Question 1

As a planet moves away from aphelion,how is its orbital velocity changing with time?

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Question 2

Name the elements A,B,C,and D of the ellipse shown below.

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Question 3

Why did Copernicus's model set the scale of the solar system?

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Question 4

Why do astronauts feel "weightless" inside the International Space Station?
A) They are so far from Earth that the gravitational force is very small.
B) They follow the same orbit as the space station.
C) The space station rotates to cancel the effect of gravity.
D) The space station is continually accelerating away from Earth.

Accepted Answer

Astronauts inside the International Space Station feel weightless because they are continuously falling towards Earth, while also following the same orbit as the space station. This creates a feeling of weightlessness, also known as microgravity. While the gravitational force is still present, it is counterbalanced by the centripetal force caused by their orbital motion.

Question 5

Why did Ptolemy's work remain popular in Europe through 1500 CE?

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Question 6

A monkey throws a pineapple to its playmate.The pineapple,with a mass of 0.5 kg,is accelerated to the left at a rate of 6 m/s².The monkey has a mass of 2 kg.What is its acceleration? A) 1 m/s² B) 1.5 m/s² C) 3 m/s² D) 6 m/s²

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Question 7

Planet A has twice the mass of planet B.Experiments determine that a bowling ball on planet A weighs eight times as much as it does on planet B.Relative to the radius of planet B,what is the radius of planet A?
A) Planet A has four times the radius of planet B.
B) Planet A has twice the radius of planet B.
C) Planet A has the same radius as planet B.
D) Planet A has half the radius of planet B.

Accepted Answer

The weight of an object on a planet is directly proportional to the mass of the planet and inversely proportional to the square of the radius of the planet. Given that the bowling ball weighs eight times as much on planet A as on planet B and planet A has twice the mass of planet B, we can use the formula for gravitational force (F = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are the masses involved, and r is the distance between the centers of the two masses) to determine the relationship between the radii of the two planets. The increase in weight by a factor of 8 due to doubling the mass implies that the radius must be halved to maintain the relationship, as the weight (or gravitational force) varies inversely with the square of the radius.

Question 8

The acceleration experienced by Earth due to the Moon's gravity is ________ the acceleration experienced by the Moon due to Earth's gravity.(Note that the Moon is about 1% of the mass of Earth.) A) 10^-4 times B) 10^-2 times C) equal to D) 10⁴

Accepted Answer

The gravitational force between two bodies is equal and opposite, but the acceleration depends on the mass. Since the Moon is about 1% of Earth's mass, the acceleration of Earth due to the Moon is about 1% (or 10^-2 times) of the acceleration of the Moon due to Earth.

Question 9

Sally Scientist applies an equal force to two objects.The first has a mass of 40 kg and the second has a mass of 10 kg.If the first object accelerates at 10 m/s²,what is the acceleration of the second? A) 2.5 m/s² B) 5.0 m/s² C) 10 m/s² D) 40 m/s²

Accepted Answer

According to Newton's second law of motion, $F = ma$, where $F$ is the force applied, $m$ is the mass of the object, and $a$ is the acceleration of the object. If the same force is applied to both objects, the acceleration of the second object, which has 1/4th the mass of the first (10 kg vs. 40 kg), will be 4 times greater than the acceleration of the first object. Since the first object accelerates at 10 m/s², the second object will accelerate at $10 m/s² \times 4 = 40 m/s²$.

Question 10

Why did Tycho Brahe's observations challenge the prevailing astronomical paradigm?

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Question 11

The gravitational force experienced by Earth due to the Moon is ________ the gravitational force experienced by the Moon due to Earth.(Note that the Moon is about 1% of the mass of Earth.)
A) 10-4 times
B) 10-2 times
C) equal to
D) 104

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the gravitational force experienced by Earth due to the Moon is equal and opposite to the gravitational force experienced by the Moon due to Earth. The masses of the objects do not affect this law.

Question 12

Why did Galileo's discovery of the moons of Jupiter support the heliocentric model?

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Question 13

Pluto has a perihelion of about 50 AU and an aphelion of 30 AU.What is the ratio of the gravitational force at aphelion to the gravitational force at perihelion?
A) 1
B) 5/3
C) 25/9
D) 25/3

Accepted Answer

The gravitational force is proportional to the inverse square of the distance, so the ratio of the gravitational force at aphelion to the gravitational force at perihelion is equal to the square of the ratio of the distances: (30/50)^2 = 9/25. To get the ratio of the gravitational forces, we have to invert this ratio, giving 25/9.

Question 14

Planet A has nine times the mass of planet B,but they have equal radii.How fast would you have to launch a rocket from planet A for it to escape the pull of its gravity,if the corresponding speed for planet A is 10 m/s?
A) 3 m/s
B) 10 m/s
C) 30 m/s
D) 90 m/s

Accepted Answer

Escape velocity is given by the formula: Ve= sqrt(2GM/R), where Ve is the escape velocity, G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet. 
Since the radius is the same for both planets, we can use the ratio of their masses (9:1) to find the ratio of their escape velocities. 
Ve(A)/Ve(B) = sqrt(2GM(A)/R)/sqrt(2GM(B)/R) 
Ve(A)/Ve(B) = sqrt(M(A)/M(B)) 
Ve(A)/10 = sqrt(9) 
Ve(A) = 30 m/s

Question 15

Both the Ptolemaic and Copernican models required equants.What assumption and observed phenomena necessitated these additions?

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Question 16

A planet follows the orbit around the Sun shown in the following figure.What is the orbital period?

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Question 17

The scientist who explained orbits as an effect of gravity was:
A) Nicolaus Copernicus.
B) Johannes Kepler.
C) Galileo Galilei.
D) Isaac Newton.

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Question 18

When planets undergo retrograde motion,they are also brighter on the sky than usual.How does the Copernican model account for this phenomenon?

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Question 19

Suppose the Sun suddenly quadrupled its mass,while Earth remained at the same distance from it.What is the ratio of Earth's orbital period after the change to that before it?
A) 1:16
B) 1:4
C) 1:2
D) 1:1

Accepted Answer

According to Kepler's third law, the square of the period of a planet's orbit is proportional to the cube of its semi-major axis (T^2 ∝ a^3). Since Earth's semi-major axis (average distance from the Sun) remains the same, its period is only determined by the Sun's mass. When the Sun quadruples its mass, the gravitational force between Earth and Sun increases, causing the orbital velocity of Earth to increase. According to the conservation of angular momentum, this increased velocity will cause Earth to move in a larger orbit with a longer orbital period.

The period, T, of a planet's orbit can be determined by the relation:

T^2 ∝ a^3 / M
where M is the mass of the central body (the Sun in this case).

Since the mass of the Sun quadruples, the new period, T', can be found by solving:

(T')^2 ∝ a^3 / (4M)
or
(T')^2 = T^2 * (4M / M) = 16 T^2

Taking the square root:

T' / T = 4^(1/2) / 2 = 2^(3/2) / 2 = 1.41

Therefore, the ratio of Earth's orbital period after the change to that before it is approximately 1:2.

Question 20

A child's top begins to spin.As it spins,a battery shrinks the top.How does the rate at which the top spins change as it shrinks? What physical principle determines this?

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Quiz 3: A Universe of Universal Laws

As a planet moves away from aphelion,how is its orbital velocity changing with time?

Name the elements A,B,C,and D of the ellipse shown below.

Why did Copernicus's model set the scale of the solar system?

Why do astronauts feel "weightless" inside the International Space Station?

Why did Ptolemy's work remain popular in Europe through 1500 CE?

A monkey throws a pineapple to its playmate.The pineapple,with a mass of 0.5 kg,is accelerated to the left at a rate of 6 m/s².The monkey has a mass of 2 kg.What is its acceleration?

Planet A has twice the mass of planet B.Experiments determine that a bowling ball on planet A weighs eight times as much as it does on planet B.Relative to the radius of planet B,what is the radius of planet A?

The acceleration experienced by Earth due to the Moon's gravity is ________ the acceleration experienced by the Moon due to Earth's gravity.(Note that the Moon is about 1% of the mass of Earth.)

Sally Scientist applies an equal force to two objects.The first has a mass of 40 kg and the second has a mass of 10 kg.If the first object accelerates at 10 m/s²,what is the acceleration of the second?

Why did Tycho Brahe's observations challenge the prevailing astronomical paradigm?

The gravitational force experienced by Earth due to the Moon is ________ the gravitational force experienced by the Moon due to Earth.(Note that the Moon is about 1% of the mass of Earth.)

Why did Galileo's discovery of the moons of Jupiter support the heliocentric model?

Pluto has a perihelion of about 50 AU and an aphelion of 30 AU.What is the ratio of the gravitational force at aphelion to the gravitational force at perihelion?

Planet A has nine times the mass of planet B,but they have equal radii.How fast would you have to launch a rocket from planet A for it to escape the pull of its gravity,if the corresponding speed for planet A is 10 m/s?

Both the Ptolemaic and Copernican models required equants.What assumption and observed phenomena necessitated these additions?

A planet follows the orbit around the Sun shown in the following figure.What is the orbital period?

The scientist who explained orbits as an effect of gravity was:

When planets undergo retrograde motion,they are also brighter on the sky than usual.How does the Copernican model account for this phenomenon?

Suppose the Sun suddenly quadrupled its mass,while Earth remained at the same distance from it.What is the ratio of Earth's orbital period after the change to that before it?

A child's top begins to spin.As it spins,a battery shrinks the top.How does the rate at which the top spins change as it shrinks? What physical principle determines this?