Question

Determine the resultant force on the screw eye, given one rope is horizontal, the other rope is vertical, and the force in the rope is 175 lb.

Option 1:
The resultant force on the screw eye is 175 lb, acting at an angle due to the combined horizontal and vertical forces.

Option 2:
The resultant force on the screw eye is the vector sum of the horizontal and vertical forces, resulting in a force of 175 lb.

Option 3:
The resultant force on the screw eye is the square root of the sum of the squares of the horizontal and vertical forces, equaling 175 lb.

Option 4:
The vertical force contributes to the resultant force, making it greater than 175 lb in the given scenario.

Answer 1

The correct choice for determining the resultant force on the screw eye is Option 3: the square root of the sum of the squares of the horizontal and vertical forces. This uses the Pythagorean theorem as both forces are perpendicular to each other.

Step-by-step explanation:

To determine the resultant force on the screw eye when one rope is horizontal and the other is vertical, and both ropes experience a force of 175 lb, we must apply the principles of vector addition. Given that force is a vector quantity with both magnitude and direction, the resultant force can be found by adding the individual vectors along their respective axes. Since one force is horizontal and the other is vertical, they are perpendicular to each other.

Option 3 is the correct choice: The resultant force on the screw eye is the square root of the sum of the squares of the horizontal and vertical forces. According to the Pythagorean theorem, this means that if both the horizontal and vertical components of the force are 175 lb each, the resultant force R can be calculated as R = √(175^2 + 175^2), which yields a value greater than 175 lb.