ENGINEERING SCIENCE N4 TUTORIAL ASSIGNMENT
1.1. Two vehicles move simultaneously, vehicle P moves at 220 km/h east while vehicle Q moves at
220 km/h in a direction W30° N. Calculate the velocity of vehicle P relative to Q.
(4)
1.2.
Various options are given as possible answers to the following questions. Choose the answer and write
only the letter (A–D) next to the question number (3.1–3.4) in the ANSWER BOOK.
The minute arm of a tower clock is 1,8 m long. It took 35 minutes to move from 2 to 9.
1.2.1
The angular displacement of the minute arm is …
A
2,345 rad.
B
3,665 rad.
C
3,345 rad.
D
2,665 rad.
1.2.2
The arc length produced by the tip of the minute arm is …
A
4,835 m.
B
5,524 m.
C
6,597 m.
D
4,524 m.
1.2.3
The angular velocity of the minute arm is …
A
2,327 × 10-3 m.
B
1,745 × 10-3 m.
C
2,117 × 10-3 m.
D
1,227 × 10-3 m.
1.2.4
The linear velocity/tangential velocity of the minute arm is:
A
B
C
D
2,447 ×10-3 m/s.
4,189 × 10-3 m/s.
4,447 × 10-3 m/s.
3,141 × 10-3 m/s.
(4 × 2)
[8]
1.3.A priest is in a rested motorcar, with a mass of 780 kg, at the top of a slope of 80%. When he releases the brakes of
the motorcar, it moves freely down for 25 m due to gravitational force to the bottom of the slope and then immediately
onto a horizontal road until it comes to a rest at the bottom of the slope.
Calculate the following:
1.3.1
1.3.2
The velocity of the motorcar at the bottom of the slope.
(3)
The deceleration of the motorcar on the horizontal road, if it took 12 seconds to
travel on the horizontal road.
(2)
1.3.3 What is the kinetic energy of the motorcar after 12 seconds on the horizontal road?
(1)
1.4. The plunger of a hydraulic press has a diameter of 90 mm with a stroke length of 480 mm while the diameter of
the ram is 180 mm. The mechanical advantage of the plunger is 18.
Calculate:
1.4.1. The force to be applied to the leaver to lift a load of 4,2 Mg if efficiency is 96%
(5)
1.4.2. The number of the pumping strokes needed to lift the load of 220 mm at efficiency of 96%.[4]
1.5. The plunger of a two-cylinder pump has a diameter of 150 mm and a stroke length of 250 mm.
Calculate:
1.5.1 The volume delivered in l/s.
1.5.2. The slip% if the volume delivered in 16.789 l/s.
TUTORIAL 2
2.1. A stone is thrown at a velocity of 29 m/s at an angle of 35° to the horizontal.
(4)
(2)
Calculate the following:
2.1.1 The maximum height that the stone reaches
.2.1.2 The horizontal displacement or range
(2 × 3)
(6)
2.2.
An aeroplane flies to its destination, 300 km directly east of its starting point. The pilot wants to complete the
flight in 50 minutes. A wind blows in a north-eastern direction at 10 m/s.
Calculate the following:
2.3.1
2.3.2
The velocity of the aeroplane
The direction of the flight
(4)
(2)
2.4. The spindle of a drilling machine rotating at 1 500 r/min slows down to 600 r/min while making 48 revolutions.
Calculate the following:
2.4.1 The angular retardation of the drilling machine in rad/s2
2.4.2 The time taken to slow down
(2)
(5)
2.5. A motorcar with a mass of 1,2 tonnes is at rest at the top of an incline of 1 : 30. The length of the incline is
62 metres. The frictional force of 200 N is constant (uniform). The brakes are released and the car moves
downwards due to the gravitational force, and then onto a horizontal road.
Calculate the following:
2.5.1 The velocity of the car at the bottom of the incline
(6)
2.5.2 The force applied by the motorcar on the horizontal road
(1)
2.5.3 The distance where the car will come to rest if it continues to travel on the horizontal road
2.6. A beam ABCDE, with A on the left-hand side, is 10 m long and simply supported at A and D.
Point loads of 50 N and 30 N are at B and E respectively. AB = 2 m and DE = 2 m.
An evenly distributed load of 2 N/m is between A and D.
2.6.1
2.6.2
2.6.3
(3)
First draw the beam, then calculate the reaction forces of A and D.
(5)
Calculate the bending moments at B and D and at a point C halfway between B and D.
(3)
Draw the bending moment and shearing force diagrams with the main values indicated on the diagram.
(7)
TUTORIAL 3
1.1A ship that can cruise at 42 km/h in still waters sets course due south-west. It is driven off course by a current
flowing West 22° North at a velocity of 7,2 km/h.
Calculate the following:
1.1.1 The resultant velocity in magnitude and direction.
(5)
1.1.2 The distance the ship will cruise in 5 hours.
(1)
1.2
A bullet is fired at an angle of 29o to the horisontal at a velocity of 410 m/s.
Calculate the following:
1.2.1 The maximum height reached by the bullet.
1.2.2 The horisontal displacement when the bullet hits the ground.
(2)
(2)
1.3
Two vehicles start moving simultaneously at a fork in a road. Vehicle V travels at a speed of 125 km/h northeast. Vehicle W travels at 125 km/h directly east.
Calculate the velocity of vehicle W relative to the velocity of vehicle V in magnitude and direction.
(5)
1.4.
A point on the rim of a wheel with a diameter of 500 mm has a velocity of
Calculate the following:
1.4.1 The revolutions per minute (rev/min).
1.4.2 The angular velocity in rad/s at which the wheel is turning.
The engine of a vehicle develops 67 kW at a speed of 1 200 r/min.
Calculate the torque developed.
The following data refers to a single-acting hydraulic jack:
1.5.
1.6.
200 km/h.
(3)
(2)
(2)
Diameter of the ram
Diameter of the plunger
Plunger stroke length
Mechanical advantage on the lever
1.6.1
1.6.2.
=
=
=
=
510 mm
15 % diameter of the ram
100 mm
25
Calculate the following:
The force to be applied to the lever to lift a load of 5 tons if the slip is 9%.
(5)
The number of pumping strokes needed to lift a load 410 mm if there is no slip. [5]
1.7. The plungers of a three-cylinder pump have diameters of 12 cm and a stroke length of 50 cm. The pressure
during the delivery stroke is 1 000 kPa.
Calculate the following:
1.7.1. The power required to drive the pump at 350 r/min if the efficiency of the motor is 90 %.
(5)
1.7.2. The volume of water delivered per minute in ℓ/min if there is a slip of 13 %.
(4)
1.8. A body is projected at such an angle that the maximum height is two-thirds of the range. The initial velocity is
350 m/s. Calculate the angle of the projectile.
[5]
1.9. Two vehicles start simultaneously at a fork in a road. Vehicle A travels north-east at 90 km/h and vehicle B
travels west at 110 km/h. Calculate the velocity of vehicle A relative to the velocity of vehicle B in
magnitude and direction.
(5)
1.10. An aeroplane can travel at 200 km/h in still air. A wind is blowing at 60 km/h from the south-west.
Calculate the following:
1.101 The direction in which the pilot must steer in order to travel due north
1.10.2 The velocity of the aeroplane in relation to the ground
(2 x 2½) (5)
1.11. A train starts from rest on the top of a 2% incline and runs 1 km down the incline under the force due to gravity
only. The resistance against motion is constant at 60 N/ton. Calculate the velocity of the train at the foot of the
incline after 1 km by making use of the law of the conservation of energy.
HINT: Let the mass of the train be m.kg
[5]
1.12. The piston of a single-acting water pump has a diameter of 100 mm and a delivery stroke of 80 mm. The water
must be pumped to a vertical height of 20 m
Calculate:
1.12.1 The volume of water which is being pumped per delivery stroke
(3)
1.12.2 The mass of water pumped per delivery stroke
(2)
1.12.3 The work done per stroke
(3)
TUTORIAL 4
1.
A beam ABCDE, with A on the left-hand side, is 10 m long and simply supported at A and D. D is 2 m from
E. Point loads of 50 N and 30 N are at B (2 m from A) and E respectively. An evenly distributed load of
2 N/m is between A and D. C is a point half way between B and D.
1.1
1.2
1.3
1.4
Make a neat labelled drawing of the beam.
Calculate the reaction forces at supports A and D.
Calculate the bending moments at B, C and D.
Draw the shearing force and bending moment diagrams with the main values indicated on the
diagrams.
2. An aeroplane can travel at 150 km/h in still air. The wind is blowing at
50 km/h from the south-west.
Calculate the following:
2.1
The direction in which the pilot must steer in order to travel due north.
2.2. The velocity of the aeroplane in relation to the ground.
(1)
(4)
(3)
(3 x 2)
3. The mechanical advantage of the lever is 10. The efficiency is 85%. The diameter of the ram piston is 300 mm
(6)
and that of the plunger is 30 mm.
Calculate the force exerted by the ram piston if an effort of 150 N is applied to the lever of a hydraulic press. [5]
4. A two-cylinder waterpump is running at 120 r/min. The diameter of the plunger is 150 mm and the stroke length is
250 mm. Calculate the following:
4.1. The volume of water delivered in litres every second. [2]
4.2. The pressure needed to pump the water through a height of 30 m.
(4)
5. A ship cruises at 12 km/h in still waters and sets course due south west. It is driven off course by a current flowing
W 15° N at a rate of 4 km/h.
5.1. Draw a neat vector diagram to represent the information. Include the resultant in the diagram.
5.2. Calculate the magnitude and direction of the resultant velocity.
(3)
(2)
6. A projectile is launched at an angle of 30° with the horizontal, with a velocity of 125 m/s.
Calculate the following:
6.1
6.2
6.3
The time taken for the projectile to hit a target at ground level on the same horizontal plane
The maximum range that a projectile of this kind can reach
The height reached by the projectile above the horizontal after travelling for 5 seconds
(2)
(1)
(2)
7. Ship A sails at 30 km/h north 48° west, whilst ship B is sailing at 20 km/h south 15° east.
7.1
Draw a neat vector diagram and show clearly the vector representing the velocity of ship A relative to ship B
7.2. Calculate the velocity of ship A relative to ship B in magnitude and direction.
(2)
8. A machine has a torque of 50 Nm at its spindle. The diameter of the spindle is 50 50 cm and the rotational
frequency is 3 rad/s.
Calculate the following:
8.1. The work done by the machine in 25 seconds
8.2. The input power if the efficiency is 75%
(2 x2)
9. The force on a crankshaft with a length of 2,4 m changes from 0 N to 400 N during one revolution.
Calculate the following:
9.1
9.2
The average torque during ONE revolution
The average work done during ONE revolution
10. Calculate the force exerted by the ram piston if an effort of 200 N is applied to the lever of a hydraulic press.
The mechanical advantage of the lever is 15 and the efficiency on the press is 93%. The diameter of the plunger
is 0,1 times that of the diameter of the ram. [5]