Learning Goal To understand the concept of moment of a force

Learning Goal:

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.

Part A

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 as shown in the figure. (Figure 1) 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 N?m , 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.

Solution

F₂ acts along the axis of the stool support where A is located. Therefore the moment arm for F₂ about A is zero and the moment due to F₂ about A is zero.

Moment due to F₁ about A = F₁ x d_{1 ,} F₁ = 300N

Maximum moment about A the suppport can withstand = 160N

Equating, 300 x d₁ = 160

d₁ = 160 / 300 = 0.53 m.