FIGURE 8.1 below shows a system of four forces acting on the same point. Answer the questions that follow. HINT: Draw and complete the diagram for the forces shown in FIGURE 8.1. Show ALL the horizontal and vertical components before doing the calculations. Calculate the following: 8.1.1 The sum of the horizontal components 8.1.2 The sum of the vertical components 8.1.3 The magnitude of the resultant 8.1.4 The angle and direction of the resultant

NSC Mechanical Technology Fitting and Machining Basic First Aid: FIGURE 8.1 below shows a system

FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Question 8

FIGURE 8.1 below shows a system of four forces acting on the same point. Answer the questions that follow. HINT: Draw and complete the diagram for the forces shown ... show full transcript

Worked Solution & Example Answer:FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Step 1

8.1.1 The sum of the horizontal components

96%

114 rated

Answer

To find the sum of the horizontal components, we analyze the forces acting horizontally:

The horizontal component of the 120 N force at an angle of 70° is given by: $= 120 imes 0.342 = 41.04 \, N$$$
The horizontal component of the 55 N force at an angle of 60° is: $= 55 imes 0.5 = 27.5 \, N$$$

Thus, the total horizontal components: $ext{Total horizontal} = 41.04 \, N + 27.5 \, N = 68.54 \, N$

Step 2

8.1.2 The sum of the vertical components

99%

104 rated

Answer

For the vertical components, we consider:

The vertical component of the 25 N force is: $25 \, N$
The vertical component of the 40 N force is: $40 \, N$
The vertical component of the 120 N force:
$= 120 imes 0.940 = 112.8 \, N$$$
The vertical component of the 55 N force:
$= 55 imes 0.866 = 47.63 \, N$$$

Combining these: $ext{Total vertical} = 25 + 40 + 112.8 + 47.63 = 225.43 \, N$

Step 3

8.1.3 The magnitude of the resultant

96%

101 rated

Answer

The magnitude of the resultant vector can be calculated using:

= ext{sqrt}(68.54^2 + 225.43^2) \\ = ext{sqrt}(4693.8116 + 50880.0649) \\ = ext{sqrt}(55573.8765) \\ = 235.77 \, N$$

Step 4

8.1.4 The angle and direction of the resultant

98%

120 rated

Answer

The angle of the resultant can be found using:

= an^{-1}igg( rac{225.43}{68.54}igg) \\ = an^{-1}(3.29) \\ heta \\ ext{Angle} = 73.2°$$ Thus, the direction of the resultant is 73.2° above the horizontal.

FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

Worked Solution & Example Answer:FIGURE 8.1 below shows a system of four forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2022 - Paper 1

8.1.1 The sum of the horizontal components

8.1.2 The sum of the vertical components

8.1.3 The magnitude of the resultant

8.1.4 The angle and direction of the resultant

Join the NSC students using SimpleStudy...