Moments：練習問題

How can the stability of a stool be significantly increased?

An object is in equilibrium under the action of several forces. Which of the following conditions must be met for the object to have no resultant turning effect?

The diagram shows a uniform plank of length \(4.0\text{ m}\) and weight \(100\text{ N}\) supported by a pivot at its left end and a vertical rope at its right end. A man weighing \(600\text{ N}\) stands on the plank at a distance of \(1.0\text{ m}\) from the pivot.
Calculate the tension in the rope.

Which of the following modifications would most effectively increase the stability of a tall cabinet?

A force \(F\) is applied to a wrench to loosen a bolt, as shown in the diagram. Which labeled distance represents the perpendicular distance required to calculate the moment of force \(F\) about the center of the bolt?

Calculate the moment of a force of \(25\text{ N}\) applied to a lever at a perpendicular distance of \(0.40\text{ m}\) from the pivot.

A force of \(10\text{ N}\) is applied to the handle of a door at an angle. If the perpendicular distance from the hinge to the line of action of this force is \(0.75\text{ m}\), calculate the resulting moment.

A uniform beam of weight \(60\text{ N}\) and length \(4.0\text{ m}\) is pivoted at its left end. It is held in a horizontal position by a cable attached to its right end. The cable makes an angle of \(30^\circ\) with the beam. Calculate the tension in the cable.

A uniform lever of length \( 1.6\text{ m} \) is balanced horizontally at its centre on a pivot. A load of \( 40\text{ N} \) is placed at the far left end of the lever, as shown in the diagram.

(a) Calculate the moment produced by the \( 40\text{ N} \) load about the pivot. State the unit in your answer.
(b) An upward vertical force \( F \) is applied at the far right end of the lever to keep the lever in horizontal equilibrium. Calculate the magnitude of force \( F \).
(c) Explain why the weight of the uniform lever itself does not create a moment about the pivot.