VCE Systems Engineering
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1 VCE Systems Engineering Mechanical formula and Electrotechnology formula and worked examples - speed (m/s) or (ms distance (m) metre time (s) second ) metre per second speed = distance time A car travels 000 metres in 50 seconds at a constant speed. Its speed will be 0m/s. 0m/s = 000m 50s force (N) Newton mass (kg) Kilogram acceleration (m/s ) or (ms ) metre per second - force = mass acceleration The car has a mass of 500kg and accelerated at m/s before reaching constant speed. The force needed will be 3000N. 3000N = 500kg m/s
2 VCE SYSTEMS ENGINEERING work done (J) joule force (N) newton distance (m) metre work done = force in the direction moved distance A car tyre weighing 50N is lifted straight up from the ground by a mechanic to a height of 0.6m. The force and the displacement are in the same direction. The work done is 90J. 90J = 50N 0.6m If the mechanic takes seconds power (W) watt to perform the task, work done (J) joule time (s) second power = work done time the power needed will be 45 watts. 90J 45W = s energy (J) joule work done (J) joule power (W) watt time (s) second energy = work done energy = power time The energy needed to lift the tyre will be 90 joules. 90J = 45W s VCAA February 00 Page of
3 VCE SYSTEMS ENGINEERING mechanical advantage (MA) load (N) newton effort (N) newton mechanical advantage = load effort If an effort of 50N is needed to lift a load of 300N using a block and tackle system the mechanical advantage will be or : or 300N MA = = or : or 50N The effort, for the block and tackle system velocity ratio (VR) shown, will travel a distance four times distance moved by effort (m) distance moved by load (m) velocity ratio = distance moved by effort distance moved by load that of the load. The velocity ratio will be 4 to. 4 VR = or 4 :, expressed as a ratio VCAA February 00 Page 3 of
4 VCE SYSTEMS ENGINEERING efficiency (%) mechanical advantage (MA) velocity ratio (VR) input energy (J) joule useful output energy (J) joule mechanical advantage efficiency (%) = 00 velocity ratio useful output energy efficiency (%) = 00 total energy input The efficiency of the block and tackle system calculated using MA and VR is 50 %. efficiency (%) = = The efficiency calculated using energy values will also be 50%. If the 300N load is lifted through a height of 0.5m, the 50N effort is pulled a distance of m. The useful ouput energy is 50J ( ) The total input energy is 300J (50 ) 50J efficiency(%) = 00 = J VCAA February 00 Page 4 of
5 VCE SYSTEMS ENGINEERING moment (Nm) newton-metre force (N) newton distance (m) metre moment = force perpendicular distance to turning point 0. m. 0 m Effort 60 N Load 300 N The moment of the load about the turning point in the lever system shown is 60Nm. 60Nm = 300N 0.m The moment of the effort will also be 60Nm if system is in equilibrium. 60Nm = 60N m VCAA February 00 Page 5 of
6 VCE SYSTEMS ENGINEERING torque (Nm) newton-metre twisting force (N) newton distance (m) metre torque = twisting force perpendicular distance to turning point A spanner is is used to tighten a nut to the recommended torque of 6Nm. A twisting force of 80N acting 0 cms from the turning point will be required. 6 Nm = 80N 0.m VCAA February 00 Page 6 of
7 VCE SYSTEMS ENGINEERING Effort = 5N Load = 50N pressure (Pa) pascal force (N) newton area (m ) metre pressure = force area Area = 0.0 m Area = 0. m The pressure exerted by the 5N effort over the 0.0m area of the small cylinder in the hydraulic system shown is 500 Pa. 5N 500Pa = 0.0 m The pressure will balance a load of 50N over the 0.m area of the larger cylinder. 50N 500Pa = 0. m VCAA February 00 Page 7 of
8 VCE SYSTEMS ENGINEERING gear ratio of simple gear train number of teeth on driver gear number of teeth on driven gear gear ratio = number of teeth on driven gear number of teeth on driver gear Driver 30 teeth Driven 60 teeth The gear ratio of the simple gear train shown where the driver gear has 30 teeth and the driven gear 60 teeth is or :. 60 teeth = or : expressed as a ratio 30 teeth speed of driven gear (rpm) speed of driver gear (rpm) speed of driven gear = speed of driver gear gear ratio The driven gear will rotate slower than the driver. The driven gear rotates at 50 rpm if the driver gear gear ratio rotates at 00 rpm. 50 rpm = 00 rpm VCAA February 00 Page 8 of
9 VCE SYSTEMS ENGINEERING total gear ratio of compound gear trains gear ratios total gear ratio = gear ratio gear ratio... motor 0 teeth driver 30 teeth driven 0 teeth driver Axle A Axle B 40 teeth driven The four gears above make up a compound gear train. The 0 teeth driver gear meshes with the 30 teeth 3 driven gear, giving a gear ratio of or 3 : ( gear ratio ). The 0 teeth driver gear meshes with the 40 teeth 4 driven gear, giving a gear ratio of or 4 : ( gear ratio ). The total gear ratio of the compound gear train will be : 3 4 = or : The first driver gear will rotate times faster than the final driven gear VCAA February 00 Page 9 of
10 VCE SYSTEMS ENGINEERING voltage (V) volt current (I) amp resistance ( Ω) ohm ( Ohm's law ) voltage = current resistance Vs = volts R = 6 ohms The current in the simple circuit above will be amps. volts = amps 6 ohms power (W) watt volt (V) volt current (I) amp power = voltage current The power dissipated in the 6 ohms resistor will be 4 watts. 4 watts = volts amps VCAA February 00 Page 0 of
11 VCE SYSTEMS ENGINEERING resistors in series total resistance ( Ω) ohms resistors in series resistors in parallel R t = R + R +... = R R R t R t = 00 ohms + ohms ohms = 4 ohms = + = R t = 9 ohms R t 00 Ω Ω 330 Ω 8 Ω 8Ω resistors in parallel frequency (Hz) hertz period (s) second frequency = period Period = 0ms The frequency of the waveform shown is 50Hz. 50Hz = 0.0s VCAA February 00 Page of
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