Guidance

Applied Mechanics Written Examination Syllabus

Published 6 May 2014

The expected learning outcome is that the student:

1.  Vector Representation

1.1 Understands the use of vectors for graphical solutions.

1. Recalls the procedures for the addition and subtraction of parallel and non-parallel vectors by both graphical and analytical methods.
2. Recalls the terms: Resultant and Equilibrant.
3. Explains that three non-parallel vectors must be concurrent for equilibrium.
4. Resolves vectors into mutually perpendicular components.
5. Solves problems involving coplanar-concurrent and coplanar non-concurrent vector quantities.
6. Solves problems involving non-coplanar concurrent vector quantities.

2. Statics

2.1 Understands the conditions of equilibrium of a body subject to a system of coplanar and non-coplanar forces and/or moments, and applies the conditions of equilibrium to solve relevant practical problems.

1. Recalls a moment of force.
2. Resolves forces applied obliquely into perpendicular components.
3. States the Principle of Moments.
4. States the conditions for equilibrium of a rigid body subject to a number of non-concurrent coplanar forces.
5. Describes the classification of the lever:
   1. as one of three orders;
   2. straight or cranked;
   3. simple or compound.
6. Solves problems related to 2.1.1 to 2.1.5.
7. Describes concurrent coplanar force systems.
8. Solves problems on 2.1.7 involving up to four forces in equilibrium to include the static condition of crank and overhung connecting rod.
9. Describes concurrent non-coplanar force systems.
10. Solves problems on 2.1.9 involving up to four forces in equilibrium.
11. Resolves forces acting on a body resting on a frictionless plane inclined to the horizontal.
12. Defines moments of mass, volume and area.
13. Understands the principle of Rapson’s slide.
14. Solves problems related to 2.1.11 to 2.1.13.

3. Friction

3.1 Discusses the effect of friction when one rigid body slides or tends to slide over another rigid body, and applies the principles established to the solution of practical problems.

1. Sates the ‘laws of dry friction’.
2. Defines the terms for a body sliding or tending to slide over a horizontal plane.
   1. static friction;
   2. sliding friction;
   3. normal reaction;
   4. plane reaction;
   5. friction angle;
   6. limiting friction force.
3. Discusses the forces involved when a body is stationary or sliding at uniform speed on a plane inclined to the horizontal.
4. Solves problems involved in holding or causing the body to ascend and descend the plane at uniform speed by means of:
   1. a force acting parallel with the plane;
   2. a force acting horizontally;
   3. the least force;
   4. forces acting at any angle.
5. Solves problems involving wedges and cotters.
6. Solves problems involving static equilibrium when friction forces are involved.
7. Solves problems involving work lost due to friction.

4. Kinematics

4.1 Solves problems involving linear, angular and relative motion.

1. Recalls the terms: displacement, speed, velocity and acceleration and states the units for both linear and angular cases.
2. Sketches distance/time graphs for both constant speed and uniform acceleration and defines the slope.
3. Sketches velocity/time graphs for both constant speed and uniform acceleration and relates the slope and area to the motion.
4. States the equations of motion for constant acceleration in both linear and angular terms.
5. Derives the relationship between linear and angular motion.
6. Solves problems related to 4.1.1 to 4.1.5.
7. Derives the equations for the horizontal and vertical components of the motion of a projectile.
8. Solves problems on individual and double projectiles.
9. Defines relative and absolute velocity.
10. Determines the relative velocity of unconnected bodies.
11. Solves problems involving closest approach and elapsed time related to 4.1.10 above.
12. Determines the relative velocity of connected bodies in simple mechanisms.

N.B.   (Objectives 4.1.7 to 4.1.12 to be solved by analytical and/or graphical methods).

5. Dynamics

5.1  Applies the laws of motion to translational dynamics.

1. Recalls Newton’s laws of motion and discusses the concept of inertia.
2. Defines power.
3. Defines linear momentum and impulse.
4. Discusses the Conservation of Momentum.
5. Defines kinetic energy, potential energy and work done.
6. Discusses the Conservation of Energy.
7. Solves problems involving momentum, impulse, energy, work done and power, to include impact of non-elastic bodies.
8. Explains the traction of vehicles on horizontal and inclined planes.
9. Considers tractive effort as the algebraic sum of the forces arising from:
   1. force to overcome the component of weight of the vehicle on the inclined plane
   2. acceleration forces;
   3. friction forces.
10. Expresses the friction forces as tractive resistance in terms of force per tonne of vehicle.
11. Solves problems involving motion on an inclined plane.
12. Solves problems in which bodies are hauled by a connected body or winch in ascent and/or descent of an inclined plane.
13. Solves problems in which bodies are hauled up inclined planes and the hauling force is limited by conditions of overturning of the body.

5.2 Applies the laws of motion to rotational dynamics.

1. Derives the relationship between torque, angular acceleration and moment of inertia.
2. States the expression for the moment of inertia of an annular disc.
3. Determines the moment of inertia for composite flywheels comprising of plain and annular discs.
4. Explains the concept of radius of gyration.
5. Discusses the concept of a thin rim type flywheel.
6. States the expression for the work done by a torque.
7. Represents graphically angular work done.
8. States the expression for the power developed by a torque.
9. Derives the expression for the kinetic energy of rotation.
10. Shows that the vertical force acting on a freely suspended mass is given by the expression: mg±ma.
11. Solves problems involving connected masses passing over frictionless light pulleys, including inclined planes.
12. Solves problems involving masses connected to separate ropes on stepped flywheels and to include inertia and friction.
13. Discusses the concept of fluctuation of speed and energy.
14. Solves problems involving 5.2.13 above.
15. Solves problems involving combinations of translational and rotational motion.
16. Defines angular momentum (moment of momentum).
17. States the conservation of angular momentum.
18. Derives the expression for the rate of change of angular momentum and hence angular impulse.
19. Solves problems involving angular momentum and impulse.
20. Derives the simple expression for the torque to overcome friction on a thrust collar bearing.
21. Solves problems on 5.2.20 above.
22. Solves problems involving torque and power transmitted by single flat plate friction clutches; relevant formulae to be given.
23. Repeats 5.2.22 for cone friction clutches.

5.3 Describes centripetal and centrifugal effects and solves associated problems.

1. Derives the expression for the centripetal acceleration of a body moving in a circular path with uniform angular velocity.
2. Relates centripetal acceleration and centripetal force.
3. Recognises that centrifugal force is an inertial reaction to centripetal force.
4. Determines by graphical or analytical means whether a rotating coplanar force system is in equilibrium.
5. Determines the out-of-balance force and the balancing mass required for systems not in equilibrium.
6. Calculates the forces on bearings supporting out-of-balance shafts.
7. Discusses the conical pendulum.
8. Solves problems involving conical pendulums.
9. Discusses centrifugal governors.
10. Sketches and describes the Watt governor, Porter governor and the Hartnell governor.
11. Solves problems related to 5.2.10 by analytical and graphical methods.
12. Describes the effects of vehicles negotiating curved paths.
13. Solves problems due to the overturning effect on a vehicle negotiating a curved track in the horizontal plane.
14. Solves problems due to the centrifugal force on a vehicle negotiating a banked or superelevated track, neglecting overturning.
15. Solves problems when frames are subjected to a dynamic force, such as the centrifugal force, arising when the mass on the end of a crane cable swings in the plane of the frame.
16. Solves problems involving torque and power transmitted by centrifugal clutches.

5.4 Describes and solves problems involving simple harmonic motion SHM.

1. Defines SHM.
2. Derives expressions for displacement, velocity and acceleration of the projection, on a diameter, of a point moving in a circular path at constant angular velocity and hence concludes the motion is SHM.
3. Defines amplitude, frequency and periodic time.
4. Derives the general expression: frequency = (1/2π)√(Acceleration/Displacement).
5. Derives the expression for the acceleration of a mass vibrating on a helical spring and concludes the motion is SHM.
6. Derives the expression for the frequency of a mass vibrating on a helical spring.
7. States the assumptions made for the spring mass effect.
8. Repeats 5.3.5 and 5.3.6 above for a simple pendulum.
9. Repeats 5.3.5 and 5.3.6 above for a liquid in a U-Tube.
10. Repeats 5.3.5 and 5.3.6 above for a simply supported massless beam with a central paint load (expression for deflection to be given).
11. Solves problems on 5.3.2 to 5.3.10 above.
12. Discusses Scotch Yoke mechanism as pure SHM.
13. Discusses the reciprocating crank/connecting rod mechanism with reference to SHM and modified SHM.
14. Describes the component forces of the piston effort.
15. Explains the effect of friction at the crosshead.
16. Discusses crankshaft torque with reference to piston effort.
17. Solves problems involving 5.3.13 to 5.3.16 above (expressions for instantaneous displacement, velocity and acceleration of piston to be given as required).
18. Determines crankshaft speed from piston speed.
19. Discusses cam operation.
20. Describes the following cam profiles:
    1. giving SHM motion to the follower;
    2. a motion resulting from a cam which has an elliptical silhouette;
    3. a motion resulting from a cam which is cylindrical but eccentrically mounted;
    4. a motion in which the cam provides a Period of dwell of the follower.
21. Solves problems involving spring force, friction, gravitational force, accelerating force and reaction force for on centre line followers for the cams at 5.3.20.

6.  Machines

6.1 Understands the principles involved in the determination of movement ratio for geared mechanisms.

1. Recalls the term movement ratio (velocity ratio).
2. Determines the movement ratio for simple and compound gear trains.
3. Solves problems related to 6.1.2 above.

7. Strength of Materials

7.1 Revises the terminology and solves simple problems in strength of materials.

1. Recalls the terms, with units as appropriate: direct stress and strain; shear stress and strain; Modulus of Elasticity E; Modulus of Rigidity G; proof stress; and factor of safety.
2. Solves problems involving simple and stepped bars subjected to axial loading.
3. Solves problems involving the shear stress in simple components e.g. jointed stays.
4. Discusses the effect of axial loading on compound members.
5. Solves problems involving compound members subjected to direct axial loads.

7.2 Discusses the effect of temperature change on the physical dimensions of components.

1. Determines the stresses set up in simple and stepped bars subjected to linear thermal strain.
2. Discusses the effects of temperature change on composite members.
3. Solves problems involving differential thermal expansion (and contraction).
4. Solves problems involving compound members subjected to both direct loading and temperature change, e.g. nut, bolt and tube assembly.

7.3  Solves problems involving shear forces and bending moments on simply supported and cantilever beams.

1. Determines the support reactions for beams subjected to point and/or uniformly distributed loads.
2. Recalls the terms Shear Force, SF, and Bending Moments, BM.
3. Calculates the SF and BM at any point along a beam.
4. Explains the need for a sign convention when dealing with SFs and BMs.
5. Sketches the SF and BM diagrams for the four standard cases:
   1. simply supported beam with point load at mid span;
   2. cantilever with point load at free end;
   3. simply supported beam with UDL along total length;
   4. cantilever with UDL along total length.
6. Draws to scale SF and BM diagrams for beams subjected to combinations of point loads and uniformly distributed loading.
7. Repeats 7.3.6 above when beam is subjected to an offset bracketed load.
8. Explains the relationship between SF and BM.
9. Calculates the position and magnitude of maximum bending moment.
10. Defines ‘point of contraflexure’.
11. Calculates the position of any point of contraflexure on a loaded beam.
12. Discusses the concept of uniformly varying distributed loading, e.g. hydrostatic loading.
13. Sketches SF and BM diagrams for the loading case given at 7.3.12 above.
14. Discusses slope and deflection of loaded beams.
15. States the expression for the maximum deflection for the four standard cases listed at 7.3.5 above.

7.4 Solves problems related to the Theory of Simple Bending.

1. Lists the assumptions necessary in deriving the bending theory.
2. Derives the expression: M/I = σ/γ = E/R.
3. Shows that the NA of the section passes through the centroid.
4. Defines Section Modulus ‘Z’.
5. Sketches simple diagrams showing the bending stress distribution across the beam section.
6. Solves problems using the bending theory, together with the concepts of 7.3.6 and 7.3.15.
7. Discusses the concept of combined bending and direct stress.
8. Describes how eccentric and inclined loading can induce both bending and direct stresses.
9. Solves problems referring to the loading cases identified above involving sections symmetrical and non-symmetrical above their NA.
10. Sketches the stress distribution diagrams for the above, inserting principal values and postion of zero stress.

7.5 Solves problems relating to the stability of axially loaded columns.

1. Discusses the concept of buckling and defines the term ‘slenderness ratio’.
2. Discusses the four basic end conditions for struts.
3. Discusses the use of the Euler formulae for struts.
4. Solves problems using given Euler formulae, for any of the four basic conditions.

7.6 Derives and uses the simple theory of torsion for members of circular sections.

1. Lists the assumptions necessary in deriving the torsion theory.
2. Derives the expression: T/J = GΘ/L = τ/R.
3. Recalls the expression for the power transmitted by a rotating shaft.
4. Defines torsional stiffness.
5. solves problems applying the expressions above to uniform and stepped shafts of solid and/or hollow section and to shaft and pulley arrangements.
6. States the relationship between the torque transmitted by a shaft and the shear force induced in the coupling bolts.
7. Solves problems involving shaft coupling bolts associated with 7.5.5 above.
8. Compares the masses of solid and hollow shafts.
9. Determines the stresses set up in the materials of compound shafts.

7.7 Applies the theory of torsion to close coiled helical springs.

1. Develops the formula for stress and deflection of a helical spring subjected to an axial load.
2. Solves problems on the design of such springs.

7.8 Solves problems relating to the concept of elastic strain energy.

1. Defines strain energy and resilience.
2. Derives the expression: U = (σ²AL)/2E.
3. Solves problems by applying 7.8.2 above for members subjected to gradually applied loading.
4. Discusses the concept of impact loading.
5. Solves problems involving conversion of PE and/or KE into strain energy to determine the maximum instantaneous stress and deformation.
6. Derives expressions for the strain energy of a helical spring in terms of both linear deflection and torque.
7. Solves problems involving strain energy of springs.

7.9 Solves problems involving the concept of stresses on oblique planes of stressed material.

1. Shows that a material subjected to a direct force experiences both direct and shear stresses on an oblique plane.
2. Determines the direct and shear stresses on an oblique plane of a material subjected to axial force and mutually perpendicular forces (or stresses).
3. Shows that the maximum shear stress occurs on a 45’ plane.
4. Discusses the concept of complementary shear stress.
5. Repeats 7.9.2 above, including applied shear stress.
6. Recalls the, expressions for hoop and longitudinal stress in a thin cylinder subjected to internal pressure.
7. Solves problems involving direct and shear stresses on oblique seams of thin cylinders.

8. Hydrostatics

8.1 Solves problems involving hydrostatic forces on immersed areas.

1. Recalls the terms: mass, density, relative density, pressure, gauge pressure and absolute pressure.
2. Derives the expression for the pressure at any depth in a liquid.
3. Determines pressures from given piezometer, manometer and barometer readings.
4. Derives the general expression for the resultant hydrostatic force on an area immersed at any depth in a liquid.
5. Defines the term ‘centre of pressure’.
6. Derives the general expression for the position of the Centre of Pressure of an area immersed at any depth in a liquid.
7. Solves problems relating to the resultant thrust and centre of pressure for: bulkheads, tanks, door and lock gates, positioned vertically and inclined.(Immersed areas limited to rectangular, circular, triangular and trapezoidal).
8. Determines the resultant thrust and centre of pressure for a vertical rectangular area wetted by two immiscible liquids.
9. Repeats 8.1.7 and 8.1.8 above when the free surface is subjected to a gas pressure.

8.2 Applies Archimedes Principle to solve problems.

1. States Archimedes Principle with reference to floating and submerged bodies.
2. Solves problems applying 8.2.1 above and to include bodies floating in two immiscible liquids.
3. Solves problems applying 8.2.1 above for bodies descending vertically through liquids, the motion being frictionless.

9. Hydrodynamics

9.1 Discusses the concepts of energy related to the steady flow motion of liquids and solves associated problems.

1. Discusses the volumetric and mass flow rates of liquids and states the continuity equation.
2. Explains the concept of coefficient of velocity C_v, coefficient of contraction C_c, and coefficient of discharge C_d for a sharp edged orifice.
3. Applies 9.1.2 above to solve problems involving flow of liquids through sharp edged orifices.
4. Identifies the various forms of energy possessed by a liquid in motion and states the expression for these in terms of energy and equivalent head.
5. Applies the principle of the conservation of energy and hence derives the Bernoulli expression.
6. Discusses the effect of friction related to flow problems and explains how this is included with the Bernoulli statement.
7. Applies the above to a venturi meter.
8. Explains the concept of the coefficient of discharge, C_d, with reference to a venturi meter.
9. Solves problems applying 9.1.5 above to: parallel and tapering pipes and venturi meters positioned horizontally, vertically and inclined; both frictionless and systems with friction to be included.
10. States D’Arcy’s formula for friction losses in pipelines.
11. Discusses ‘equivalent length’ of pipes to allow for energy losses at bends and valves.
12. Solves problems related to 9.1.9 and 9.1.10 above.

9.2 Solves problems related to changes in momentum of liquids in motion.

1. Recalls that force is equal to the rate of change of momentum.
2. Derives an expression for the instantaneous pressure rise due to rapid valve closure and solves associated problems.
3. Determines the resultant force on pipe bends due to change of momentum.
4. Determines the reaction force at hydraulic nozzles.
5. Determines the power of a hydraulic jet.
6. Solves problems related to the impact of jets on stationary flat plates positioned perpendicular and inclined to jet.
7. Repeats 9.2.6 above for moving plates.
8. Draws the velocity diagram for the impact of a jet on a curved vane.
9. Discusses the principles of a centrifugal pump.
10. Determines impeller width for constant and variable radial flow velocity through impeller.
11. Determines volumetric flow rate through impeller.
12. Determines the work done on the fluid passing through a centrifugal pump.
13. Derives the expression for manometric head and determines manometric efficiency.
14. Solves problems involving: impeller speed, blade angles for shockless flow, fluid velocity, pump efficiency, capacity and power.

10. Mathematical Solutions of Control System Problems

10.1 Derives equations and in certain cases solves mathematical problems related to control.

1. Solves mathematical problems related to pneumatic and hydraulic systems given, where necessary, the relevant formulae.
2. Be able to analyse a simple pneumatic or hydraulic control system and derive the equation of motion.