The concept of weight

A rucksack full of books has a mass of $6\ \text{kg}$, as shown in the figure.

Calculate its weight on Earth using $P = m\times g$, taking $g = 9.8\ \text{m/s}^2$.

A bag of cement weighs $196\ \text{N}$ on Earth ($g = 9.8\ \text{m/s}^2$). Rearrange for mass in the expression $P = m\times g$ and calculate it.

The value $g = 9.8\ \text{m/s}^2$ is also expressed as $9.8\ \text{N/kg}$. Explain in your own words what it means that "each kilogram weighs $9.8\ \text{N}$" and calculate the weight of a box containing $12\ \text{kg}$ of oranges.

A car with a mass of $1200\ \text{kg}$ carries four passengers of $70\ \text{kg}$ each. Take $g \approx 10\ \text{m/s}^2$.

1. a) What is the total mass of the combination?
2. b) What total weight is supported between the four tires?
3. c) How many newtons of weight does each passenger add?

A person has a mass of $75\ \text{kg}$.

1. a) Make a quick estimate of their weight taking $g \approx 10\ \text{m/s}^2$.
2. b) Refine the result using the exact value $g = 9.8\ \text{m/s}^2$.

An astronaut with all their equipment has a mass of $90\ \text{kg}$ and is on the Moon, where $g = 1.6\ \text{m/s}^2$. Calculate their weight there. Has their mass changed compared to what it was on Earth? Justify your answer.

State whether each of these statements refers to mass or weight, and correct any that are incorrectly phrased:

1. a) "This watermelon weighs $4\ \text{kg}$."
2. b) "My mass is $540\ \text{N}$."
3. c) "With a force meter we measure mass in newtons."

In the lab, you want to measure the mass and weight of a bag of potatoes.

1. a) Which instrument would you use for each quantity, and in which unit would you give each result?
2. b) Draw in your notebook the setup you would use with a force meter to measure the weight.

You can do it on paper and send a photo with your answer.

The rover of a mission to Mars has a mass of $200\ \text{kg}$, as shown in the figure.

1. a) Calculate its weight on Earth ($g = 9.8\ \text{m/s}^2$).
2. b) Calculate its weight on Mars ($g = 3.7\ \text{m/s}^2$).
3. c) By how many newtons does the rover become "lighter" when travelling to Mars? Has its mass changed? Justify your answer.

A bathroom scale reads $55\ \text{kg}$ when a person steps onto it. In reality, the scale measures the force with which the person pushes down on it and converts it to kilograms assuming that $g = 9.8\ \text{m/s}^2$.

1. a) What force, in newtons, is the scale measuring?
2. b) If we took that scale to the Moon ($g = 1.6\ \text{m/s}^2$), what force would it measure with the same person?
3. c) What "mass" would the scale read then, continuing to convert using $g = 9.8\ \text{m/s}^2$?
4. d) Explain why the scale gives an incorrect reading on the Moon even though the person has not changed.

A crane can exert a maximum force of $20\,000\ \text{N}$.

1. a) What maximum mass can it lift on Earth ($g = 9.8\ \text{m/s}^2$)?
2. b) What maximum mass could it lift on the Moon ($g = 1.6\ \text{m/s}^2$)?
3. c) An advertisement claims: "Our crane would lift six times more mass on the Moon than on Earth." Check using your results whether the claim is correct and justify your answer.

The gravity on the surface of some bodies in the Solar System is: Venus $8.9\ \text{m/s}^2$, Mars $3.7\ \text{m/s}^2$, Jupiter $24.8\ \text{m/s}^2$ and the Moon $1.6\ \text{m/s}^2$, as shown in the chart (Earth is added as a reference).

1. a) Calculate the weight of a $60\ \text{kg}$ person on each of them.
2. b) Order them from smallest to largest weight.
3. c) On which one would they weigh almost the same as on Earth ($g = 9.8\ \text{m/s}^2$)?

In a lunar module, a force meter reads $16\ \text{N}$ when a rock is hung from it ($g_{\text{Luna}} = 1.6\ \text{m/s}^2$), as shown in the figure.

1. a) What is the mass of the rock?
2. b) What would the same force meter read with the same rock on Earth ($g = 9.8\ \text{m/s}^2$)?

An astronaut of $60\ \text{kg}$ travels through the Solar System and notices that on one of the worlds they visit they weigh about $2.5$ times more than on Earth.

1. a) How much do they weigh on Earth ($g = 9.8\ \text{m/s}^2$)?
2. b) What is the approximate value of $g$ on that world?
3. c) From this list, deduce which world it is: Moon $1.6\ \text{m/s}^2$, Mars $3.7\ \text{m/s}^2$, Venus $8.9\ \text{m/s}^2$ and Jupiter $24.8\ \text{m/s}^2$.
4. d) Calculate their exact weight on that world.

A space probe of $15\ \text{kg}$ arrives at Jupiter, where $g = 24.8\ \text{m/s}^2$. Calculate its weight there and compare it with its weight on Earth ($g = 9.8\ \text{m/s}^2$): how many extra newtons does it weigh?

In a gym, an Olympic weight plate has a mass of $25\ \text{kg}$.

1. a) How much does it weigh on Earth ($g = 9.8\ \text{m/s}^2$)?
2. b) How much would it weigh in a gym set up on a lunar base ($g = 1.6\ \text{m/s}^2$)?
3. c) Would it take an athlete the same effort to lift it on the Moon as on Earth? Give reasons for your answer, thinking about the force they have to overcome.

How many $70\ \text{kg}$ people would have to step onto a platform together to equal the weight of a $1400\ \text{kg}$ car? Solve it first by comparing masses and then check it using weights, taking $g \approx 10\ \text{m/s}^2$.

A school lab takes a beam balance with its weights and a force meter to the Moon, and measures a rock with them, as shown in the figure.

1. a) The balance balances with weights totaling $60\ \text{kg}$. What is the mass of the rock? Would it balance with the same weights on Earth?
2. b) What does the force meter read when the rock is hung from it on the Moon ($g = 1.6\ \text{m/s}^2$)? What about on Earth ($g = 9.8\ \text{m/s}^2$)?
3. c) Explain why one of the instruments gives the same result in both worlds and the other does not.

Due to the flattening of the Earth and its rotation, $g$ is $9.83\ \text{m/s}^2$ at the poles and $9.78\ \text{m/s}^2$ at the equator. A ship carries $20\,000\ \text{kg}$ of scientific equipment from the pole to the equator, as shown in the figure.

1. a) Calculate the weight of the cargo in each of the two locations.
2. b) By how many newtons does the weight change during the voyage?
3. c) Has the mass of the cargo changed? If weighed with a balance at both ports, what would it read at each?

An astronaut of $60\ \text{kg}$ travels through the Solar System and notices that on one of the worlds they visit they weigh about $2.5$ times more than on Earth.

1. a) How much do they weigh on Earth ($g = 9.8\ \text{m/s}^2$)?
2. b) What is the approximate value of $g$ on that world?
3. c) From this list, deduce which world it is: Moon $1.6\ \text{m/s}^2$, Mars $3.7\ \text{m/s}^2$, Venus $8.9\ \text{m/s}^2$ and Jupiter $24.8\ \text{m/s}^2$.
4. d) Calculate their exact weight on that world.