Please solve the following questions. This is not an assignment, it will not be graded, and you do not need to submit your solutions to anyone. The questions are simply intended to help you practice for the exam.

These questions will not appear in the exam itself. Students who don't genuinely attempt to solve the questions on their own, and only memorize the solutions, will have a very hard time in the actual exam!

These questions are not multiple-choice, to encourage you to think of the answers on your own, but the questions in the actual exam will be multiple-choice.

If you need any clarifications for these questions, you can ask for them on the course Teams channel.

Question 1 Show/hide solution

If I throw a ball in empty space with no gravity, it will keep moving forever at a constant speed in the same direction. However, this won't happen if I throw a ball on Earth. Explain why using Newton's first law.

Solution: According to Newton's first law, an object will continue moving at a constant speed in a straight line unless acted on by an outside force. On Earth, the force of gravity will act on the ball and pull it down towards the ground.

Question 2 Show/hide solution

According to Newton's second law, when does an object's momentum change?

Solution: If a force is applied to it.

Question 3 Show/hide solution

An proton is pulling an electron towards it by exerting an electric force on it. Does the electron exert a force on the proton?

Solution: Yes, according the Newton's third law the electron exerts an equal and opposite force, pulling the proton towards it.

Question 4 Show/hide solution

Explain how a rocket works using Newton's laws.

Solution: The rocket pushes gas out behind it. According to Newton's third law, there must be an equal and opposite force, pushing the rocket forward. According to Newton's second law, this force accelerates the speed of the rocket.

Question 5 Show/hide solution

I have a block of concrete and an inflated balloon. Both have the same volume. Which one will have a larger mass, and why?

Solution: The block of concrete is more dense, so it will have a larger mass, since density is mass per unit volume and both objects have the same volume.

Question 6 Show/hide solution

I have a block of lead and a bucket of water. Both have the same mass. Which one will have a larger volume, and why?

Solution: The water has a smaller density, so it will have a larger volume, since density is mass per unit volume and both objects have the same mass. In other words, the water has less mass per unit volume, so it needs more volume to achieve the same amount of mass.

Question 7 Show/hide solution

If the Earth had an orbital radius twice as large, how will its angular momentum change?

Solution: Angular momentum is mass times velocity times distance. If we increase the distance by a factor of 2, then angular momentum will also increase by the same factor.

Question 8 Show/hide solution

If the mass of the Earth doubled, how would the force of gravity between the Earth and the Moon change?

Solution: The force of gravity between two objects is proportional to the masses of both objects, so if we increase one of the masses by a factor of 2, the force will also increase by the same factor.

Question 9 Show/hide solution

If the distance between the Earth and the Moon tripled, how would the force of gravity between the Earth and the Moon change?

Solution: The force of gravity between two objects is INVERSELY proportional to the SQUARE of the distance between the objects, so if we increase distance by a factor of 3, the force will DECREASE by a factor of 3 squared, or 9.

Question 10 Show/hide solution

Does the Andromeda galaxy, 2.5 million light years away, exert any gravity on you personally?

Solution: In principle, yes. Both the Andromeda galaxy and you have mass, and anything that has mass anywhere in the universe attracts anything else with mass anywhere in the universe, so the Andromeda galaxy and you attract each other gravitationally. However, this force is so tiny that you will never be able to measure it.

Question 11 Show/hide solution

"The astronauts on the International Space Station do not experience any gravity." True or false?

Solution: False. They feel weightless, since they are in free fall, so technically they are falling all the time. However, gravity is still acting on them, which is exactly why the space station stays in orbit.

Question 12 Show/hide solution

"A planet moves fastest when it is at the perihelion (the point closest to the Sun) compared to any other point, due to Kepler's second law". True or false?

Solution: True. Kepler's second law says a planet moves faster in its orbit when it is closer to the Sun, and the perihelion is the point where the planet is closest to the Sun.

Question 13 Show/hide solution

Which planet has the most eccentric orbit? And what does this mean for the shape of its orbit?

Solution: Mercury has the most eccentric orbit. This means that the shape of Mercury's orbit is the most different from a circle (or "the most elliptic") compared to the other planets.

Question 14 Show/hide solution

Where is the Kuiper belt located?

Solution: 30-50 AU away from the Sun.

Question 15 Show/hide solution

If Superman throws a ball with enough force, can he send that ball into an orbit around Earth?

Solution: Yes. More force means more acceleration and thus larger velocity. If thrown in just the right direction with just the right force, the ball can be made to "fall" around the Earth, which is exactly what an orbit is.

Question 16 Show/hide solution

"Kepler's laws give a 100% precise description of the orbits of planets in the solar system." True or false?

Solution: False. Kepler's laws only take the gravitational effects of the Sun into account. However, due to Newton's law of gravitation, now we know that the planets also exert gravity on each other, and this is not taken into account in Kepler's laws. This causes subtle differences in the orbits of the planets compared to what Kepler's laws say. In addition, today we know that Newton's laws aren't 100% precise either, and general relativity provides a much more precise description of the orbits.

Question 17 Show/hide solution

What has more momentum: a 1 kg ball moving at 5 m/s or a 5 kg ball moving at 1 m/s?

Solution: Momentum is mass times velocity. In both cases, the product of mass and velocity is 5, so in fact, both ball have the same momentum.

Question 18 Show/hide solution

A ball was moving at a velocity of 3 m/s. It then accelerated with an acceleration of 6 m/s² for 2 seconds. What was its final velocity?

Solution: 3 + 2 × 6 = 15 m/s.

Question 19 Show/hide solution

During a plane flight, when is the plane's frame an inertial frame and when is it not an inertial frame?

Solution: Remember that an inertial frame is one that doesn't rotate or accelerate. When the plane is taking off and landing, it's accelerating, so it's not an inertial frame. Once it's in the air, as long as it's maintaining constant speed (no acceleration) and constant direction (no rotation), it's an inertial frame.

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