Work and power

Work is calculated as $W = F \cdot d$, 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) $\text{N} \cdot \text{m}$

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.

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.

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 ($\text{W}$).

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.

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?

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.

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.