Revision Test 8
This Revision Test covers the material contained in Chapters 24 to 26.The marks for each question are shown in
brackets at the end of each question.
- State whether the following are scalar or vector
quantities:
(a) A temperature of 50◦C
(b) A downward force of 80N
(c) 300J of work
(d) A south-westerly wind of 15 knots
(e) 70m distance
(f) An acceleration of 25m/s^2 at 30◦to the
horizontal (6) - Calculate the resultant and direction of the force
vectors shown in Fig. RT8.1, correct to 2 decimal
places. (7)
5N7NFigure RT8.1- Four coplanar forces act at a pointAas shown
in Fig. RT8.2 Determine the value and direc-
tion of the resultant force by (a) drawing (b) by
calculation using horizontal and vertical compo-
nents. (10)
5N4N8N7N458 458AFigure RT8.2- The instantaneous values of two alternating volt-
ages are given by:
v 1 =150sin(ωt+π/ 3 )volts andv 2 =90sin(ωt−π/ 6 )voltsPlot the two voltages on the same axes to scales
of 1cm=50 volts and 1cm=π
6rad.Obtain a sinusoidal expression for the resultant
v 1 +v 2 in the formRsin(ωt+α): (a) by adding
ordinates at intervals and (b) by calculation.
(13)- If velocityv 1 =26m/s at 52◦andv 2 =17m/s
at− 28 ◦calculate the magnitude and direction
ofv 1 +v 2 , correct to 2 decimal places, using
complex numbers. (10) - Givena=− 3 i+ 3 j+ 5 k,b= 2 i− 5 j+ 7 kand
c= 3 i+ 6 j− 4 k, determine the following:
(i)− 4 b(ii)a+b−c(iii) 5b− 3 c.(8) - Ifa= 2 i+ 4 j− 5 kandb= 3 i− 2 j+ 6 kdetermine:
(i)a·b(ii)|a+b|(iii)a×b(iv) the angle between
aandb. (14) - Determine the work done by a force ofFnewtons
acting at a pointAon a body, whenAis displaced
topointB, the co-ordinates ofAandBbeing (2, 5,
−3) and (1,−3, 0) metres respectively, and when
F= 2 i− 5 j+ 4 knewtons. (4) - A force ofF= 3 i− 4 j+knewtons acts on a line
passing through a pointP. Determine momentM
and its magnitude of the forceFabout a pointQ
whenPhas co-ordinates (4,−1, 5) metres andQ
has co-ordinates (4, 0,−3) metres. (8)