Final answer:
To produce a state of equilibrium on the body, a force of 4.12 pounds to the left and 7.12 pounds downward is needed, which can also be expressed as a single resultant force calculated using the Pythagorean theorem and trigonometry.
Step-by-step explanation:
To achieve equilibrium for a body, the first condition that needs to be satisfied is that the net external force on the system must be zero, meaning net F = 0. In the given scenario, a body is subjected to three different forces: 2 pounds to the right, 5 pounds upward, and 3 pounds at a 45-degree angle from the horizontal. To find the single force that would balance these out, we must take vector components into account and sum them accordingly.
The force acting at 45 degrees can be split into horizontal and vertical components using trigonometry. The horizontal component (3 pounds × cos(45)) is approximately 2.12 pounds to the right, and the vertical component (3 pounds × sin(45)) is also approximately 2.12 pounds upward. Summing the horizontal forces: 2 pounds to the right + 2.12 pounds to the right = 4.12 pounds to the right. Summing the vertical forces: 5 pounds upward + 2.12 pounds upward = 7.12 pounds upward.
To create equilibrium, a single force with an equal magnitude but opposite direction is required. Therefore, a force of 4.12 pounds to the left and 7.12 pounds downward is needed. This can also be presented as a single resultant force by using the Pythagorean theorem: √(4.12² + 7.12²) pounds, which would be directed at an angle of tan⁻¹(7.12/4.12) from the horizontal.