Question

A force \( F = 40 \, \text{kN} \) is applied on the hook as shown. The equivalent force-couple system at B is

• A. 40 kN in +y direction and \( M = 0 \)
• B. 40 kN in -y direction and \( M = 0 \)
• C. 40 kN in +y direction and \( M = 4000 \, \text{Nm} \) counter clockwise
• D. 40 kN in -y direction and \( M = 4000 \, \text{Nm} \) clockwise

Hint:

When calculating the moment in a force-couple system, use the perpendicular distance from the line of action of the force to the point of interest.

Answer 1

The Correct Option is D

In this problem, we need to find the equivalent force-couple system at point \( B \). The given force \( F = 40 \, \text{kN} \) acts downward at point \( A \), and we are asked to determine its equivalent system at point \( B \), which is at a distance of 100 mm along the horizontal direction.

Step 1: Analyze the force direction.
The force is applied in the negative \( y \)-direction (downward).

Step 2: Calculate the moment.
The moment \( M \) at point \( B \) is calculated as: \[ M = F \times d = 40 \, \text{kN} \times 0.1 \, \text{m} = 4000 \, \text{Nm}. \] Since the force is acting downward, the moment will cause a clockwise rotation.

Step 3: Conclusion.
The equivalent force-couple system at point \( B \) is a force of 40 kN in the negative \( y \)-direction and a moment of 4000 Nm in the clockwise direction.

Final Answer: \text{(D) 40 kN in -y direction and \( M = 4000 \, \text{Nm} \) clockwise}