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.
1. State whether the following are scalar or vector
quantities:
(a) A temperature of 50 ◦ C
(b) A downward force of 80 N
(c) 300 J of work
(d) A south-westerly wind of 15 knots
(e) 70 m distance
(f) An acceleration of 25 m/s 2 at 30 ◦ to the
horizontal
(6)
2. Calculate the resultant and direction of the force
vectors shown in Fig. RT8.1, correct to 2 decimal
places.
(7)
5 N
7 N
Figure RT8.1
3. Four coplanar forces act at a point A as shown
in Fig. RT8.2 Determine the value and direction of the resultant force by (a) drawing (b) by
calculation using horizontal and vertical components.
(10)
5 N
4 N
8 N
7 N
458
458
A
Figure RT8.2
4. The instantaneous values of two alternating voltages are given by:
v 1 = 150 sin(ωt + π/3) volts and
v 2 = 90 sin(ωt − π/6) volts
Plot the two voltages on the same axes to scales
of 1 cm = 50 volts and 1 cm =
π
6
rad.
Obtain a sinusoidal expression for the resultant
v 1 + v 2 in the form R sin(ωt + α): (a) by adding
ordinates at intervals and (b) by calculation.
(13)
5. If velocity v 1 = 26 m/s at 52 ◦ and v 2 = 17 m/s
at −28 ◦ calculate the magnitude and direction
of v 1 + v 2 , correct to 2 decimal places, using
complex numbers.
(10)
6. Given a = −3i + 3j + 5k, b = 2i − 5j + 7k and
c = 3i + 6j − 4k, determine the following:
(i) −4b (ii) a + b − c (iii) 5b − 3c.
( 8 )
7. If a = 2i + 4j −5k and b =3i − 2j +6k determine:
(i) a ·b (ii) |a +b| (iii) a × b (iv) the angle between
a and b.
(14)
8. Determine the work done by a force of F newtons
acting at a point A on a body, when A is displaced
to point B, the co-ordinates of A and B being (2, 5,
−3) and (1, −3, 0) metres respectively, and when
F = 2i −5j + 4k newtons.
(4)
9. A force of F =3i −4j + k newtons acts on a line
passing through a point P. Determine moment M
and its magnitude of the force F about a point Q
when P has co-ordinates (4, −1, 5) metres and Q
has co-ordinates (4, 0, −3) metres.
(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.
1. State whether the following are scalar or vector
quantities:
(a) A temperature of 50 ◦ C
(b) A downward force of 80 N
(c) 300 J of work
(d) A south-westerly wind of 15 knots
(e) 70 m distance
(f) An acceleration of 25 m/s 2 at 30 ◦ to the
horizontal
(6)
2. Calculate the resultant and direction of the force
vectors shown in Fig. RT8.1, correct to 2 decimal
places.
(7)
5 N
7 N
Figure RT8.1
3. Four coplanar forces act at a point A as shown
in Fig. RT8.2 Determine the value and direction of the resultant force by (a) drawing (b) by
calculation using horizontal and vertical components.
(10)
5 N
4 N
8 N
7 N
458
458
A
Figure RT8.2
4. The instantaneous values of two alternating voltages are given by:
v 1 = 150 sin(ωt + π/3) volts and
v 2 = 90 sin(ωt − π/6) volts
Plot the two voltages on the same axes to scales
of 1 cm = 50 volts and 1 cm =
π
6
rad.
Obtain a sinusoidal expression for the resultant
v 1 + v 2 in the form R sin(ωt + α): (a) by adding
ordinates at intervals and (b) by calculation.
(13)
5. If velocity v 1 = 26 m/s at 52 ◦ and v 2 = 17 m/s
at −28 ◦ calculate the magnitude and direction
of v 1 + v 2 , correct to 2 decimal places, using
complex numbers.
(10)
6. Given a = −3i + 3j + 5k, b = 2i − 5j + 7k and
c = 3i + 6j − 4k, determine the following:
(i) −4b (ii) a + b − c (iii) 5b − 3c.
( 8 )
7. If a = 2i + 4j −5k and b =3i − 2j +6k determine:
(i) a ·b (ii) |a +b| (iii) a × b (iv) the angle between
a and b.
(14)
8. Determine the work done by a force of F newtons
acting at a point A on a body, when A is displaced
to point B, the co-ordinates of A and B being (2, 5,
−3) and (1, −3, 0) metres respectively, and when
F = 2i −5j + 4k newtons.
(4)
9. A force of F =3i −4j + k newtons acts on a line
passing through a point P. Determine moment M
and its magnitude of the force F about a point Q
when P has co-ordinates (4, −1, 5) metres and Q
has co-ordinates (4, 0, −3) metres.
(8)