FireTeam Mechanical Aptitude - Part 2.1

e. 12cm Explanation: As each beam is connected to in sequence, any action performed on the string at A, will also affect the weight B in the same proportion.

A series of beams are connected as shown with string. They are all supported at their centre point. How far do you need to move A in order to raise B by 12cm? a. 4cm b. 6cm c. 8cm d. 9cm e. 12cm

e. Wheel A travels less distance than B Explanation: Wheel A is on the inside of the roundabout. As such it is only 10m away from the centre. Wheel B is 2m further away from the centre. As the distance further away from the centre increases, so does the distance the wheel must travel to complete a full circle. Wheel A and B do not turn. They are fixed in the forward direction.

Assuming the car does not skid as it goes around the roundabout; which statement is true? a. The wheels travel the same distance b. Wheel B turns fewer times c. Wheel A travels further than wheel B d. Wheel A turns more quickly e. Wheel A travels less distance than B

e. C turns clockwise at 25 RPM Explanation: Axle A is the start of the system, as indicated by the word 'input.' The disc on axle A is half the diameter of the one it is directly connected to on axle B. So, for every 1 rotation of A, B would perform half a rotation.The second disc on axle B is connected to a disc on axle C, and is once again half the diameter of the disc on C. So, for every 1 rotation of B, there is half a rotation of C. So, for every 1 rotation of A, there is 0.5 rotations of B, and therefore 0.25 rotations of C. If A is rotating at 100 RPM (revolutions per minute), then C is rotating at a quarter of that, or 25 RPM.Axle A rotates clockwise, so B and C will also rotate in the same direction.

Consider the belt drive system. Which of the following statements is true? a. B turns anti-clockwise at 50 RPM b. C turns anti-clockwise at 25 RPM c. A and C turn clockwise and B turns anti-clockwise d. C turns clockwise at 400 RPM e. C turns clockwise at 25 RPM

c. C Explanation: C would require the greatest length of rope to lift the weight by that distance. The distance that the weight is lifted by depends on how many pulleys there are. Each pulley used is an occasion when the rope is looped around. The more times the rope is looped around, the further it has to be pulled to raise the pulley and the weight attached to it.

Considering the above systems, if you want to lift the weight by 100mm, which rope will have to be pulled further? a. A b. B c. C d. They are all the same e. B and C do not work

d. B, D and F are turning anti-clockwise. Explanation: Gear A is indicated to be rotating clockwise by the arrow. If A rotates clockwise, then B must rotate in the opposite direction; anti-clockwise. So on and so forth, B, D, and F will rotate anti-clockwise, whilst A, C and E will rotate clockwise.

Gear A is rotating clockwise at 60 Revolutions per Minute (RPM). Which statement is correct? a. A, D and E are turning clockwise. b. B, D and E are turning anti-clockwise. c. All the gears are turning clockwise. d. B, D and F are turning anti-clockwise. e. All the gears except A are turning anti-clockwise.

a. 60mm clockwise Explanation: The gears are in a 3:1 ratio, so for every movement of Gear A, Gear B will rotate by thrice as many degrees. Pointer B is twice the length of pointer A, so again any movement of the pointer is doubled. So, 10mm multiplied by 3 and by 2 gives you 60mm. As Gear A is moving anticlockwise, Gear B must move clockwise.

Gear A is three times as large as Gear B. How far will pointer B travel and in which direction? a. 60mm clockwise b. 30mm anti-clockwise c. 20mm clockwise d. 60mm anti-clockwise e. 20mm anti-clockwise

b. 30 RPM Explanation: There are 2 ways to solve this question. Gear A has 20 teeth, and is rotating at 60 RPM (revolutions per minute), so for every minute that passes 60 rotations of Gear A occur, which means that 60 lots of 20 teeth have spun around and connected with 1 tooth of another gear, in this case B. And then every one tooth of Gear B has connected with one of Gear C. So, 60 * 20 = 1200 teeth each minute, and as Gear C has 40 teeth, this works out as 1200 / 40 = 30 RPM. Also, Gear A has half the number of teeth as Gear C, so for every rotation of A, C performs a half rotation. Gear B merely transfers the rotation from A to C, without altering it.

Gearwheel A has 20 teeth, B has 10 teeth and C has 40 teeth. If A is turning at 60 Revolutions per Minute (RPM), how fast is C turning? **More teeth = Less RPMs a. 60 RPM b. 30 RPM c. 120 RPM d. 70 RPM e. 40 RPM

c. Three times Explanation: Wheel 1 is 3 times as large as Wheel 2, so Wheel 2 must rotate 3 times before it reaches the same point it started at on Wheel 1.

How many times does Wheel 2 have to rotate before A and S meet again? a. Once b. Twice c. Three times d. Never e. Tooth A is constantly in sequence with point S

a. 60 km/h Explanation: The revs correspond to the revolutions per minute of the wheels. If the revs triple, and the gear remains the same, then the speed of the car will triple as a result of the wheels spinning 3 times as fast.

If the driver increases his revs from 1,000 to 3,000 RPM but does not change gear, how fast will he be going? a. 60 km/h b. 30 km/h c. 20 km/h d. He will be traveling backward e. 80 km/h

b. B must be lighter than A Explanation: The distance from the fulcrum (point on which the beam rests) and the weight used are proportional to the force produced. As a weight is placed further away from the fulcrum, the force increases. Therefore, if the distance doubles, to create the same force as on the other side, the weight used must be halved.

If you want the beam to balance: a. B must be heavier than A b. B must be lighter than A c. B must have an equal weight to A d. It does not work like that e. B must be higher than A

d. 10 RPM anticlockwise Explanation: For every 2 rotations of A, there is one rotation of the next shaft. For every 3 rotations of this shaft, there is just one rotation in the next. In the next shaft, every 4 rotations become one rotation in the last shaft. So, for every 4 * 3 * 2 (24) rotations at A there is just one rotation at B. Hence, if A is rotating at 240 rpm clockwise, then B will rotate at 10rpm in an anticlockwise direction. As a gear rotates in one direction, whichever gears it is meshed with will rotate in the opposite direction. Imagine this in your head, for the teeth of one gear to move in a direction they will push the teeth of the gear they're meshed with in the opposite direction. This means that the gear shaft A is in contact with will rotate anticlockwise, the following after that will rotate clockwise, and lastly, shaft B will rotate anticlockwise.

In Revolutions per Minute (RPM), how fast, and in which direction, is output shaft B? a. 5,760 RPM clockwise b. 10 RPM clockwise c. 240 RPM clockwise d. 10 RPM anticlockwise e. 5,760 RPM anticlockwise

b. 100mm Explanation: The part indicated by 50mm will rotate all the way around, this means that it will push away 50mm in one direction and 50mm in the exact opposite. This gives it a total length of double 50mm, which is 100mm.

Mr Brunel's steam engine has a crankshaft with a crank throw of 50mm. What is stroke length of the piston? a. 500mm b. 100mm c. 75mm d. 100 m/s e. 50 m/s

d. The Same Explanation: All the bikes have the pedals and wheels located in the same place. All of the pedals have a 3:1 ratio to the wheels, so neither bike will have to be pedalled faster.

Mr. Starley has 3 bicycles. One is chain driven, one belt, and one shaft. When traveling at 10mph, which one will have to be pedaled faster? a. A b. B c. C d. The Same e. None of the above

d. B and C and D Explanation: The distance in B, C and D of F to the pivot point is the same, so these scenarios are all equally feasible. In A, the distance is shorter, so more force is required to lift the weight.

Some of these beams are a bit wonky, but they still work, and F is always the same distance from the pivot point. Ignoring the weight of the beams themselves, which takes the least force at F to lift the weight? a. A b. B c. A and B d. B and C and D e. D

e. Use a long spanner but hold it at B Explanation: A similar concept to question 4 is employed here. Using a longer spanner and holding it at point B - the furthest point of the spanner from the nut - will give the best conditions to use the least amount of force to loosen the nut.

The nut is very tight. The easiest scenario to loosen the nut would be to: a. Use a short spanner and hold it at A b. Use a short spanner and hold it at B c. Use a spanner which grips the nut tightly d. Use a long spanner but hold it at A e. Use a long spanner but hold it at B

e. 20 RPM anti-clockwise Explanation: The shaft is attached to C, so the direction and speed of the shaft are related to what C is doing. If A moves clockwise, then B must also be moving clockwise, so C is moving anticlockwise.

The outer ring A is rotating at 5 RPM. A has 100 teeth. Two satellite gears, B, have 20 teeth. Sun gear C is connected to the shaft and has 25 teeth. How fast, and in which direction, is the shaft turning? a. 1 RPM clockwise b. The system is jammed c. 20 RPM clockwise d. 1 RPM anti-clockwise e. 20 RPM anti-clockwise

c. A ends up higher than B Explanation: Point A is hooked to the beam at a distance further away from the hinge than B, as such any movement at C will result in the hook of A moving more than the hook of B. As the hooks loop over a pulley, the direction changes, so as C moves downwards, point A of the beam moves upwards.

What would happen if point C was moved downwards? a. Beam A-B moves up but stays level b. A ends up lower than B c. A ends up higher than B d. A and B both drop e. A rises and B drops

c. C Explanation: C would require the least force to lift the weight. This is because of the pulley system employed in scenario C. The more pulleys you have the more parts of the rope act on the weight.

Which of the above systems requires the least force at F to lift the weight of 1 kg? a. A b. B c. C d. They are all the same e. B and C do not work

a. A Explanation: Distance and weight are proportional to the force created by the weights on either side. Side B has a 1kg weight 2m away. Whereas, side A has a 2kg weight which is 1.5m away from the pivot point of the seesaw. The weight on side A is twice that of side B, but the distance of the weight from the pivot is more than half, so side A has a greater force than B, and this will be the side to drop to the ground first.

Which side will drop to the ground when the weights are released? a. A b. Neither, it will be perfectly balanced c. B d. Both e. Impossible to tell

d. The front wheels Explanation: The car is moving at a constant speed, so it is covering the same distance in the same time, so the wheels are rotating to keep up with this. The larger wheels need to rotate fewer times to cover the same distance, so the front wheels are turning more quickly as they are doing more rotations in the same period of time as the rear wheels.

Which wheels are turning more quickly? a. The rear wheels b. They are the same c. The rear wheels while the car is speeding up d. The front wheels e. The rear wheels while the car slows down