Two forces act on a body. A horizontal force of 5 N and a vertical force of 12 N. What is the magnitude of the resultant force?
Understand the Problem
The question asks for the magnitude of the resultant force acting on a body when two forces, one horizontal and one vertical, are applied. The approach will involve using the Pythagorean theorem to calculate the resultant force based on the given horizontal and vertical force magnitudes.
Answer
$13\, \text{N}$
Answer for screen readers
The magnitude of the resultant force is $13, \text{N}$.
Steps to Solve
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Identify Forces
The problem states two forces: a horizontal force of 5 N and a vertical force of 12 N. -
Apply the Pythagorean Theorem
We use the Pythagorean theorem to find the resultant force ($R$). The theorem states: $$ R = \sqrt{F_{h}^2 + F_{v}^2} $$ where $F_{h} = 5, \text{N}$ and $F_{v} = 12, \text{N}$. -
Calculate the Resultant
Substituting the values into the equation: $$ R = \sqrt{(5)^2 + (12)^2} $$
Calculate $(5)^2$ and $(12)^2$: $$ R = \sqrt{25 + 144} $$
Then, $$ R = \sqrt{169} $$
Now, solve for $R$: $$ R = 13, \text{N} $$
The magnitude of the resultant force is $13, \text{N}$.
More Information
The resultant force represents the combined effect of the two perpendicular forces acting on the body. In this case, the two forces, when added using the Pythagorean theorem, yield a resultant force of 13 N, which reflects how vector forces can be combined to determine a single resultant.
Tips
- Misapplying the Pythagorean theorem: It is essential to only use this method for perpendicular forces. Ensure they are at a right angle before applying the theorem.
- Incorrect squaring: Make sure to square the magnitudes correctly; small arithmetic errors can lead to incorrect results.
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