2023 NABTEB GCE Advanced Mechanical Engineering Science

NABTEB GCE 2023 ADVANCED MECHANICAL ENGINEERING SCIENCE

SECTION A
“`ANSWER ALL QUESTIONS“`

(1a)
(i) Coplanar force: A coplanar force refers to a set of forces that act on a single plane or are confined to a two-dimensional space. These forces share the same plane and can be represented using vector quantities indicating their magnitude and direction.

(ii) Parallel force: Parallel forces are forces that have the same direction but may or may not have the same line of action. These forces can act on different points or along different paths but share the characteristic of having parallel lines of action.

(1b)
A body is said to be in equilibrium when the net force acting on it is zero and the net torque acting on it is also zero. The body is at rest or moving with a constant velocity in a straight line, and it is not rotating or experiencing any rotational acceleration.
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(2)
Time = Distance/Speed
For a speed of 50 km/h:
Time = (600 km)/(50 km/h)
Time = 12 hours
For a speed of 60 km/h:
Time = (600 km)/(60 km/h)
= 10 hours
Difference in time = (Time at 50 km/h) – (Time at 60 km/h)
= 12 hours – 10 hours
= 2 hours

It will take 2 hours longer for the car to travel a distance of 600 km at a speed of 50 km/h compared to 60 km/h.
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(3a)
Work is said to have been done when a force is applied to an object and the object is displaced in the direction of the force. Work occurs when energy is transferred to or from an object due to the application of a force.

(3b)
The efficiency of a machine is usually less than 100% due to various factors such as mechanical losses, friction, heat dissipation, and other types of energy losses. These factors result in the machine not being able to convert all the input energy into useful output energy. Some energy is lost in the form of heat, sound, or other forms of non-useful energy. Consequently, this decreases the overall efficiency of the machine.
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(4a)
(i) Translational motion
(ii) Rotational motion
(iii) Vibrational motion
(iv) Circular motion

(4b)
(i) Translational motion: Translational motion refers to the movement of an object from one point to another in a straight line, without any rotation or change in shape. It involves a change in the position of an object without any alteration in its orientation or internal configuration.

(iii) Vibrational motion: Vibrational motion refers to the back-and-forth or oscillatory movement of an object around a fixed position. It occurs when an object is acted upon by a restoring force, such as the tension in a guitar string or the spring in a pendulum.
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(5a)
Joule’s law of heating states that the amount of heat generated in a conductor is directly proportional to the square of the current passing through it, the resistance of the conductor, and the time for which the current flows.

(5b)
Given:
Current (I) = 5A
Resistance (R) = 10Ω
Time (t) = 1hour
Time (t) = 60×60
Time (t) = 3600 seconds
Energy (E) = ?
Energy (E) = Power (P) x Time (t)
Power (P) = [Current (I)]² x Resistance (R)
P = I²R
E = I²Rt
E = (5)²x10x3600
E = 25x10x3600
E = 900,000Joules
E = 900kJ
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(6a)
Linear expansivity is a thermodynamic property that measures how much a substance expands or contracts when subjected to a change in temperature. It quantifies the change in length or size of a material per unit change in temperature.

(6b)
(PICK FIVE ONLY)

(i) Thermometers: Expansion of the liquid or gas inside a thermometer tube due to temperature changes allows for accurate temperature measurement.

(ii) Bimetallic Strips: Bimetallic strips consist of two different metal layers bonded together. The differing expansion rates of the metals cause the strip to bend when heated, leading to applications in thermostats and temperature-activated switches.

(iii) Bridges: Expansion joints and expansion bearings are used in bridges to accommodate the thermal expansion and contraction of the bridge materials, ensuring structural integrity.

(iv) Railroad Tracks: Gaps are provided between railroad tracks to account for the expansion and contraction of the metal tracks due to temperature variations.

(v) Window Panes: Gaps around windows allow for thermal expansion and contraction of the window panes, preventing damage due to temperature changes.

(vi) Electrical Wiring: Expansion joints are used in electrical wiring systems to compensate for the expansion and contraction of metal conductors caused by temperature changes.

(vii) Pipelines: Expansion loops and compensators are incorporated into pipelines to absorb thermal expansion and contraction, preventing damage or rupture.

(viii) Glass Manufacturing: Controlled cooling and heating of glass during the manufacturing process exploit thermal expansion properties to obtain desired shapes and finishes.

(ix) Automotives: Engine components, such as pistons, cylinders, and engine blocks, are designed with clearances to accommodate thermal expansion, preventing seizure or damage due to temperature changes.

(x) Space Exploration: In space applications, materials with predictable thermal expansion properties are used to ensure the stability and functionality of spacecraft and satellites in extreme temperature variations.
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(7a)
Heat capacity is a measure of the amount of heat energy required to raise the temperature of a substance by a certain amount. It is an intrinsic property of a material and depends on its mass, composition, and phase.

(7b)
Heat loss by aluminum block = Heat gain by water
mₐcₐ (θₐ – T) = mwcw (T – θw)
0.2 x 900 (85 -T) = 0.1 x 4200 (T – 15)
15300 – 180T = 420T – 6300
420T + 180T = 15300 + 6300
600T = 21600
T = 21600/600
T = 36°C
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(8a)
(PICK TWO ONLY)
(i) Carnot engine
(ii) Stirling engine
(iii) Diesel engine
(iv) Gas turbine engine
(v) Steam turbine engine
(vi) Rankine cycle engine

(8b)
(i) Intake: The first stroke is the intake stroke, where the piston moves downward, creating a vacuum that draws in a mixture of air and fuel into the combustion chamber through the open intake valve.

(ii) Compression: The second stroke is the compression stroke. The piston moves back up, compressing the air-fuel mixture, which increases its pressure and temperature. Both the intake and exhaust valves are closed during this stroke.

(iii) Combustion: The third stroke is the power stroke or combustion stroke. Just before the piston reaches the top, a spark plug ignites the compressed air-fuel mixture. The rapid combustion causes a rapid increase in pressure, which pushes the piston down forcefully. This downward motion is converted into rotational motion through the crankshaft.

(iv) Exhaust: The fourth stroke is the exhaust stroke. As the piston reaches the bottom, the exhaust valve opens, and the piston moves back up, pushing the burnt gases out through the open exhaust valve. This prepares the cylinder for the next intake stroke.
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(9a)
(PICK FOUR ONLY)
(i) Reflecting light in dressing rooms.
(ii) Rear-view mirrors in vehicles.
(iii) Decorative purposes in home décor.
(iv) Optical illusions in funhouses.
(v) Periscope systems in submarines.
(vi) Dental mirrors for oral examinations.
(vii) Telescope systems for aligning mirrors.
(viii) Laser systems for directing and reflecting beams.

(9b)
(PICK TWO ONLY)

(i) Virtual images are formed by the reflection or refraction of light rays, while real images are formed by the actual convergence of light rays.

(ii) Virtual images cannot be captured on a screen or projected onto a surface, while real images can be captured or projected.

(iii) Virtual images are always upright, while real images can be either upright or inverted.

(iv) Virtual images have a negative focal length, while real images have a positive focal length.

(v) Virtual images are always located on the same side as the object, while real images are located on the opposite side.

(vi) Virtual images cannot be focused with a lens or observed directly, while real images can be focused and observed directly.
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(10a)
Total internal reflection is a phenomenon that occurs when a light ray traveling from a medium with a higher refractive index to a medium with a lower refractive index encounters an interface at an angle greater than the critical angle.

(10b)
Given:
Angle of incidence (i) = 50°
Refractive index of water (n2) = 1.33
Refractive index of air (n1) = 1
Applying Snell’s law:
sin(i)/sin(r) = n2/n1
sin(50°)/sin(r) = 1.33/1
sin(50°) = 1.33xsin(r)
sin(r) = sin(50°)/1.33
sin(r) = 0.766 / 1.33
r = sin-¹(0.766/1.33)
r = 39.6°
Angle of refraction (r) = 39.6°
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