HW 5 CHP 4 (AS101)
D) A net force acting on an object will always cause a change in the object's _________.
momentum Force is actually defined as the rate of change in momentum.
E) As you watch the video, notice that the size of the tidal bulges varies with the Moon's phase, which depends on its orbital position relative to the Sun. Which of the following statement(s) accurately describe(s) this variation?
- High tides are highest at both full moon and new moon. - Low tides are lowest at both full moon and new moon. As the video shows, the tidal bulges are largest and the tidal minima are smallest at full moon and new moon. Those are the times when the tidal forces of the Sun and Moon align (and therefore add to one another). Therefore, high tides are higher and low tides are lower at these times, which are called spring tides. (In contrast, we have neap tides at first- and third-quarter moons, when high tides are not as high and low tides are not as low.)
M) Imagine another solar system, with a star of the same mass as the Sun. Suppose a planet with a mass twice that of Earth (2 M earth) orbits at a distance of 1 AU from the star. What is the orbital period of this planet?
1 year The planet's mass is so small compared to the star's mass that it has essentially no effect on the planet's orbit. (W know this from Newton's version of Kepler's third law.) The fact that the planet has the same orbital distance as Earth therefore means it must have the same orbital period as Earth.
C) Consider again the experimental trials from Part A. This time, you wish to test how the size of an object affects the rate of its fall. Which pair of trials should you compare?
1. Mass = 0.5 kg Size = marble Height = 30 m 2. Mass = 0.5 kg Size = basketball Height = 30 m
According to the law of universal gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass?
Earth's orbit would not change.
If you want to make a rocket turn left, you need to:
Fire an engine that shoots out gas to the right.
If Earth were twice as far from the Sun, the force of gravity attracting Earth to the Sun would be:
one-quarter as strong.
4.51) Find the orbital period for the planet in each case. (Hint: The calculations for this problem are so simple that you will not need a calculator.) A) A planet with twice Earth's mass orbiting at a distance of 1 AU from a star with the same mass as the Sun.
p = 1 year Earth and Sun. The Earth's mass doubles but E so small compared to Sun. Doesn't matter. Don't need to change formula. p^2 = a^3 p^2 = 1^3 p=1 year
B) A planet with the same mass as Earth orbiting at a distance of 1 AU from a star with sixteen times the Sun's mass.
p = 3 months p^2 = 4 x pie ^2 x a^3 / GM 16 times Sun's mass Take 1/6 and times it by regular formula of 1 yr p^2= 1/16 * 1 yr p= square root of (1/16) p= 1/4 years p= 3 months
E) Calculate the orbital period of a spacecraft in an orbit 300 kilometers above Earth's surface.
p shuttle = 5400 s
G) Suppose the Sun suddenly shrunk, reducing its radius by a half (but keeping its mass the same). The force of gravity exerted on Earth by the Sun would ____________.
remain the same
D) Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.
the Moon has a larger acceleration than Earth, because it has a smaller mass Newton's second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa.
D) If you are standing on a scale in an elevator, what exactly does the scale measure?
the force you exert on the scale
B) Assume you have completed the two trials chosen in Part A. Which of the following possible outcomes from the trials would support Newton's theory of gravity? Neglect effects of air resistance.
Both balls fall to the ground in the same amount of time.
T) At which lunar phase(s) are tides most pronounced (for example, the highest high tides)?
Both new and full moons These are the spring tides, when the tidal forces of the Sun and Moon work together.
J) Which of the following scenarios involves energy that we would typically calculate with Einstein's formula E=mc2?
A small amount of the hydrogen in of a nuclear bomb becomes energy as fusion converts the hydrogen to helium. Hydrogen fusion in a nuclear bomb converts a small amount of the mass (about 0.7%) of the hydrogen into energy (the rest becomes helium). Any time that mass is converted to energy we can calculate the amount of energy with Einstein's formula.
D) Suppose that the Sun were to collapse from its current radius of about 700,000 km to a radius of only about 6000 km (about the radius of Earth). What would you expect to happen as a result?
A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. Submit
C) As the cloud shrinks in size, its central temperature __________ as a result of its __________. Drag words indicating what happens to the first blank and indicating the reason to the second blank.
As the cloud shrinks in size, its central temperature *increases* as a result of its *gravitational potential energy being converted to thermal energy*. 1. increases 2. gravitational potential energy being converted to thermal energy
B) Drag words indicating what happens to the first blank and indicating the reason to the second blank.
As the cloud shrinks in size, its rate of rotation *speeds up* because *its total angular momentum is conserved*. 1. speeds up 2. its total angular momentum is conserved
D) If you actually performed and compared the two trials chosen in Part C, you would find that, while the basketball and marble would hit the ground at almost the same time, it would not quite be exact: The basketball would take slightly longer to fall to the ground than the marble. Why?
Because air resistance has a greater effect on the larger ball.
Which one of the following describes an object that is accelerating?
A car going around a circular track at a steady 100 miles per hour.
Which person is weightless?
A child in the air as she plays on a trampoline.
C) Why are astronauts weightless in the Space Station?
Because the Space Station is constantly in free-fall around the Earth You are weightless whenever you are in freefall, and the Space Station and other objects orbiting Earth are in a constant state of freefall.
B) Suppose you drop a 10-pound weight and a 5-pound weight on the Moon, both from the same height at the same time. What will happen?
Both will hit the ground at the same time. The acceleration of gravity on the Moon is smaller than it is on Earth, but it still is the same for all objects. Therefore both objects will fall at the same rate. (And because there is no air on the Moon, they'll hit at the same time no matter what shape or density they have.)
Concept Quiz A) Which of the following represents a case in which you are not accelerating?
Driving in a straight line at 60 miles per hour
P) Each of the following lists two facts. Which pair of facts can be used with Newton's version of Kepler's third law to determine the mass of the Sun?
Earth is 150 million km from the Sun and orbits the Sun in one year. A single planet's orbital distance and orbital period are all we need to determine the Sun's mass Newton's version of Kepler's third law.
L) Suppose that the Sun shrank in size but that its mass remained the same. What would happen to the orbit of the Earth?
Earth's orbit would be unaffected. The force of gravity between Earth and the Sun, and hence the orbital distance and speed of Earth, depends only on the Sun's mass (and the Earth-Sun distance), not on the Sun's size.
E) Suppose you are in an elevator that is traveling upward at constant speed. How does your weight compare to your normal weight on the ground?
It is the same. As long as the elevator is not accelerating, your weight on a scale in the elevator will be the same whether the elevator is on the ground or rising (or falling) at constant speed.
E) Suppose that two asteroids are orbiting the Sun on nearly identical orbits, and they happen to pass close enough to each other to have their orbits altered by this gravitational encounter. If one of the asteroids ends up moving to an orbit that is closer to the Sun, what happens to the other asteroid?
It will end up on an orbit that is farther from the Sun.
C) The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.
Largest acceleration -to sun -to earth -to moon -to asteroid -to hydrogen atom Smallest acceleration
4.52) A) Find Earth's approximate mass from the fact that the Moon orbits Earth in an average time of 27.3 days at an average distance of 384,000 kilometers. (Hint: The Moon's mass is only about 1/80 of Earth's.)
M earth = 6 x 10^24 kg p^2 = 4 x pie ^2 x a^3 / GM p= 27.3 days --> 2,358,720 sec a= 384,000 km --> 384,000,000 meters G= 6.67x10^-11 M=? Find M = 4 x pie ^2 x a^3 / G x (81/80) x p^2 M= 5.95 x 10^24 kg
F) Estimate the mass of the Milky Way Galaxy from the fact that the Sun orbits the galactic center every 230 million years at a distance of 27,000 light-years. (As we'll discuss in Chapter 23, this calculation actually tells us only the mass of the galaxy within the Sun's orbit.)
M galaxy = 1.88 x 10^41 kg
B) Find Jupiter's mass from the fact that its moon Io orbits every 42.5 hours at an average distance of 422,000 kilometers.
M jupiter = 1.9 x 10^27 kg p^2 = 4 x pie ^2 x a^3 / GM p= 42.5 hrs --> 153,00 sec a= 422,000 km --> 422,000,000 meters G= 6.67x10^-11 M=? Find
D) Pluto's moon Charon orbits Pluto every 6.4 days with a semimajor axis of 19,700 kilometers. Calculate the combined mass of Pluto and Charon. p^2 = 4 x pie ^2 x a^3 / GM p= 6.4 days --> 552,960 sec a= 19,700 km --> 19,700,000 meters G= 6.67x10^-11 M=? Find
M pluto + M charon = 1.48 x 10^22 kg
A) Each diagram shows a single experimental trial in which you will drop a ball from some height. In each case, the ball's size, mass, and height are labeled. Note that two diagrams show a basketball, one diagram shows a bowling ball of the same size but larger mass, and one diagram shows a much smaller marble with the same mass as the basketball. You have a timer that allows you to measure how long it takes the ball to fall to the ground. Which pair of trials will allow you to test the prediction that an object's mass does not affect its rate of fall?
Mass = 5.0kg Size = bowling ball Height = 20m
A) As shown in the video, Earth has two tidal bulges at all times. Approximately where are these bulges located?
One faces the Moon and one faces opposite the Moon. The tidal bulges face toward and away from the Moon, because they are caused primarily by the gravitational attraction between Earth and the Moon. Friction explains why the bulges are slightly ahead of the Earth-Moon line, rather than directly on the Earth-Moon line. We'll ignore that detail for now.
F) Imagine Earth's identical twin planet "Farth" is twice as far away from the Sun as Earth is. Compared to the force of gravity the Sun experiences due to Earth, how strong is the force of gravity the Sun experiences due to Farth?
One-fourth as strong.
C) You discover a planet orbiting a distant star that has about the same mass as the Sun, with an orbital period of 63 days. What is the planet's orbital distance?
R planet = 4.64 x 10^10 meters p^2 = 4 x pie ^2 x a^3 / GM p= 63 days --> 5.44 x 10^6 sec G= 6.67x10^-11 kg M= 1.989 x 10^30 kg a= ? Find
Q) When space probe Voyager 2 passed by Saturn, its speed increased (but not due to firing its engines). What must have happened?
Saturn must have lost a very tiny bit of its orbital energy. Voyager 2 gained orbital energy by taking it from Saturn.
E) Einstein's theory, like Newton's, predicts that, in the absence of air resistance, all objects should fall at the same rate regardless of their masses. Consider the following hypothetical experimental results. Which one would indicate a failure of Einstein's theory?
Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates.
A) The following five diagrams show pairs of astronomical objects that are all separated by the same distance d. Assume the asteroids are all identical and relatively small, just a few kilometers across. Considering only the two objects shown in each pair, rank the strength, from strongest to weakest, of the gravitational force acting on the asteroid on the left.
Strongest Force -to sun -to earth -to moon -to asteroid -to hydrogen atom Weakest Force
B) The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.
Strongest Force -to sun -to earth -to moon -to asteroid -to hydrogen atom Weakest Force
C) The following diagrams show five pairs of asteroids, labeled with their relative masses (M) and distances (d) between them. For example, an asteroid with M=2 has twice the mass of one with M=1 and a distance of d=2 is twice as large as a distance of d=1. Rank each pair from left to right based on the strength of the gravitational force attracting the asteroids to each other, from strongest to weakest.
Strongest force -M=2, M=2, d=1 -M=1, M=2, d=1 -M=1, M=1, d=1 -M=1, M=2, d=2 -M=1, M=1, d=2 Weakest force
A) Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Assume the spaceship has the same mass throughout the trip (that is, it is not burning any fuel). Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest.
Strongest force -closest to Earth -btwn Earth and midpoint -@ midpoint -past midpoint and btwn moon -closest to moon Weakest force Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as the spaceship gets farther from Earth.
B) The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.
Strongest force -closest to moon -btwn moon and midpoint -@ midpoint -btwn Earth and midpoint -closest to Earth Weakest force
4.56 C) The Moon's orbital period is about one month. Apply Kepler's 3rd law to find the approximate orbital period of Swisscheese. (Hint: If you form the ratio of the orbital distances of Swisscheese and the Moon, you can solve this problem with Kepler's original version of his third law rather than looking up all the numbers you'd need to apply Newton's version of Kepler's third law.)
T swisscheese = 2.83 months
U) Which of the following best explains why the Moon's orbital period and rotation period are the same?
The Moon once rotated faster, but tidal friction slowed the rotation period until it matched the orbital period. For the same basic reason, nearly all moons orbiting large planets show the same face to the planet at all times.
G) Suppose the Sun were suddenly to shrink in size but that its mass remained the same. According to the law of conservation of angular momentum, what would happen?
The Sun would rotate faster than it does now. Angular momentum is the product mass ( velocity (of rotation) ( radius. Shrinking the Sun's radius does not affect its mass, so the rotational velocity must increase in order to keep angular momentum constant.
C) Suppose object A has three times as the mass of object B. Identical forces are exerted on the two objects. Which statement is true?
The acceleration of object B is three times that of object A.
R) Suppose that a lone asteroid happens to be passing Jupiter on an unbound orbit (well above Jupiter's atmosphere and far from all of Jupiter's moons.) Which of the following statements would be true?
The asteroid's orbit around Jupiter would not change, and it would go out on the same unbound orbit that it came in on. This is true because orbits cannot change spontaneously, and there is nothing in this situation to add or subtract to the asteroid's orbital energy.
H) Suppose you kick a soccer ball straight up to a height of 10 meters. Which of the following is true about the gravitational potential energy of the ball during its flight?
The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point. Gravitational potential energy is greater at for a larger height because the ball has a greater distance that it can fall (and it accelerates as it falls).
C) As you found in Part A, your weight will be greater than normal when the elevator is moving upward with increasing speed. For what other motion would your weight also be greater than your normal weight?
The elevator moves downward while slowing in speed.
K) A rock held above the ground has potential energy. As the rock falls, this potential energy is converted to kinetic energy. Finally, the rock hits the ground and stays there. What has happened to the energy?
The energy goes to producing sound and to heating the ground, rock, and surrounding air. Energy is always conserved, so the energy of the rock cannot simply disappear. Instead, it dissipates (becomes "spread out") among so many molecules in the air and ground that we no longer notice it.
B) explain
The orbital period would be longer because the orbital distance is greater. This is supported by Kepler's 3rd law which is the more distant a planet is that orbits the sun, then the greater the orbital period would be. And then that was realized that it could apply to any object orbiting something, not just something orbiting the sun. Submit
N) Imagine another solar system, with a star more massive than the Sun. Suppose a planet with the same mass as Earth orbits at a distance of 1 AU from the star. How would the planet's year (orbital period) compare to Earth's year?
The planet's year would be shorter than Earth's. This is true because the greater mass of the star would mean a stronger force of gravity at any given distance, which in turn would mean a higher orbital velocity.
D) One tidal bulge faces toward the Moon because that is where the gravitational attraction between Earth and the Moon is strongest. Which of the following best explains why there is also a second tidal bulge?
The second tidal bulge arises because gravity weakens with distance, essentially stretching Earth along the Earth-Moon line. Tides are created by gravity, and the tidal force is caused by the fact that gravity weakens with distance. Therefore, the parts of Earth that are closer to the Moon feel a stronger gravitational attraction to the Moon, and the parts of Earth that are farther away feel a weaker gravitational attraction to the Moon. This varying gravitational attraction essentially stretches Earth along the Earth-Moon line, creating tidal bulges on both sides.
This tutorial will help you understand how the force of gravity determines the motion of stars and planets. Launch the Motion and Gravity tutorial. Answer the ungraded questions in the tutorial and the graded follow-up questions below. A) Suppose a parachutist is falling toward the ground, and the downward force of gravity is exactly equal to the upward force of air resistance. Which statement is true?
The velocity of the parachutist is not changing with time.
A) Drag words indicating what happens to the first blank and indicating the reason to the second blank.
The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward *gradually becomes stronger* because *the strength of gravity follows an inverse square law with distance*. 1. gradually becomes stronger 2. the strength of gravity follows an inverse square law with distance
I) Suppose you heat an oven to 200°C (about 400°F) and boil a pot of water. Which of the following explains why you would be burned by sticking your hand briefly in the pot but not by sticking your hand briefly in the oven?
The water can transfer heat to your arm more quickly than the air. The boiling water has a lower temperature (212°F) than the air in the hot oven (400°F), but because it is much more dense, heat is transferred to your arm at a higher rate due to the more frequent collisions between your arm and the water molecules.
S) Which of the following best describes the origin of ocean tides on Earth?
Tides are caused by the difference in the force of gravity exerted by the Moon across the sphere of the Earth. This is an accurate statement; be sure you understand it.
V) Suppose the Moon's orbit were unchanged, but it rotated faster (meaning it did not have synchronous rotation). Which of the following would be true?
We would no longer always see nearly the same face of the Moon. Seeing nearly the same face is a consequence of synchronous rotation, so once this rotation changes, we'd no longer see the same face at all times.
D) In words, describe how tides would differ due to the presence of this second moon. Consider the cases when the two moons are on the same side of Earth, on opposite sides of Earth, and 90∘90∘ apart in their orbits.
With a second moon, a third tidal bulge would be created. This would create larger tides when the two moons are on the same side of the Earth and if they were on opposite sides. If the two moons were 90 degrees apart in their orbits, the tides would be smaller. Answer Key: Swisscheese would create a third tidal bulge on the Earth. When the moons were on the same side of the Earth or on opposite sides, these bulges would add together to create extra large tides. When they were 90 degrees apart, the bulges would partially cancel, creating smaller tides. When the moons were lined up in their new or full phases, the bulges they raised would also add with the tidal bulge due to the Sun, creating extra large tides.
B) Most people are familiar with the rise and fall of ocean tides. Do tides also affect land?
Yes, though land rises and falls by a much smaller amount than the oceans. Tides affect the entire Earth, but they are much more noticeable for the oceans because water flows so much more easily than land. Still, the land rises and falls about 1 centimeter with the tides.
Suppose you visit another planet:
Your mass would be the same as on Earth, but your weight would be different.
D) Jupiter's moon Europa (mass = 0.008 M earth, radius = 0.25 R earth). g= GM/R^2 G= 6.67 x 10 ^-11 M earth = 6x10^24) R earth = (6,371,000 m)
a Europa = 1.3 m/s^2
C) Jupiter (mass = 317.8 M earth, radius = 11.2 R earth). g= GM/R^2 G= 6.67 x 10 ^-11 M earth = 6x10^24) R earth = (6,371,000 m)
a Jupiter = 25 m/s^2
4.54) Calculate the acceleration of gravity on the surface of each of the following worlds. A) Mars (mass = 0.11 M earth, radius = 0.53 R earth).
a Mars = 3.8 m/s^2 g= GM/R^2 G= 6.67 x 10 ^-11 M= .11 * (6x10^24) R= .53 * (6,371,000 m)
E) Mars's moon Phobos (mass = 1.1×10^16 kg, radius = 12 km). g= GM/R^2 G= 6.67 x 10 ^-11 M earth = 6x10^24) R earth = (6,371,000 m)
a Phobos = .0051 m/s^2
B) Venus (mass = 0.82 M earth, radius = 0.95 M earth). g= GM/R^2 G= 6.67 x 10 ^-11 M earth = 6x10^24) R earth = (6,371,000 m)
a Venus = 8.9 m/s^2
F) The planets never travel in a straight line as they orbit the Sun. According to Newton's second law of motion, this must mean that _________.
a force is acting on the planets Because the planets are not traveling in straight lines, the planets are always accelerating, and Newton's second law tells us that a force must be acting to cause the acceleration.
If the Moon were closer to Earth, high tides would:
be higher than they are now.
F) You have found that tides on Earth are determined primarily by the position of the Moon, with the Sun playing only a secondary role. Why does the Moon play a greater role in causing tides than the Sun?
because the gravitational attraction between Earth and the Moon varies more across Earth than does the gravitational attraction between Earth and the Sun The Sun exerts a stronger gravitational force on Earth, which is why Earth orbits the Sun. However, tides are caused by the variation in the gravitational attraction across Earth. Even though the gravitational attraction between Earth and the Moon is smaller than the attraction between Earth and the Sun, the Moon's much closer distance makes this attraction vary more across Earth. That is why tides are due primarily to the Moon, with only a secondary effect from the Sun.
Consider the statement "There's no gravity in space." This statement is:
completely false
As an interstellar gas cloud shrinks in size, its gravitational potential energy:
gradually transforms into other forms of energy.
A) Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward with increasing speed, your weight will be __________.
greater than your normal weight at rest
B) Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________.
less than your normal weight at rest
Suppose Earth had a second moon, called Swisscheese, with an average orbital distance double the Moon's and a mass about the same as the Moon's. A) Is Swisscheese's orbital period longer or shorter than the Moon's?
longer Increased a means increased p
B) A kilogram is a measure of an object's ____________.
mass
O) Newton showed that Kepler's laws are _________.
natural consequences of the law of universal gravitation Kepler discovered his laws by looking for a mathematical way to explain Tycho's observations of the planets. His laws successfully predicted planetary positions, but he did not know why they were true. Newton showed that they are true as a result of the universal law of gravitation.
H) When the Sun dies it will become a white dwarf, which will be roughly the same size as the Earth. Assuming the Sun doesn't lose any mass as it becomes a white dwarf, the force of gravity exerted on Earth due to the Sun will ____________.
not change as the Sun turns into a white dwarf
D) A bowling ball and a small marble will fall downward to the surface of the Moon at the same rate because ____________.
the ratio of the force of gravity exerted on an object to the object's mass is the same.
Compared to its angular momentum when it is farthest from the Sun, Earth's angular momentum when it is nearest to the Sun is:
the same
E) If you stood on a planet with four times the mass of Earth, and twice Earth's radius, how much would you weigh?
the same as on Earth
C) Any particular location on Earth experiences __________.
two high tides and two low tides each day The video shows that any location on Earth passes through both tidal bulges and both tidal minima (the places where the tides are smallest) each day, which means two high tides and two low tides. Again, recall that this is true for both land and oceans, though tides are more noticeable in the oceans because water flows so much more readily than land.