Two forces act on a body: a horizontal force of 5 N and a vertical force of 5 N. What is the resultant force?
Understand the Problem
The question is asking to calculate the resultant force from two specific forces acting on a body, one horizontal and one vertical, and to determine which option correctly states that resultant force.
Answer
The resultant force is approximately $7.1 \, \text{N}$ at $45^\circ$.
Answer for screen readers
The resultant force is approximately $7.07 , \text{N}$ at $45^\circ$ to the horizontal.
Steps to Solve
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Identify the forces involved There are two forces: a horizontal force ($F_x = 5 , \text{N}$) and a vertical force ($F_y = 5 , \text{N}$).
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Use the Pythagorean theorem to find the resultant force The magnitude of the resultant force ($R$) can be calculated using the Pythagorean theorem:
$$ R = \sqrt{F_x^2 + F_y^2} $$
Substituting the known values:
$$ R = \sqrt{(5 , \text{N})^2 + (5 , \text{N})^2} $$
- Calculate the resultant force Now perform the calculation:
$$ R = \sqrt{25 + 25} = \sqrt{50} \approx 7.07 , \text{N} $$
- Determine the direction of the resultant force To find the angle ($\theta$) of the resultant force relative to the horizontal, use the tangent function:
$$ \tan(\theta) = \frac{F_y}{F_x} $$
Then solve for $\theta$:
$$ \theta = \tan^{-1}\left(\frac{5}{5}\right) = \tan^{-1}(1) = 45^\circ $$
The resultant force is approximately $7.07 , \text{N}$ at $45^\circ$ to the horizontal.
More Information
The calculated resultant force indicates that both forces contribute equally to the total force acting on the body. The angle confirms that the forces are balanced, creating a diagonal resultant.
Tips
- Failing to correctly apply the Pythagorean theorem, particularly when determining the components of the forces.
- Miscalculating the angle using the inverse tangent function, often because of incorrect component ratios.
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