7.1 Define the following terms: 7.1.1 A force 7.1.2 Forces in equilibrium 7.1.3 Resultant of a system of forces 7.2 A load of 40 kN causes a tensile stress of 20 MPa in a round brass bar - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2017 - Paper 1

Forces are said to be in equilibrium when the resultant force acting on a body is zero. This means that the sum of all the forces acting in any direction must be equal to zero, leading to a balanced state where there is no movement.

The resultant of a system of forces is a single force that represents the combined effect of all individual forces acting on a body. It can be determined by vector addition of the forces.

To find the diameter of the brass bar under the load:

1. Calculate the area using the stress formula:

   $$Stress = \frac{Force}{Area}$$

   Rearranging gives:

   $$Area = \frac{Force}{Stress} = \frac{40,000 N}{20 \times 10^6 N/m^2} = 0.002 \, m^2$$

2. Use the area to get the diameter:

   $$A = \pi \frac{D^2}{4} \Rightarrow D = \sqrt{\frac{4 \times A}{\pi}} = 0.0505 \, m \, \Rightarrow 50.55 \, mm$$

For the equilibrium of the beam:

1. Calculate the sum of the vertical forces:

   $$R_A + R_B = 800 N + 350 N + (80 N/m \times 6.2 m)$$ $$R_A + R_B = 800 + 350 + 496 = 1646 N$$

2. Resolve moments about point A to find R_B:

   $$R_B \times 6.2 = (800 \times 3.1) + (350 \times 1.7)$$

   After calculating:

   $$R_B = \frac{(800 \times 3.1) + (350 \times 1.7)}{6.2} = 693.96 N$$

3. Find R_A using the previously determined R_B:

   $$R_A = 1646 - R_B = 1646 - 693.96 = 952.03 N$$

Hence, the reactions at supports A and B are:

• R_A = 952.03 N
• R_B = 693.96 N