Understanding the Forces
When two forces act at an angle to each other, we can find the resultant force and the individual components of each force. Here we have two forces: 5 kg-wt and 10 kg-wt, acting at an inclination of 60 degrees.
Force Breakdown
- Force 1 (F1): 5 kg-wt
- Force 2 (F2): 10 kg-wt
- Angle (θ): 60 degrees
Calculating Components
To find the components of each force, we use trigonometric functions:
- F1 Components:
- F1x = F1 * cos(θ)
- F1y = F1 * sin(θ)
- F2 Components:
- F2x = F2 * cos(θ)
- F2y = F2 * sin(θ)
Resolving Forces
Using the angle of inclination:
- F1 Components:
- F1x = 5 * cos(60) = 5 * 0.5 = 2.5 kg-wt (horizontal)
- F1y = 5 * sin(60) = 5 * (√3/2) = 5 * 0.866 = 4.33 kg-wt (vertical)
- F2 Components:
- F2x = 10 * cos(60) = 10 * 0.5 = 5 kg-wt (horizontal)
- F2y = 10 * sin(60) = 10 * (√3/2) = 10 * 0.866 = 8.66 kg-wt (vertical)
Resultant Force
Now, to find the resultant force in the x and y directions:
- Resultant in x direction (Rx):
- Rx = F1x + F2x = 2.5 + 5 = 7.5 kg-wt
- Resultant in y direction (Ry):
- Ry = F1y + F2y = 4.33 + 8.66 = 13 kg-wt
Final Calculations
The magnitude of the resultant force (R) can be calculated using the Pythagorean theorem:
- R = √(Rx^2 + Ry^2) = √(7.5^2 + 13^2)
This will give you the magnitude of the resultant force acting due to both forces at the specified angle.