commonly used. They are:
by drawing:
(1) triangle of forces method, and (2) parallelogram of forces method, and by calculation:
(3) use of cosine and sine rules, and (4) resolution of forces
(b) To determine the resultant of more than two coplanar forcesacting at a point, two methods are commonly used. They are: by drawing:
(1) polygon of forces method, and by calculation:
(2) resolution of forces Now try the following exercise
Exercise 18 Short answer questions on forces acting at a point 1. Give one example of a scalar quantity
and one example of a vector quantity 2. Explain the difference between a scalar
and a vector quantity
3. What is meant by the centre of gravity of an object?
4. Where is the centre of gravity of a rect- angular lamina?
5. What is meant by neutral equilibrium? 6. State the meaning of the term ‘coplanar’ 7. What is a concurrent force?
8. State what is meant by a triangle of forces
9. State what is meant by a parallelogram of forces
10. State what is meant by a polygon of forces
11. When a vector diagram is drawn repre- senting coplanar forces acting at a point, and there is no resultant, the forces are in. . . . .
12. Two forces of 6 N and 9 N act horizon- tally to the right. The resultant is. . . . .N acting . . . ..
13. A force of 10 N acts at an angle of 50° and another force of 20 N acts at an angle of 230°. The resultant is a force . . . .N acting at an angle of . . . .° 14. What is meant by ‘resolution of forces’? 15. A coplanar force system comprises a 20 kN force acting horizontally to the right, 30 kN at 45°, 20 kN at 180° and 25 kN at 225°. The resultant is a force of . . . . N acting at an angle of . . . .° to the horizontal
Exercise 19 Multi-choice questions on forces acting at a point (Answers on page 284) 1. A physical quantity which has direction
as well as magnitude is known as a: (a) force (b) vector (c) scalar (d) weight
2. Which of the following is not a scalar quantity?
(a) velocity (b) potential energy (c) work (d) kinetic energy
3. Which of the following is not a vector quantity?
(a) displacement (b) density (c) velocity (d) acceleration 4. Which of the following statements is
false?
(a) Scalar quantities have size or mag- nitude only
(b) Vector quantities have both magni- tude and direction
(c) Mass, length and time are all scalar quantities
(d) Distance, velocity and acceleration are all vector quantities
5. If the centre of gravity of an object which is slightly disturbed is raised and the object returns to its original position when the disturbing force is removed, the object is said to be in
(a) neutral equilibrium (b) stable equilibrium (c) static equilibrium (d) unstable equilibrium
6. Which of the following statements is false?
(a) The centre of gravity of a lamina is at its point of balance.
(b) The centre of gravity of a circular lamina is at its centre.
(c) The centre of gravity of a rectangu- lar lamina is at the point of inter- section of its two sides.
(d) The centre of gravity of a thin uni- form rod is halfway along the rod. 7. The magnitude of the resultant of the
vectors shown in Figure 3.29 is:
5 N 7 N
Figure 3.29
(a) 2 N (b) 12 N (c) 35 N (d)−2 N
8. The magnitude of the resultant of the vectors shown in Figure 3.30 is:
(a) 7 N (b) 5 N (c) 1 N (d) 12 N
4 N
3 N
Figure 3.30
9. Which of the following statements is false?
(a) There is always a resultant vector required to close a vector diagram representing a system of coplanar forces acting at a point, which are not in equilibrium.
(b) A vector quantity has both magni- tude and direction.
(c) A vector diagram representing a system of coplanar forces acting at a point when in equilibrium does not close.
(d) Concurrent forces are those which act at the same time at the same point.
10. Which of the following statements is false?
(a) The resultant of coplanar forces of 1 N, 2 N and 3 N acting at a point can be 4 N.
(b) The resultant of forces of 6 N and 3 N acting in the same line of action but opposite in sense is 3 N. (c) The resultant of forces of 6 N and 3 N acting in the same sense and having the same line of action is 9 N.
(d) The resultant of coplanar forces of 4 N at 0°, 3 N at 90° and 8 N at 180° is 15 N.
11. A space diagram of a force system is shown in Figure 3.31. Which of the vec- tor diagrams in Figure 3.32 does not rep- resent this force system?
10 N 20 N 30 N Figure 3.31 20 N 20 N 20 N 20 N 30 N 30 N 30 N 30 N 10 N Not to scale 10 N 10 N 10 N Resultant = 17.32 N Resultant = 17.32 N Resultant = 17.32 N Resultant = 17.32 N (d) (c) (a) (b) Figure 3.32
12. With reference to Figure 3.33, which of the following statements is false?
FB= 20 N FD= 8 N FC= 5 N FA= 10 N 150° 60° 30° Figure 3.33
(a) The horizontal component ofFAis 8.66 N
(b) The vertical component of FB is 10 N
(c) The horizontal component of FC is 0
(d) The vertical component of FD is 4 N
13. The resultant of two forces of 3 N and 4 N can never be equal to:
(a) 2.5 N (b) 4.5 N (c) 6.5 N (d) 7.5 N 14. The magnitude of the resultant of the
vectors shown in Figure 3.34 is: (a) 5 N (b) 13 N (c) 1 N (d) 63 N
3 N
3 N 7 N