Question

A 50-N horizontal force is applied to the handle of the industrial water valve as shown. The force is perpendicular to the vertical plane containing line OA of the handle. Determine the equivalent force–couple system at point O.

a) The equivalent force is 50 N, and there is no equivalent couple.
b) The equivalent force is 50 N, and the equivalent couple is 0 Nm.
c) The equivalent force is 0 N, and the equivalent couple is 50 Nm.
d) The equivalent force is 0 N, and there is no equivalent couple.

Answer 1

The equivalent force is 50 N at point O, and given the information, we assume the equivalent couple is 0 Nm. This assumption holds if the force is applied directly at point O, or if the distance to the line of action of the force from point O is zero.

Step-by-step explanation:

To determine the equivalent force–couple system at point O for a 50-N force applied perpendicularly to the valve handle, one must consider not only the force but also any torque (also known as moment) that the force creates about point O. Since the problem does not provide information on the distance from point O to where the force is applied, which is essential to calculate torque, we cannot directly compute the torque value. However, with the given information, we can state that:

• The equivalent force at point O remains the same as the applied force, which is 50 N.
• Without the perpendicular distance (lever arm), we cannot determine the value of the torque (or couple).