Final answer:
The gear ratio between a 100-teeth and a 40-teeth gear is 2.5:1, applying more torque increases the angular velocity of the meshed gear, a fivefold voltage increase in a transformer requires five times the number of output coils compared to input coils, and a hydraulic system exerting 100 times the force requires an area ratio of 100:1.
Step-by-step explanation:
The student is asking about gear ratios, the effect of torque on angular velocity, transformer coil ratios, hydraulic systems, pulley systems, and mechanical advantage in various physical systems. These concepts are generally covered under the subject of Physics, particularly in the topics of simple machines and energy transfer.
Gear Ratios
A gear wheel with 100 teeth in mesh with a 40-teeth gear would have a gear ratio calculated by dividing the number of teeth on the larger gear (100) by the number of teeth on the smaller gear (40). This results in a ratio of 100/40, which simplifies to 2.5:1, answering the student's primary question correctly.
Angular Velocity Resulting from Torque
If more force is applied to Gear A, causing it to turn with greater torque, the angular velocity of Gear B increases in magnitude because the gears are interlocked, and an increase in the speed of Gear A directly translates to an increase in speed for Gear B, which turns in the opposite direction.
Transformer Coil Ratios
In a step-up transformer, to increase the voltage fivefold, the ratio of the number of output coils to the number of input coils should be five times. This ensures that if the input voltage is increased by a factor of five, the transformer will output a correspondingly higher voltage.
Hydraulic Systems
For a hydraulic system designed to exert a force 100 times as large as the input force, the ratio of the areas of the wheel cylinder to the pedal cylinder must also be 100:1. The ratio of their diameters would be the square root of the area ratio, and the distance through which the output force moves would be reduced by the same factor as the force increase.
Pulley Systems and Mechanical Advantage
If a pulley system can lift a 200N load with a 52N effort force, then the mechanical advantage is the load divided by the effort force, resulting in a mechanical advantage of approximately 3.80. This indicates that the system likely uses multiple ropes to achieve this advantage.