Math Problem Statement

calcular fuerza neta

calcular fuerza neta

Solution

The image you uploaded shows two forces: a 20 N force pointing to the right (positive x-axis) and a 10 N force pointing downward (negative y-axis). To calculate the net force, we can treat this as a vector problem, combining the forces in the x and y directions.

Steps to calculate the net force:

  1. Force in the x-direction (horizontal):

    • The 20 N force is along the positive x-axis.
    • So, Fx=20NF_x = 20 \, \text{N}
  2. Force in the y-direction (vertical):

    • The 10 N force is along the negative y-axis.
    • So, Fy=10NF_y = -10 \, \text{N}
  3. Magnitude of the net force: The magnitude of the net force vector is the square root of the sum of the squares of the components in the x and y directions:

    Fnet=Fx2+Fy2F_{\text{net}} = \sqrt{F_x^2 + F_y^2} Substituting the values:

    Fnet=(20)2+(10)2=400+100=50022.36NF_{\text{net}} = \sqrt{(20)^2 + (-10)^2} = \sqrt{400 + 100} = \sqrt{500} \approx 22.36 \, \text{N}

  4. Direction of the net force: To find the direction, we calculate the angle θ with respect to the positive x-axis:

    θ=tan1(FyFx)\theta = \tan^{-1}\left(\frac{F_y}{F_x}\right)

    Substituting the values:

    θ=tan1(1020)=tan1(0.5)26.57\theta = \tan^{-1}\left(\frac{-10}{20}\right) = \tan^{-1}(-0.5) \approx -26.57^\circ

Final Answer:

The magnitude of the net force is approximately 22.36 N, and its direction is 26.57° below the positive x-axis.

Would you like further details or have any questions about this? Here are some related questions:

  1. How would the result change if the direction of the 10 N force was along the positive y-axis?
  2. What would happen if both forces were acting at an angle instead of along the axes?
  3. How does the angle affect the magnitude of the net force?
  4. What is the physical significance of calculating the net force in this case?
  5. Can you describe how vector components are used in other real-world scenarios like velocity or displacement?

Tip: When dealing with forces in multiple directions, always break the forces down into their components before calculating the resultant.

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Math Problem Analysis

Mathematical Concepts

Vector Addition
Trigonometry
Force Calculations

Formulas

F_{net} = \sqrt{F_x^2 + F_y^2}
\theta = \tan^{-1}(F_y / F_x)

Theorems

Pythagorean Theorem
Basic Trigonometric Identities

Suitable Grade Level

Grades 10-12