An astronaut with a mass of 70 kg weighs about 686 N on Earth, but on the Moon, with the same mass, their scales would read only about 115 N. Nothing about their body has changed. What has changed is the planet pulling on them.
You drop your keys and they fall to the floor, accelerating; when you hold a loaded backpack you feel a downward pull that tires your arm, while the Moon moves along its orbit without falling onto us. How can the same physical law explain both the motion of the stars and planets and the force you feel in your hand when you hold up a weight?
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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 $g = 9,8\ \text{m/s}^2$.
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.
In the recordings of the Apollo missions, the astronauts moved around in nimble leaps while wearing suits and equipment of more than $80\ \text{kg}$ that on Earth would have stopped them getting back up. Which properties of a planet determine how strongly it attracts bodies on its surface?
To calculate the weight of a body on another celestial body, you must first obtain the gravity $g$ of that body using the law of gravitation, 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 ($g = 9,8\ \text{m/s}^2$)?
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?
Comparing the weight of the same body in different places
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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 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.
Back to the start: The $115\ \text{N}$ that the scales would read on the Moon come from applying $P = m \cdot g_{\text{Luna}} = 70 \cdot 1{,}64 \approx 115\ \text{N}$: the astronaut's mass is still $70\ \text{kg}$, but the Moon pulls on each kilogram with six times less force than the Earth.
Summary
Let's practice! 8 medium exercises in this section