Question

Calculate the resultant of two forces of 5.0 N and 7.0 N which are at right angles to each other.

Answer 1

The magnitude of the resultant force of two perpendicular forces of 5.0 N and 7.0 N is calculated using the Pythagorean theorem, resulting in a force of 8.6 N.

Step-by-step explanation:

To calculate the resultant of two perpendicular forces, we use the Pythagorean theorem. The forces of 5.0 N and 7.0 N form the legs of a right triangle, with the result being the hypotenuse. So we have:

Resultant (R) = √((5.0 N)² + (7.0 N)²)

R = √(25 + 49)

R = √(74)

R = 8.6 N

Therefore, the magnitude of the resultant force is 8.6 N, which is at an angle to the original forces reflecting their perpendicular relationship.

Answer 2

8.6N

Step-by-step explanation:

But we can compute the magnitude of the resultant force vector

Use Pythagorean Theorem

Resultant Force magnitude = √(5² + 7²) = √(25 + 49) = √74 = 8.6N

We are not given which force acts horizontally (in the x direction) and which force acts vertically in the y-direction so we cannot compute the exact angle for the resultant vector

If 5N is the horizontal force and 7N is the vertical force then the resultant force acts at an angle of tan⁻¹(7/5) = 54.46°

If 5N is the vertical force and 7N the horizontal force then the angle of the resultant force is tan⁻¹(5/7) = 35.54°