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 $g = 9.8\ \text{m/s}^2$.

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?

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.

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.

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.

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 ($g = 9.8\ \text{m/s}^2$)?

Gravity at a height $h$ above the Earth's surface is calculated using $g(h) = \frac{G\times M}{(R + h)^2}$. Use $M = 5.97\times10^{24}\ \text{kg}$, $R = 6.37\times10^{6}\ \text{m}$, $G = 6.67\times10^{-11}\ \text{N}\times\text{m}^2/\text{kg}^2$ and $h = 4\times10^{5}\ \text{m}$, the height at which the International Space Station orbits.

1. a) Calculate the value of $g$ at that height.
2. b) Compare it with $9.8\ \text{m/s}^2$ at the surface: has it decreased much?

The BepiColombo probe is traveling toward Mercury.

1. a) Calculate the surface gravity of Mercury using $g = \frac{G\times M}{R^2}$, with $M = 3.30\times10^{23}\ \text{kg}$, $R = 2.44\times10^{6}\ \text{m}$ and $G = 6.67\times10^{-11}\ \text{N}\times\text{m}^2/\text{kg}^2$.
2. b) How much will the probe weigh on Mercury if its mass is $300\ \text{kg}$?
3. c) Compare that weight with its weight on Earth: where does it weigh more and what is the difference in newtons?

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.

The height reached in a vertical jump with initial velocity $v_0$ is $h = \frac{v_0^2}{2\times g}$. An athlete pushes off with $v_0 = 3\ \text{m/s}$, as shown in the figure.

1. a) What height does it reach on Earth ($g = 9.8\ \text{m/s}^2$)?
2. b) What height would it reach on the Moon ($g = 1.6\ \text{m/s}^2$)?
3. c) How many times higher does the athlete jump on the Moon? Relate that factor to the ratio of the two gravities.