Question

To understand the concept of moment of a force and how to calculate it using a scalar formulation.

The magnitude of the moment of a force with a magnitude F around a point O is defined as follows:
MO=Fd
where d is the force's moment arm. The moment arm is the perpendicular distance from the axis at point O to the force's line of action.
A stool at a restaurant is anchored to the floor. When a customer is in the process of sitting down, a horizontal force with magnitude F1 is exerted at the top of the stool support. When the customer is seated, a vertical force with magnitude F2 is exerted on the stool support. If the maximum moment magnitude that the stool support can sustain about point A is MA = 160 Nm , what is the maximum height d1 that the stool can have if the magnitudes of the two forces are F1 = 300 N and F2 = 720 N . Assume that moments acting counterclockwise about point A are positive whereas moments acting clockwise about A are negative.

Answer 1

When analyzing forces in a structure or machine, it is conventional to classify forces as external forces;

constraint forces or internal forces.

External forces arise from interaction between the system of interest and its surroundings.

Examples of external forces include gravitational forces; lift or drag forces arising from wind loading;

electrostatic and electromagnetic forces; and buoyancy forces; among others. Force laws governing these

effects are listed later in this section.

Constraint forces are exerted by one part of a structure on another, through joints, connections or contacts

between components. Constraint forces are very complex, and will be discussed in detail in Section 8.

Internal forces are forces that act inside a solid part of a structure or component. For example, a stretched

rope has a tension force acting inside it, holding the rope together. Most solid objects contain very

complex distributions of internal force. These internal forces ultimately lead to structural failure, and also

cause the structure to deform. The purpose of calculating forces in a structure or component is usually to

deduce the internal forces, so as to be able to design stiff, lightweight and strong components. We will

not, unfortunately, be able to develop a full theory of internal forces in this course – a proper discussion

requires understanding of partial differential equations, as well as vector and tensor calculus. However, a

brief discussion of internal forces in slender members will be provided in Section 9.

Step-by-step explanation: