Physics Quiz: Resultant Force Calculation

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Questions and Answers

What is the value of the horizontal component of force F₁ (F1x)?

50N
42.4N (correct)
35N
70.7N

What is the vertical component of force F₁ (F1y)?

35N (correct)
70.7N
42.4N
50N

What is the total resultant force (R) acting on the object?

95N (correct)
85N
125N
100N

At what angle is the resultant force applied with respect to the horizontal?

<p>25.8° (D)</p> Signup and view all the answers

Which of the following equations accurately represents the total horizontal force (Rx)?

<p>Rx = F1 cos 45° + F2 (D)</p> Signup and view all the answers

Flashcards

Horizontal Component of a Force

The horizontal component of a force is the part of the force that acts parallel to the ground. It is calculated by multiplying the force by the cosine of the angle between the force and the horizontal.

Vertical Component of a Force

The vertical component of a force is the part of the force that acts perpendicular to the ground. It is calculated by multiplying the force by the sine of the angle between the force and the horizontal.

Resultant Force

The resultant force is the overall force acting on an object. It is calculated by adding together all the individual forces acting on the object.

Angle of the Resultant Force

The angle of the resultant force is the angle between the resultant force and the horizontal. It can be calculated using trigonometry.

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Equation for Total Horizontal Force (Rx)

The equation for calculating the total horizontal force (Rx) is Rx = F1 cos 45° + F2. This means the horizontal force is the sum of the horizontal component of force F1 and force F2.

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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
Y-axis Calculation:
- Resultant force in the y-direction:
  - Ry = F₁y + F₂y
  - Ry = (50N)(sin 45°) + 0 = 35N

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!