Work and Power

Work is calculated as $W = F \times d$, where $F$ is the force and $d$ is the displacement in the direction of the force. You push a moving box with a force of $20\ \text{N}$ and it moves $5\ \text{m}$, as shown in the diagram.

What work have you done? Express it in joules ($\text{J}$).

State which of the following expressions are units of work and which are not, and explain why:

1. a) $\text{J}$
2. b) $\text{W}$
3. c) $\text{N}$
4. d) $\text{N} \times \text{m}$

A goods lift raises a crate of crockery by exerting a force of $500\ \text{N}$ to a height of $10\ \text{m}$. Calculate the work done by the goods lift.

A sled dog pulls with a force of $30\ \text{N}$ and does a total work of $240\ \text{J}$. What distance has the sled travelled?

A fishing boat raises its anchor by exerting a force of $50\ \text{N}$ while hauling in $2\ \text{m}$ of chain. What work is done by the winch motor?

To drag a fruit crate $5\ \text{m}$ along the market floor, work of $150\ \text{J}$ was done. With what force was the crate pushed?

While waiting for the bus, you hold your heavy rucksack still at the same height for $10\ \text{min}$. You are tired, but have you done work on the rucksack in the physics sense? Explain which condition is not met.

You push with all your strength against the classroom wall for a minute, and logically it does not move. Then you push a shopping trolley and it moves $3\ \text{m}$. Observe the two situations:

In which of the two cases have you done work? Justify your answer using the definition of work.

At the airport, you carry a wheeled suitcase holding it by the handle: your hand exerts an upward force, but the suitcase moves horizontally, as shown in the diagram.

1. a) Does your force do work on the suitcase while you walk? Reason your answer thinking about the direction of the force and that of the displacement.
2. b) At what point during the trip do you actually do work on the suitcase? Give an example.

A farmer hoists a bag of animal feed of $10\ \text{kg}$ up to the loft, at a height of $3\ \text{m}$, using a pulley (take $g = 10\ \text{m/s}^2$), as shown in the diagram.

1. a) What is the minimum force they have to overcome to raise it?
2. b) What work do they perform?

A worker pushes a tool trolley in two sections: first with a force of $100\ \text{N}$ over $6\ \text{m}$, and then on level ground with $60\ \text{N}$ over $10\ \text{m}$, as shown in the diagram.

1. a) Calculate the work done in each section and the total work.
2. b) If it takes $40\ \text{s}$ for the entire journey, what average power is developed?

The motor of a blind performs work of $600\ \text{J}$ in $30\ \text{s}$. Power is calculated as $P = W/t$. What is the power of the motor? Express it in watts ($\text{W}$).

Complete the sentence with the missing words: "$\dots$ indicates the work done in each $\dots$ of time and is measured in $\dots$." Then give an example using made-up numbers.

A pump extracts water from a well and performs work of $3600\ \text{J}$ in $3\ \text{min}$.

1. a) Express the time in seconds.
2. b) Calculate the power of the pump in watts.

You push a supermarket trolley with a force of $40\ \text{N}$ over a distance of $25\ \text{m}$ and it takes you $20\ \text{s}$.

1. a) What work have you done?
2. b) What power did you develop?

A blender has a power of $200\ \text{W}$ and operates for $30\ \text{s}$. Knowing that $P = W/t$, what work (energy) has it done?

A student of $50\ \text{kg}$ climbs the school stairs, which cover a height of $5\ \text{m}$, in $10\ \text{s}$ (take $g = 10\ \text{m/s}^2$).

1. a) What force do they overcome when climbing?
2. b) What work do they perform?
3. c) What power do they develop?

A construction crane lifts a beam of $200\ \text{kg}$ to a height of $10\ \text{m}$ in $20\ \text{s}$ (take $g = 10\ \text{m/s}^2$).

1. a) Calculate the work done by the crane.
2. b) Calculate its power.
3. c) Another crane does the same work, but takes $40\ \text{s}$. Which of the two is more powerful? Justify your answer with calculations.

Ioana and Leo carry the same sports bag, which weighs $60\ \text{N}$, up to the second floor, $4\ \text{m}$ higher. Ioana takes $12\ \text{s}$ and Leo takes $8\ \text{s}$.

1. a) Do they perform the same work? Calculate it.
2. b) Who develops more power? Calculate it in both cases.

Crane A performs work of $6000\ \text{J}$ in $60\ \text{s}$; crane B performs $9000\ \text{J}$ in $180\ \text{s}$. Which of the two is more powerful? Calculate the power of each one and compare them.

An oven has a power of $2000\ \text{W}$ and a microwave, $1000\ \text{W}$.

1. a) How long does each appliance take to perform work of $4000\ \text{J}$?
2. b) Explain in your own words what it means that the oven is more powerful than the microwave.

Andrés lifts bags of cement of $250\ \text{N}$ onto scaffolding of $4\ \text{m}$, and Berta lifts bags of $500\ \text{N}$ onto scaffolding of $2\ \text{m}$, as shown in the diagram.

1. a) Who does more work per bag? Calculate it.
2. b) Andrés takes $25\ \text{s}$ per bag and Berta takes $10\ \text{s}$. Who develops more power? Calculate it.
3. c) Explain the difference between doing more work and being more powerful using this example.

In the past, engine power was measured in horsepower: $1\ \text{CV}$ is equivalent to about $735\ \text{W}$.

1. a) How many watts is a car of $100\ \text{CV}$ equivalent to?
2. b) What work can that engine perform in $10\ \text{s}$?
3. c) Why do you think the horse was used as a reference unit?

Design an experiment to measure your own power climbing stairs:

1. a) State which quantities you need to measure and what instruments you would use to measure them.
2. b) Write down, in order, the calculations you would do to obtain your power in watts.
3. c) How would you check if you are more powerful in the morning or in the afternoon?