ASTR 1210 Homework 8
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
Newton showed that Kepler's laws are _______
natural consequences of the law of universal gravitation
If you are standing on a scale in an elevator, what exactly does the scale measure?
the force you exert on the scale. neither your mass nor the gravitational force exerted on you change when you are in the elevator. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to your normal weight and a force due to the elevator's acceleration.
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
...
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. The dramatic shrinkage of the Sun would mean the loss of a huge amount of gravitational potential energy. Because energy is always conserved, this "lost" gravitational potential energy must reappear in other forms, such as heat (thermal energy) and light (radiative energy). Meanwhile, conservation of angular momentum would ensure that the collapsed Sun would spin much faster
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 free fall, and the Space Station and other objects orbiting Earth are in a constant state of free fall
Ranking strength of gravitation force acting on an asteroid
Because the distance is the same for all five cases, the gravitation force depends only on the product of the masses. And because the same asteroid is on the left in all five cases the relative strength of the gravitational force depends on the mass of the object on the right.
The animation shows a collapsing cloud of interstellar gas. As the cloud collapses, the force of gravity drawing the cloud inward ____________ because ____________.
Blank 1: gradually becomes stronger Blank 2: the strength of gravity follows an inverse square law with distance. The force of gravity between any two particles increases as the particles come closer together. Therefore, as the cloud shrinks and particles move closer together, the force of gravity strengthens. This will tend to accelerate the collapse as long as no other force resists it--which is the case during the early stages of the collapse before the internal gas pressure builds up. (once the gas pressure builds up the outward push of the pressure can counteract the inward pull of gravity, which is why the cloud eventually stops contracting)
As the cloud shrinks in size, its central temperature _______ as a result of _______.
Blank 1: increases Blank 2: gravitational potential energy being converted to thermal energy As the cloud shrinks in size, its gravitational potential energy decreases. Because energy cannot simply disappear, the "lost" gravitational potential energy must be converted into some other form. Some of it is converted into thermal energy, which raises the temperature of the gas cloud. The rest is mostly converted into radiative energy, which is released into space as light.
As the cloud shrinks in size, its rate of rotation _________ because _________.
Blank 1: speeds up Blank 2: its total angular momentum is conserved Total angular momentum is always conserved. In this case, because nothing is carrying angular momentum into or out of the cloud, the cloud's angular momentum stays constant. Maintaining constant angular momentum as the cloud shrinks requires that its rate of rotation increase, because angular momentum depends on the product of rotation rate and radius
At which lunar phases are tides most pronounced?
Both new and full moons. These are the spring tides, when the tidal forces of the Sun and Moon work together
Suppose you drop a 10lb weight and 5lb 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
What temperature scale? Water freezes into ice at 0 Liquid water boils at 100 a typical room temperature is 24
Celsius
Which of the following represents a case in which you are not accelerating? Going from 0 to 60 miles per hour in 10 seconds. Slamming on the brakes to come to a stop at a stop sign. Driving 60 miles per hour around a curve. Driving in a straight line at 60 miles per hour.
Driving in a straight line at 60 mph. This is constant velocity, which means zero acceleration
What facts are needed to 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 with Newton's version of Kepler's third law
Suppose 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, not on the Sun's size
what temperature scale? Ice Cream is stored in freezers at 26 A hot summer day might be 100
Fahrenheit
Suppose you are in an elevator that is traveling upward at constant speed. How does your weight comare 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/falling at constant speed.
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. Total energy must be conserved, so if one asteroid loses energy and moves to a closer orbit, the other must gain energy and move to a more distant orbit
What temperature scale? The coldest possible temperature is 0 Water boils into gas phase at 373. 15
Kelvin
When space probe Voyager 2 passed by Saturn, its speed increased. What must have happened?
Saturn must have lost a very tiny bit of its orbital energy
Ranking strength of gravitation force attracting the asteroids to each other, from strongest to weakest.
Strongest-->Weakest: 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
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
What is the best explanation for 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
Suppose the Sun was 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 of mass x velocity (of rotation) x radius. Shrinking the Sun's radius does not affect its mass, so the rotational velocity must increase in order to keep angular momentum constant
Suppose you kick a soccer ball straight up to a height of 10 meters. Which of the following is true about gravitational potential energy of the ball during its flight? The ball's gravitational potential energy is greatest at the instant the ball leaves your foot. The ball's gravitational potential energy is greatest at the instant it returns to hit the ground. The ball's gravitational potential energy is greatest at the instant when the ball is at its highest point. The ball's gravitational potential energy is always the same.
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)
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. When the elevator is moving downward, a downward acceleration would mean an increasing downward speed. Therefore, as your answer correctly states, an upward acceleration would mean a decreasing downward speed.
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
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 compare to Earth's?
The planet's year would be shorter. 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
Suppose you heat an oven to 400 degrees F and boil a pot of water. Why would you 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) than the air, but because it is much more dense, heat is transferred to your arm at a higher rate due to to the more frequent collisions between your arm and the water molecules.
What best describes the origin of ocean tides on Earth?
Tides are caused by the difference in the fore of gravity exerted by the Moon across the sphere of the Earth
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
what is a scenario that we would typically calculate with Einstein's formula E=mc^2
a small amount of the hydrogen in 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 of the hydrogen into energy. Any time that mass is converted into energy, we can calculate the amount of energy with Einstein's formula
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. Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making your weight greater than your normal (at rest) weight.
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. Even though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward; the situation is like that of a ball that is still on its way up after you throw it, even though it is being pulled downward with the acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal
