Find the resultant of the forces 10N and 15N with an angle of 120 between them.
To find the resultant of two forces, we can use the concept of vector addition. The resultant is the vector sum of the individual forces.
First, let's draw a diagram to visualize the situation. We have two forces: 10N and 15N, with an angle of 120 degrees between them.
10N
\
\
\
|
120°|--- 15N
Now, let's break down each force into its horizontal and vertical components. We can use trigonometry for this.
For the 10N force:
- The horizontal component (Fx1) is given by: 10N * cos(120°).
- The vertical component (Fy1) is given by: 10N * sin(120°).
Similarly, for the 15N force:
- The horizontal component (Fx2) is given by: 15N * cos(120°).
- The vertical component (Fy2) is given by: 15N * sin(120°).
Now, we can calculate the horizontal and vertical components separately:
Horizontal component (Rx) = Fx1 + Fx2
Vertical component (Ry) = Fy1 + Fy2
The resultant force, R, can be obtained using the Pythagorean theorem:
R = √(Rx² + Ry²)
Let's calculate the horizontal and vertical components:
For the 10N force:
- Fx1 = 10N * cos(120°) = -5 N (negative because it's in the opposite direction)
- Fy1 = 10N * sin(120°) = 8.66 N (rounded)
For the 15N force:
- Fx2 = 15N * cos(120°) = -7.5 N (negative because it's in the opposite direction)
- Fy2 = 15N * sin(120°) = 12.99 N (rounded)
Now, let's calculate the resultant force:
Rx = Fx1 + Fx2 = -5 N + (-7.5 N) = -12.5 N
Ry = Fy1 + Fy2 = 8.66 N + 12.99 N = 21.65 N
R = √(Rx² + Ry²) = √((-12.5 N)² + (21.65 N)²) ≈ 25.27 N
Therefore, the resultant of the forces 10N and 15N with an angle of 120 degrees between them is approximately 25.27N.
say 15 N along x axis
and 10 N 60 deg above -x axis
x force = 15 - 10 cos 60 = 10
y force = 10 sin 60 = 8.66
magnitude = sqrt(100+8.66^2)
tan angle above +x axis = .866