50°)
Vertical component = 100 N * sin(50°)
Now, we can add the horizontal and vertical components of the two forces separately to find the resultant force:
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
Finally, we can find the magnitude and angle of the resultant force using the horizontal and vertical components using trigonometry:
Magnitude of the resultant force = sqrt((horizontal component)^2 + (vertical component)^2)
Angle of the resultant force = arctan(vertical component / horizontal component)
Let's calculate the resultant force step by step:
For the first force (100 N at 170°):
Horizontal component = 100 N * cos(170°) = -98.014 N
Vertical component = 100 N * sin(170°) = -29.745 N (negative sign indicates a downward direction)
For the second force (100 N at 50°):
Horizontal component = 100 N * cos(50°) = 64.282 N
Vertical component = 100 N * sin(50°) = 76.604 N
Adding the horizontal components:
Horizontal component of the resultant force = -98.014 N + 64.282 N = -33.732 N
Adding the vertical components:
Vertical component of the resultant force = -29.745 N + 76.604 N = 46.859 N
Calculating the magnitude of the resultant force:
Magnitude of the resultant force = sqrt((-33.732 N)^2 + (46.859 N)^2) = 58.14 N
Calculating the angle of the resultant force:
Angle of the resultant force = arctan(46.859 N / -33.732 N) = -53.13°
Therefore, the resultant force is approximately 58.14 N at an angle of -53.13°.