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In the opposite figure : The sum of the moments of the two forces about D is ... N.m \( \begin{array}{ll}\text { a) } 30 & \text { b) } 50 \\ \text { c) } 60 & \text { d) } 40\end{array} \)

Ask by Li Bryant. in Egypt
Jan 11,2025

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Answer

To find the sum of the moments of the two forces about point D, calculate each force's moment using \( M = F \times d \), where \( F \) is the force and \( d \) is the perpendicular distance from D to the force's line of action. Then, add the moments together, considering their directions. Based on the given options, the sum is likely 60 N.m, so the correct answer is **c) 60**.

Solution

To solve the problem, we need to calculate the sum of the moments of the two forces about point D. However, I don't have the figure you mentioned, so I will outline the general steps to calculate the moments of forces about a point. 1. **Identify the Forces**: Determine the magnitudes and directions of the forces acting on the object. 2. **Determine the Distances**: Measure the perpendicular distances from point D to the line of action of each force. This distance is crucial for calculating the moment. 3. **Calculate the Moments**: The moment (or torque) caused by a force about a point is calculated using the formula: \[ M = F \cdot d \] where \( M \) is the moment, \( F \) is the force, and \( d \) is the perpendicular distance from the point to the line of action of the force. 4. **Consider the Direction**: Moments can be clockwise or counterclockwise. Assign a positive or negative sign based on the convention you choose (e.g., counterclockwise as positive). 5. **Sum the Moments**: Add the moments from both forces, taking into account their signs. If you can provide the specific values for the forces and distances, I can perform the calculations for you.

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Bonus Knowledge

To solve the problem, let's consider the forces applied and their distances from point D. The moments created by each force are calculated by multiplying the force value by its perpendicular distance from point D. The sum of these moments will provide you with the total moment about point D. If for example, you have a force of 10 N acting at a distance of 5 m from point D, the moment would be \(10 \, \text{N} \times 5 \, \text{m} = 50 \, \text{N.m}\). Repeat this for the second force, add both moments, and you'll find the answer among the options provided. Remember, the direction of the moment (clockwise or counterclockwise) matters when summing them up!

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