Engineering Mechanics

Students Learn About:

- mass and force
- scalar and vector quantities
- simple machines

– levers, inclined plane, screws, wheel and axle, pulley systems and gears

Students Learn To:

outline historical uses and appropriateness of materials in the design and production of engineering projects
demonstrate an understanding of the historical developments of engineering

mass and force

mass

The amount of matter that a body contains with the Sl unit being the kilogram (kg)

force

A force may be defined as a push or pull on a body. The SI unit for force is the Newton (N). Forces cannot be seen but their effects can be felt or seen. For example, when you go round a corner in a car, you do not see the forces but your body moves and you can feel the force acting on you.

gravity

The Earth exerts a gravitational force on all bodies. The amount of the gravitational force depends on the mass of the objects and the distance between them. For all objects on the earth's surface, the gravitational force accelerates at 9.8ms² towards the centre of the earth. In all calculations in this book acceleration due to gravity (g) is 10 ms², however some publications may use 9.8 ms². It should be noted that the previous edition favoured 9.8 ms² but 10 ms² is significantly easier for students to solve problems, while still maintaining acceptable accuracy

weight

Do not confuse mass with weight. Weight is a force that is created by gravity acting upon a mass. When you "weigh" yourself on the scales at home your weight force acts on the scales causing the scales to give a reading. But because we are so used to using kilograms as a measure of our weight, the scales are calibrated in kilograms instead of Newtons. This convention is misleading as weight is a force and the units must be Newtons. So in actuality when you "weigh" yourself, you are finding your mass not your weight. If you are on the moon your mass will be the same as in was on earth but your weight will be less, as the moon has less gravitational force than the earth. In space you have no weight as there is no gravity but your mass is the same as it was on earth.

Weight is the effect that the earth's gravitational force has on a body. The weight of a body is the force created by the product of a body's mass and the acceleration due to gravity. Thus the formula for weight is a variation of Newton's second law. Therefore,

W= mg

W= weight (N)

m = mass (kg)

g= acceleration due to gravity (ms²)

This means that any mass will have a unit in kilograms, while a weight will have a unit in Newtons. If you want to know what your true weight is, multiply the reading you get off the scales (your mass) by 10. So if you have a mass of 60 kg, then your weight will be 600 N.

scalar and vector quantities

scalar

Scalar quantities are those that are defined by their magnitude only, e.g., distance (20m), time (30 s), mass (22.8 kg), speed (110 km/h). These quantities are represented by a number and the relevant units.

vector

Vector quantities are those that are defined by their magnitude and their direction, e.g., displacement (1 km north), force (67 N vertically down), velocity (27 ms' west), acceleration (0.5 ms'2 vertically up) and stress (210 MPa, parallel to the applied force).

Vectors may be represented by a heavy dark line with an arrowhead which shows the following four features;

Magnitude
Direction
Sense
4 Point of Application

simple machines

Many products such as can openers, scissors, secateurs and wheelbarrows utilise simple mechanisms to aid in doing the work. Many complex engineered objects like bicycles and cars utilise a myriad of simple machines, with many coupled together to form complex machinery like a gearbox.

levers

This is the simplest machine and involves using a force acting over a distance to either magnify the user's effort (e.g. a crowbar) or to magnify the distance the effort travels (e.g. a fishing rod).

incline plane

The inclined plane in its simplest form is a basic ramp. The principle behind this is it is easier to lift or raise something progressively than to lift it the same height in one hit. This is displayed in Fig. 1.2.

🚦To Do:

For the user to lift the mower up to a height of h they must provide a force slightly larger than the weight of the mower. But on the inclined plane they only need to provide a force equal to the weight x sinθ. Thus the larger θ becomes the greater the effort. So what would be the effort required to raise a mower vertically and up a 10° ramp if the mower has a mass of 10 kg?

screws

Screws are an advanced type of inclined plane with the plane continuously wrapping around the shaft. Screws magnify effort but the distance is greatly increased. Screws are also used for fine adjustments for hand throttles etc. on tractors. Screw jacks allow users to lift large weights with relative ease.

wheel and axel

The wheel is one of humanity's most important developments. Coupled to the axle. it is a very important part of landscape products. Wheels and axles allow motors to tum and mowers to be pushed. Consider all the places these two items are used - they are numerous.

pulleys

The pulley allows the user to apply a force at a different location or in a different direction. For example, a tractor can pull out a stump going at right angles to the required direction using a pulley.

Another use for the pulley is to be placed together with other pulleys and used as a block and tackle to make lifting heavier objects easier. The pulley can also be used to transfer rotational motion from one shaft to another. An example of this is the drive belt on a tractor connecting the fan, alternator and crankshaft together.

Note that the size of a pulley transmitting rotational motion determines how fast one shaft spins compared to the other.

gears

Gears are particularly important machine components. Not only do they allow rotational motion to be transferred from one shaft to another but they can also be used to change ratios while moving. Gears are used as intermeshing devices such as in a ride-on mower gearbox.

For gear drives the ratio of the gears is decided by the comparative amount of teeth on the gears. This is similar to a pulley or belt drive because as the cog gains more teeth it will increase in diameter.

Chain drives

Chains are something of a cross between a gear system and a belt drive. They may be used as a more secure option than the pulley and belt drive. They also transmit drive over longer distances more effectively than gears. Like gears, the ratio is decided by the relative amounts of teeth in the driving and driven cogs.

SI Measurement System

In this section we discuss the Standard International Metric System of Measurement (SIMS) and some useful mechanical quantities.

The metric system was introduced to Australia to provide a system easier than the imperial system. The metric system uses a simple base of ten, whereas the imperial system had a more complicated approach to units. For example 1000 millimetres equal 1 metre, 1000 metres equal 1 kilometre while in the imperial system 36 inches equal a yard, and 1760 yards equal 1 mile. It is not a user-friendly system.

In the metric system there are base units. These are the simplest forms of standard measures. All of these base units have a definition that governs their value. From these base units are all of the derived values.

SI prefixes are used to express large variations from both the base and derived units. The base unit for distance is metres. Instead of referring to the distance between Darwin and London as 13 837 000 metres it is much simpler to say 13 837 km. Some SI units are not suited to today's applications, so all values require prefixes. For example the farad is the unit for capacitance and is very large, thus most capacitor values are microfarads or smaller.

🚦To Do:

Convert the large base values into more manageable numbers using prefixes

1000m = 1km
0.00003A = 300mA or 0.3 µA
1000000kg - 1Gg (In engineering we may actually write this as 1000 tonnes)

Engineering Mechanics

mass and force

mass

force

gravity

weight

scalar and vector quantities

scalar

vector

simple machines

levers

incline plane

🚦To Do:

screws

wheel and axel

pulleys

gears

SI Measurement System

🚦To Do:

Convert the large base values into more manageable numbers using prefixes

1000m = 1km

0.00003A = 300mA or 0.3 µA

1000000kg - 1Gg (In engineering we may actually write this as 1000 tonnes)

*Although the tonnne is not an official SI unit, it us extensivley used in industry with 1 tonne being equal to 1000kg

Useful Mathematical Formulae / Relationship

Pythgoras' Theorem

Triganomic Ratios

Surface

Deep

Transfer

Sine and Cosine Rule

the sine rule

the cosine law