Questions and Answers
What is the value of the horizontal component of force F₁ (F1x)?
What is the vertical component of force F₁ (F1y)?
What is the total resultant force (R) acting on the object?
At what angle is the resultant force applied with respect to the horizontal?
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Which of the following equations accurately represents the total horizontal force (Rx)?
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Study Notes
Resultant Force Calculation
- Two forces act on a box:
- F₁ = 50N at an angle of 45°
- F₂ = 60N at 0°
Free-Body Diagram Components
- For F₁:
- F₁x = F₁ cos 45°
- F₁y = F₁ sin 45°
- For F₂:
- F₂x = F₂
- F₂y = 0
Total Force Components
-
X-axis Calculation:
- Resultant force in the x-direction:
- Rx = F₁x + F₂x
- Rx = (50N)(cos 45°) + (60N) = 95N
- Resultant force in the x-direction:
-
Y-axis Calculation:
- Resultant force in the y-direction:
- Ry = F₁y + F₂y
- Ry = (50N)(sin 45°) + 0 = 35N
- Resultant force in the y-direction:
Resultant Force and Angle
- The total resultant force (R) is calculated from Rx and Ry.
- The angle of the resultant force can be determined using the tangent function:
- θ = arctan(Ry / Rx)
- Magnitude of the resultant can be found using the Pythagorean theorem:
- R = √(Rx² + Ry²)
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Description
Test your understanding of how to calculate the resultant force acting on an object when multiple forces are applied. This quiz will guide you through the steps to find both the magnitude and direction of the resulting force. Brush up on your knowledge of free-body diagrams and trigonometric functions!
