Homework 2 PDF

Homework 2 Friday, October 11, 2024 4:55 PM   According to the universal law of gravitation, if you triple the distance between two objects, then the gravitational force between them \_\_\_\_\_\_\_\_\_\_. - decreases by a factor of 9 - Gravity follows an inverse square law, so the force go...

Homework 2 Friday, October 11, 2024 4:55 PM   According to the universal law of gravitation, if you triple the distance between two objects, then the gravitational force between them \_\_\_\_\_\_\_\_\_\_. - decreases by a factor of 9 - Gravity follows an inverse square law, so the force goes down with the square of the distance; in this case, increasing the distance by a factor of 3 causes the force to decrease by a factor of 32 = 9.     The great contribution of Nicholaus Copernicus was to \_\_\_\_\_\_\_\_\_\_. - create a detailed model of our solar system with the Sun at the center - Although his model still had numerous flaws, it started the Copernican revolution and ultimately led to our modern understanding of the cosmos.   When a spinning ice skater pulls in his arms, he spins faster because \_\_\_\_\_\_\_\_\_\_. - His angular momentum must be conserved, so reducing his radius must increase his speed of rotation. - Remember that angular momentum is related to an objects mass × velocity × radius. The skater\'s mass stays the same but pulling in his arms reduces his \"radius,\" so his velocity or rotation must increase to keep his angular momentum constant.   The diagram shows a planet at four positions in its orbit. At which position does it have the greatest angular momentum? - The angular momentum is the same at all four points. - This is the case because angular momentum is conserved throughout the orbit     Choose the correct definition and two examples of kinetic energy. - Kinetic energy is the energy an object has due to its motion. A car driving down the highway or molecules of hot, raising up air have kinetic energy. Choose the correct definition and two examples of radiative energy - Radiative energy is energy in the form of light. Sunlight and radio waves carry this form of energy.   Choose the correct definition and two examples of potential energy. - Potential energy is energy that is stored. Two examples are mechanical energy in a compressed spring and gravitational energy in a rock on the top of a hill.   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.     How did the Ptolemaic model explain the apparent retrograde motion of the planets? - The planets moved along small circles that moved on larger circles around the Earth. - This created a \"loop-the-loop\" motion that made the planets in the model appear to sometimes go backward as viewed from Earth.   Choose the correct definitions of speed, velocity, and acceleration. - Speed is used to describe how fast the object is moving. - Velocity is used to describe how fast the object is moving and tells us in which direction it is going. - Acceleration is the rate of change of velocity in time.   What are the units of acceleration? - m/s\^2   What is the acceleration of gravity? - The acceleration of an object in free-fall. It is 9.8 m/s2   The simplest way to test the effects of mass is to compare the results of two trials that are identical except for the mass of the balls. In the language of experimental design, we say that the mass is the \"variable of interest\" for this experiment, and we therefore hold the other variables (size and height) constant so that they cannot affect the results.     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. - Newton\'s theory of gravity predicts that, in the absence of air resistance, all objects on Earth should fall with the same acceleration of gravity, regardless of mass. This means that balls dropped from the same height should take the same amount of time to reach the ground.   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. - The larger size and lower density of the basketball means it will encounter more air resistance than the marble, so it will take slightly longer to reach the ground. Newton\'s theory of gravity has been tested extensively, and while it passed many tests, it did not pass all of them. For example, its prediction for how Mercury\'s orbit changes with time disagrees slightly with observations. Einstein\'s general theory of relativity improves on Newton\'s theory: In most cases the two theories of gravity predict the same results, but in the situations where they differ, Einstein\'s theory works better than Newton\'s.   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. - Dropping the balls on the Moon removes any potential effects due to air resistance, so a result in which mass affects the rate of fall would directly contradict the prediction of Einstein\'s (as well as Newton\'s) theory.     Part complete Which of the following best describes how modern astronomers view astrology? - Astrology played an important part in the development of astronomy in ancient times, but it is not a science by modern standards. - Whenever predictions of astrology have been tested, they have proven accurate only about as often as would be expected by pure chance. The astrology practiced by those who cast predictive horoscopes can be tested by \_\_\_\_\_\_\_\_\_\_ - comparing how often the predictions come true to what would be expected by pure chance. - And in such tests, astrological predictions have never proven to be more successful than is expected by chance.   Which person is weightless during the activity shown? - The diver is the only person that is in free-fall, and hence the only one that is weightless.   Suppose you heat an oven to 400°F (about 200°C) 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 or 100°C) than the air in the hot oven, but because it is much denser, heat is transferred to your arm at a higher rate due to the more frequent collisions between your arm and the water molecules.   Scientific thinking is \_\_\_\_\_\_\_\_\_\_. - based on everyday ideas of observation and trial-and-error experiments - In that sense, modern science is just a formalization of ideas that are innate to human beings   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.   Which of the following is not consistent with the major hallmarks of science? - Science consists of proven theories that are understood to be true explanations of reality. - This is statement is not consistent with the hallmarks of science because scientific theories can never be proven beyond all doubt.   Which of the following describes a velocity (as opposed to a speed)? - 20 kilometers per hour, headed north - Velocity describes speed in a particular direction.   Which of the following is not true about a scientific theory? - A theory is essentially an educated guess.   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).   Momentum is defined as \_\_\_\_\_\_\_\_\_\_. - mass multiplied by velocity - Notice that because velocity includes direction, momentum also includes direction.   Which of the following statements about the force attracting these two galaxies is true? - It is the same force that causes an apple to fall to the ground. - It is gravity, which operates the same on Earth and in space.   What do we mean by a geocentric model of the universe? - A model designed to explain what we see in the sky while having the Earth located in the center of the universe. - The geocentric model developed in ancient Greece and was generally accepted until the time of the Copernican revolution.   Drag each statement into the correct bin based on whether it describes motion that involves acceleration or motion at constant velocity. - Acceleration refers to any change in velocity. Because velocity includes both speed and direction, acceleration is occurring whenever there is any change in speed, direction, or both. Constant velocity means that both speed and direction are unchanging. - Acceleration - a car is speeding up after being stopped, a ball is in free fall after being dropped from a high window, a car is slowing down for a stop sign, a planet is orbiting the sun in an elliptical orbit, a car is holding a steady speed around a curve, a planet is orbiting the sun in a circular orbit - Constant Velocity - an elevator is going upward at constant speed, a car is driving 100 km/hr on a straight road, a spaceship is coasting without engine power in deep space     Drag each statement into the correct bin based on whether it describes motion in which the object\'s momentum is changing. - Momentum is defined as mass times velocity, so if an object\'s velocity is changing (that is, if it is accelerating), then its momentum must also be changing. - Change in Momentum - A planet is orbiting the Sun in an elliptical orbit, a car is speeding up after being stopped, a car holding a steady speed around a curve, a ball is in freefall after being dropped from a high window, a planet is orbiting the sun in a circular orbit, a car is slowing down for a stop sign. - Constant Momentum - a car is driving 100 km/hr on a straight road, a spaceship is coasting without engine power in deep space, an elevator is going upward at constant speed.     Drag each statement into the correct bin based on whether the motion requires the action of a net force. - The only way to change an object\'s momentum is to apply a net force to it, so if an object\'s momentum is changing, then a net force must be acting upon it. For example, in the case of the planets orbiting the Sun, the net force is from gravity. In the case of the accelerating cars, the net force is from the engine. - Net Force (nonzero) - a planet is orbiting the Sun in an elliptical orbit, a car is slowing down for a stop sign, a ball is in freefall after being dropped from a high window, a car is speeding up after being stopped, a car is holding a steady speed around a curve, a planet is orbiting the Sun in a circular orbit. - No Net Force - an elevator is going upward at constant speed, a car is driving 100 km/hr on a straight road, a spaceship is coasting without engine power in deep space.     Which of the following statements correctly state general principles of motion? (Assume that the moving object\'s mass is not changing.) - An object that is accelerating is also undergoing a change in momentum. - Accelerated motion includes any motion involving a change in speed, change in direction, or both. - An object that is accelerating is also being acted upon by a (nonzero) net force. - As long as an object\'s mass is not changing, a net force will cause an object to undergo some type of acceleration. Because acceleration is a change in velocity, and momentum is mass times velocity, the accelerating object is also undergoing a change in momentum   Newton\'s Second Law of Motion tells us that the net force applied to an object equals its \_\_\_\_\_\_\_\_\_\_. - mass multiplied by acceleration - We often write this fact simply as F = ma.     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: asteroid/sun, asteroid/earth, asteroid/moon, asteroid/asteroid, asteroid/hydrogen atom :Weakest force - Because the distance is the same for all five cases, the gravitational 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 gravitational force depends on the mass of the object on the right. Continue to Part B to explore what happens if we instead ask about the gravitational force acting on the object on the right.   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.   Which of these hypothetical observations (none of them are real) would force us to reconsider our modern, Sun-centered view of the solar system? - We discover a small planet beyond Saturn that rises in the west and sets in the east each day. - If Earth is rotating from west-to-east, then all celestial objects must move from east to west across our sky. (The only exception is satellites in low-Earth orbit, where they orbit faster than Earth rotates.) So a planet going in the opposite direction across the sky would pose a direct challenge to our view of Earth as a rotating planet.   Choose the correct explanation for why does the following statement make sense (or is clearly true) or does not make sense (or is clearly false): - The statement does not make sense. Any person can experience weightlessness on Earth, it just requires a long enough free-fall.     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