A system of forces is shown in FIGURE 7.1 - NSC Mechanical Technology Welding and Metalwork - Question 7 - 2016 - Paper 1

To determine the resultant of the vertical components, we evaluate each force in the vertical direction:

• Vertical component of 2.1 kN = 2.1 kN
• Vertical component of 3.1 kN = 3.1 * sin(50°) = 2.37 kN
• Vertical component of 1.5 kN = 1.5 * sin(40°) = 0.96 kN

Adding these vertical components gives us: $R_V = 2.1 + 0.96 - 2.37 = 0.69 \, kN$

The magnitude of the equilibrium force can be calculated using the Pythagorean theorem:

$E = ext{sqrt}(R_H^2 + R_V^2)$

Substituting values: $E = ext{sqrt}(1.56^2 + 0.69^2) = ext{sqrt}(2.4336 + 0.4761) = ext{sqrt}(2.9097) \\ = 1.71 \, kN$

The angle of equilibrium can be calculated using the tangent function:

$an( heta) = \frac{R_V}{R_H}$

Substituting the computed values: $an( heta) = \frac{0.69}{1.56}$

Calculating the angle: $heta = \tan^{-1}(0.69/1.56) \approx 23.86°$

To find the stress in the bolt material, we first calculate the force acting on the bolt:

• The load is 600 kg, so the force is given by: $F = mass \times gravity = 600 \times 9.81 \, N = 5886 \: N$

Next, we find the area of the bolt (with an M16 bolt diameter approximately 16 mm): $Area = \pi \left( \frac{d}{2} \right)^2 = \pi \left( \frac{0.016 \: m}{2} \right)^2 \\ = 2.01 \times 10^{-4} \, m^2$

Finally, we calculate the stress: $Stress = \frac{Force}{Area} = \frac{5886}{2.01 \times 10^{-4}} \approx 29.84 \: MPa$

One Pascal (Pa) is defined as one Newton per square meter (1 N/m²) and is used as a measure of pressure or stress.