Exercises: Gravitational phenomena

Your cell phone slips out of your hand and luckily lands on the rug, as shown in the diagram.

What force pulled it to the ground? Did something need to touch it or push it downward? Explain what it means that gravity is a non-contact interaction.

Complete the sentence with the missing words: 'The $\dots$ of a body is the amount of matter it contains and is measured in $\dots$; the $\dots$ is the force with which a planet attracts it and is measured in $\dots$'.

In what unit is mass measured in the International System of Units? And weight? Explain with an example why they are not the same thing.

Inside a vacuum tube (without air), a coin and a feather are dropped at the same time, as shown in the diagram.

Which one reaches the bottom of the tube first? Justify your answer.

You hold two identical sheets of paper, one crumpled into a ball and the other flat, and release them at the same time from the same height, as shown in the diagram.

Which one reaches the ground first? What does the air have to do with the result?

An astronaut travels to the Moon. Without doing calculations: is his mass greater, smaller, or equal to that on Earth? And his weight? Justify both answers.

Name two everyday phenomena caused by gravity and explain each briefly.

The Earth rotates on its axis at high speed, yet we are not thrown off. Explain why in your own words.

A rucksack has a mass of $6\ \text{kg}$. On Earth, its weight is about $60\ \text{N}$ and on the Moon, about $10\ \text{N}$, as summarised in the diagram.

1. a) What is the mass of the rucksack on the Moon?
2. b) Explain why weight changes from one place to another while mass does not.

On the Moon, gravity is about $6$ times weaker than on Earth. If you jump $50\ \text{cm}$ high on Earth with the same push, approximately what height would you reach on the Moon? Justify your answer.

On most coasts, there are two high tides and two low tides every day, as outlined in the diagram.

Explain what the Moon has to do with tides and why they change throughout the day.

A skydiver falls faster and faster after jumping from an aeroplane, but when opening the parachute, their fall becomes slow and gentle, as shown by the forces in the diagram.

Explain the role of air resistance in each stage of the jump.

Jupiter is much more massive than Earth and its surface gravity is about $2.5$ times greater. A gym weight that weighs $10\ \text{N}$ on Earth would weigh about $25\ \text{N}$ on Jupiter.

1. a) Has its mass changed?
2. b) Where would it be harder for you to lift it? Justify your answer.

The International Space Station flies at an altitude of about $400\ \text{km}$, where Earth's gravity is still almost as strong as on the ground. However, the astronauts float inside the spacecraft. The diagram outlines the orbit of the station.

How is this possible? Explain it by considering how the station moves around the Earth.

On the Moon there is no air. If an astronaut drops a hammer and a feather at the same time from the same height, what will they observe? Would the same thing happen on Earth? Explain the difference.

A bathroom scale reads $70\ \text{kg}$ when a person steps on it on Earth.

1. a) What does a scale actually measure when we step on it?
2. b) If the same person weighed themselves with that scale on the Moon, would it read the same? Justify your answer considering what gravity does to the person.

You have a transparent tube containing a coin and a cork, connected to a pump that extracts the air. Predict what you will see when turning the tube upside down in three situations and explain each prediction:

1. a) With the tube full of air.
2. b) With half of the air extracted.
3. c) With a near-total vacuum.

Gravity on the surface of Mars is about $3.7\ \text{m/s}^2$, compared to $9.8\ \text{m/s}^2$ on Earth. A rover has a mass of $200\ \text{kg}$.

1. a) Where does the rover weigh more, on Earth or on Mars?
2. b) Where would it be easier to lift with a crane?
3. c) If a stone is dropped from the same height on both planets (ignoring atmospheric resistance), on which planet does it fall faster? Justify each answer.

The strongest tides, called spring tides, occur when the Sun, the Moon, and the Earth are aligned, as shown in the diagram.

1. a) Explain why the Moon causes tides in the oceans.
2. b) Reason why the tides are stronger when the Sun is also aligned.
3. c) Predict what the tides will be like when the Sun and the Moon form a right angle with the Earth.

You drop a steel ball and a polystyrene ball of the same size at the same time from the same height, as shown in the diagram.

1. a) Under normal conditions, in air, which one reaches the ground first?
2. b) What if you repeated the experiment in a vacuum?
3. c) Explain the role played by mass and air resistance in each case.

Earth's gravity pulls the Moon with a force, as shown in the diagram.

So, why doesn't the Moon fall directly onto us? Explain what it means for the Moon to be in orbit, relating its motion to Earth's gravitational pull.

Imagine a planet with the same mass as Earth but much smaller and denser, so that its surface is much closer to its center, as compared in the diagram.

1. a) Would you weigh more or less on its surface than on Earth?
2. b) Justify your answer, taking into account that gravitational attraction depends on the mass of the planet and the distance to its center.

Describe a complete space journey from the perspective of the weight felt by the astronaut:

1. a) During launch, with the rocket accelerating upwards.
2. b) In orbit around Earth.
3. c) Walking on the surface of the Moon.

Justify each sensation by relating it to gravity or the motion of the spacecraft.

A fisherman from Cádiz checks the tide timetable every day before going out to fish.

1. a) Why do tides not always happen at the same time, but are delayed a little each day?
2. b) Why are tides more pronounced during a full moon and a new moon? Justify both answers.