An astronaut of 70 kg weighs about 686 N on Earth, but on the Moon, with exactly the same mass, their scales would show only about 115 N. Nothing about their body has changed: what changes is the planet pulling on them, and that is precisely what weight measures.
When we drop an apple and a stone, the Earth pulls on both of them towards the ground with a force proportional to their mass, accelerating them at the same rate of $9{,}8\ \text{m/s}^2$. How is this everyday force connected to Newton's law of gravitation, which keeps the planets in orbit?
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A rucksack full of books has a mass of $6\ \text{kg}$, as shown in the figure. Calculate its weight on Earth using $P = m\cdot g$, taking $g = 9,8\ \text{m/s}^2$.
A rucksack full of books has a mass of $6\ \text{kg}$, as shown in the figure.
Calculate its weight on Earth using $P = m\cdot g$, taking $g = 9,8\ \text{m/s}^2$.
An astronaut in orbit floats and registers nothing on a set of scales, but if they push a module of $500\ \text{kg}$ they need to apply exactly the same force to move it as on Earth. If the difficulty of pushing it does not change in space, which quantity does a set of scales measure, and which one stays constant throughout the universe?
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A person has a mass of $75\ \text{kg}$. a) Make a quick estimate of their weight taking $g \approx 10\ \text{m/s}^2$. b) Refine the result using the exact value…
A person has a mass of $75\ \text{kg}$.
a) Make a quick estimate of their weight taking $g \approx 10\ \text{m/s}^2$.
b) Refine the result using the exact value $g = 9,8\ \text{m/s}^2$.
The rover of a mission to Mars has a mass of $200\ \text{kg}$, as shown in the figure. a) Calculate its weight on Earth ($g = 9,8\ \text{m/s}^2$). b) Calculate its…
The rover of a mission to Mars has a mass of $200\ \text{kg}$, as shown in the figure.
a) Calculate its weight on Earth ($g = 9,8\ \text{m/s}^2$).
b) Calculate its weight on Mars ($g = 3,7\ \text{m/s}^2$).
c) By how many newtons does the rover become "lighter" when travelling to Mars? Has its mass changed? Justify your answer.
To calculate the weight of an object on another celestial body, the correct approach is always in two steps: first obtain the gravity $g$ of that body using $g=G\cdot M/r^2$, and then apply $P=m\cdot g$.
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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…
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).
a) Calculate the weight of a $60\ \text{kg}$ person on each of them.
b) Order them from smallest to largest weight.
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 hanging a rock from it ($g_{\text{Luna}} = 1,6\ \text{m/s}^2$), as shown in the figure. a) What is the mass of…
In a lunar module, a force meter reads $16\ \text{N}$ when hanging a rock from it ($g_{\text{Luna}} = 1,6\ \text{m/s}^2$), as shown in the figure.
a) What is the mass of the rock?
b) What would the same force meter read with the same rock on Earth ($g = 9,8\ \text{m/s}^2$)?
The BepiColombo probe is travelling towards Mercury. a) Calculate the surface gravity of Mercury using $g = \frac{G\cdot M}{R^2}$, with…
The BepiColombo probe is travelling towards Mercury.
a) Calculate the surface gravity of Mercury using $g = \frac{G\cdot M}{R^2}$, with $M = 3,30\cdot10^{23}\ \text{kg}$, $R = 2,44\cdot10^{6}\ \text{m}$ and $G = 6,67\cdot10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$.
b) How much will the probe weigh on Mercury if its mass is $300\ \text{kg}$?
c) Compare that weight with its weight on Earth: where does it weigh more and what is the difference in newtons?
The height reached in a vertical jump with initial velocity $v_0$ is $h = \frac{v_0^2}{2\cdot g}$. An athlete pushes off with $v_0 = 3\ \text{m/s}$, as shown in the…
The height reached in a vertical jump with initial velocity $v_0$ is $h = \frac{v_0^2}{2\cdot g}$. An athlete pushes off with $v_0 = 3\ \text{m/s}$, as shown in the figure.
a) What height does it reach on Earth ($g = 9,8\ \text{m/s}^2$)?
b) What height would it reach on the Moon ($g = 1,6\ \text{m/s}^2$)?
c) How many times higher does the athlete jump on the Moon? Relate that factor to the ratio of the two gravities.
A school laboratory 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. a) The balance balances…
A school laboratory 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.
a) The balance balances with weights totalling $60\ \text{kg}$. What is the mass of the rock? Would it balance with the same weights on Earth?
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 ($g = 9,8\ \text{m/s}^2$)?
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…
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.
a) Calculate the weight of the cargo in each of the two locations.
b) By how many newtons does the weight change during the voyage?
c) Has the mass of the cargo changed? If weighed with a beam balance at both ports, what would it read at each?