Mechanisms and simple machines

Explain what a lever is and name its three elements (fulcrum, effort, and load) using the example of a park seesaw.

What is a pulley used for? Explain its purpose and give two examples of machines or installations that use one.

The figure shows three different levers, with their effort F, load R, and fulcrum. Classify each one according to the class of lever (first, second, or third class) and name an everyday object that functions like each one.

Classify these objects as first-, second-, or third-class levers, reasoning where the fulcrum is in each one: a pair of scissors, a nutcracker, a pair of tweezers, and a seesaw.

A lever has its fulcrum at $0,5\ \text{m}$ from the load and at $1,5\ \text{m}$ from the point where effort is applied. If the load is $60\ \text{N}$, apply the law of the lever, $F \cdot b_F = R \cdot b_R$, to calculate the required effort and state whether the lever provides a mechanical advantage.

Explain what a gear is and what its teeth are used for: why are two smooth touching wheels not simply used to transmit rotation?

Name two household machines or installations that use pulleys or belts (window blind, washing machine...) and explain what motion they transmit in each case.

In a pair of gears, the driver gear has 20 teeth and the driven gear has 40. If the driver rotates at $60\ \text{rpm}$, calculate the rotational speed of the driven gear and state whether the gear system multiplies force or speed.

Using the concept of gear ratio, explain why a bicycle uses a large chainring and a small sprocket to go fast on flat ground, and the opposite combination to go up a slope.

Using a $2\ \text{m}$ bar, you want to lift a load of $100\ \text{N}$ by placing the fulcrum at $0,5\ \text{m}$ from the load. Calculate the required effort by applying the law of the lever, $F \cdot b_F = R \cdot b_R$, and state the length of the effort arm remaining.

A robotics team has a motor with a torque of $0,3\ \text{N}\cdot\text{m}$ rotating at $1500\ \text{rpm}$. They need to lift a $1,5\ \text{kg}$ load hanging from the end of a $20\ \text{cm}$ arm attached directly to the motor shaft. A team member suggests: "To make the motor work less, we lengthen the arm to $40\ \text{cm}$ to have more leverage; and if it still struggles, we add a $1:5$ gear reducer, which will increase the force without changing the lifting speed." Refute both statements with technical arguments and calculations: calculate the initial and final load torque on the motor shaft (take $g = 10\ \text{N/kg}$), explain the conceptual error regarding the arm length, and justify which physical quantity will inevitably be sacrificed if the reducer is used.

A winch winds up a rope to lift a bucket: the cylinder has a radius of $10\ \text{cm}$ and the crank handle describes a radius of $40\ \text{cm}$. Calculate the effort that must be applied to the crank to lift a load of $80\ \text{N}$, reasoning from the equilibrium of moments as in a lever.

The figure shows two gears in mesh: the driver gear has 12 teeth and rotates at $90\ \text{rpm}$ in the direction shown. Calculate the speed at which the driven gear of 36 teeth rotates, and determine its direction of rotation.

You are designing a construction wheelbarrow with a total length of $1,4\ \text{m}$, where the wheel axle is located at one end ($0\ \text{m}$) and the handles at the other ($1,4\ \text{m}$). A load of $60\ \text{kg}$ will be transported (take $g = 10\ \text{N/kg}$). Due to occupational risk prevention regulations, the operator must not exert a vertical force greater than $150\ \text{N}$ when lifting it.

1. a) Model the wheelbarrow as a lever: classify it and calculate the maximum distance from the wheel axle at which the centre of gravity of the load bucket must be located to comply with the standard.
2. b) If the operator shifts the load, placing it exactly directly above the wheel axle, how much vertical force will be needed to hold it? What mechanical and practical stability drawback arises from doing this?
3. c) Justify how the force supported by the operator varies as they lift the handles, tilting the wheelbarrow with respect to the horizontal.

A $60\ \text{kg}$ box needs to be lifted to a mezzanine located $3\ \text{m}$ high. The available person weighs $50\ \text{kg}$ ($500\ \text{N}$), so if they pull downwards on a rope, they can only apply at most their own weight before being lifted off the ground (take $g = 10\ \text{N/kg}$).

1. a) Design a pulley system indicating the minimum number of fixed and movable pulleys needed so that the person can raise the load by pulling vertically downwards on the rope comfortably.
2. b) Calculate the exact theoretical force they will exert, the metres of rope they will have to pull in to raise the box the $3\ \text{m}$, and the mechanical work performed.
3. c) Compare that work with the work they would perform if they lifted the box by hand, and explain why the simple machine does not save energy.