Mechanical Engineering Principles

FORCES ACTING AT A POINT 37

6. The following coplanar forces act at a
   point: forceA, 15 N acting horizontally
   to the right, force B,23Nat81° to
   the horizontal, forceC, 7 N at 210° to
   the horizontal, forceD, 9 N at 265°to the
   horizontal, and forceE, 28 N at 324°to
   the horizontal. Determine the resultant of
   the five forces by resolution of the forces.
   [34.96 N at− 10. 23 °to the horizontal]

3.11 Summary

(a) To determine theresultant of two coplanar

forcesacting at a point, four methods are

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 theresultant 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


4. State what is meant by a polygon of
   forces


5. When a vector diagram is drawn repre-
   senting coplanar forces acting at a point,
   and there is no resultant, the forces are
   in..........


6. Two forces of 6 N and 9 N act horizon-
   tally to the right. The resultant is.....N
   acting.......


7. 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
   ......Nactingatanangleof....°


8. What is meant by ‘resolution of forces’?


9. 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