Two forces act as 60N horizontal and 80N vertical.

Calculate the resultant.

To find the resultant of two forces acting at right angles to each other, we can use the Pythagorean theorem. In this case, we have a horizontal force of 60N and a vertical force of 80N. Since these forces are perpendicular, we can visualize them as forming a right triangle, where one side represents the horizontal force and the other side represents the vertical force.

Calculating the Resultant Force

The formula to calculate the resultant force (R) when two forces are at right angles is:

R = √(F1² + F2²)

Here, F1 is the horizontal force (60N) and F2 is the vertical force (80N). Let's plug in the values:

• F1 = 60N
• F2 = 80N

Now, substituting these values into the formula:

R = √(60² + 80²)

Calculating the squares:

• 60² = 3600
• 80² = 6400

Now, add these two results together:

3600 + 6400 = 10000

Next, take the square root of 10000:

R = √10000 = 100N

Understanding the Result

The resultant force of 100N represents the combined effect of the two forces acting together. This means that if you were to apply these two forces simultaneously, the overall effect would be equivalent to applying a single force of 100N at an angle. To find the angle of this resultant force relative to the horizontal, you can use trigonometric functions.

Finding the Angle

To determine the angle (θ) that the resultant makes with the horizontal, we can use the tangent function:

tan(θ) = Opposite / Adjacent

In this case, the opposite side is the vertical force (80N) and the adjacent side is the horizontal force (60N):

tan(θ) = 80 / 60

Calculating this gives:

tan(θ) = 1.3333

To find θ, take the arctangent (inverse tangent) of 1.3333:

θ = arctan(1.3333) ≈ 53.13°

Summary of Results

In summary, the resultant force of the two forces acting at right angles is:

• Magnitude: 100N
• Direction: Approximately 53.13° above the horizontal

This approach not only gives you the magnitude of the resultant force but also its direction, providing a complete picture of how the forces interact. If you have any further questions or need clarification on any part of this process, feel free to ask!