Unit 4 - A Bit of Physics PDF

ASTR 1205 Unit 4 Dr. Bryan Rowsell Unit 4: A Wee bit o’ Physics 4.1 Describing Motion: Examples from Everyday Life Speed vs. Velocity vs. Acceleration These are all very different terms in science. You might think the first two are synonymous. Speed is...

ASTR 1205 Unit 4 Dr. Bryan Rowsell Unit 4: A Wee bit o’ Physics 4.1 Describing Motion: Examples from Everyday Life Speed vs. Velocity vs. Acceleration These are all very different terms in science. You might think the first two are synonymous. Speed is how fast something is moving. Examples: The car is travelling at 100 km/hr. The snail is moving at 23 feet/day. Velocity is how fast something is moving and in what direction. In mathematical terms, speed is a scalar, velocity is a vector (magnitude and direction). The car is travelling at 100 km/hr east. The snail is moving at 23 feet/day to the right. A Bit of Physics ·4−1· 4.1: Describing Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell Consider this situation: a racecar driver goes a steady 60 km/hr around a corner in the racetrack. Which of the following is true in this situation? (a) speed is constant, velocity is changing (b) speed is changing, velocity is constant (c) both speed and velocity are constant (d) both speed and velocity are changing Acceleration is a change in velocity over time (a change of speed and/or direction!): If you drop a ball down an elevator shaft, which figure shows the position of the ball photographed every 0.2 seconds? (a), (b), or (c)? Before you answer….think about this: Would you rather lie down under a bowling ball dropped from 5 cm above your stomach, or 5 m above your stomach? A Bit of Physics ·4−2· 4.1: Describing Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell Acceleration due to Gravity Gravity accelerates all objects on Earth 10 m/s2 down, or toward the centre of Earth’s mass. The direction of the acceleration of gravity defines down. 10 m/s2 means: Each second of falling adds 10 m/s to an object’s speed. Acceleration due to gravity is the same for all objects. In the absence of air resistance, a feather and hammer fall at the same rate… a measure of the amount of matter in an object mass (m) in units of grams or kilograms momentum (p) mass in motion, p = mv. force (F) a push or pull that causes a change in momentum If a force is applied to an object and the object’s mass remains constant, what will happen? (a) The object’s speed must change. (b) The object’s direction must change. (c) The object’s speed and/or direction must change. (d) The objects speed and direction must both change. (e) None of the above. mass vs. weight? Weight is the force that a scale measures due to gravity, F = mg g is the acceleration due to gravity, roughly 10 m·s−2. Thus, the units for force are kg·m·s−2, or N (Newtons). What happens to your weight in an elevator? A Bit of Physics ·4−3· 4.1: Describing Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell Compared to their values on Earth, on another planet your (a) mass and weight would both be the same. (b) mass and weight would both be different. (c) mass would be the same, but your weight would be different. (d) weight would be the same, but your mass would be different. On which body would your __________ be the highest? (a) Earth (c) Jupiter (b) Moon Myth: Astronauts in space are weightless because there’s no gravity in space. Fact: There is gravity in space! Astronauts in space are weightless because they are in a constant state of free fall (acceleration toward the Earth!). You experience weightlessness whenever you’re in free-fall, that is, whenever there’s nothing to prevent you from falling. A Bit of Physics ·4−4· 4.1: Describing Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell The gravity astronauts experience in the ISS is called microgravity. 4.2 Newton’s Laws of Motion Isaac Newton (1642 – 1727) English physicist and mathematician Had to work from home during a pandemic (his home happened to be a manor with an apple tree…) Book Mathematical Principles of Natural Philosophy or Principia laid the foundations for classical mechanics Shares credit for development of calculus Realized that the same physical laws that operate on Earth also operate in the heavens. This is important for astronomy. A Bit of Physics ·4−5· 4.2: Newton’s Laws of Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell Newton’s First Law of Motion: Every body remains in a state of rest or uniform motion unless acted upon by a net external force. i.e. a body at rest tends to stay at rest; a body in motion tends to stay in motion. Newton’s Second Law of Motion: The amount of acceleration of a body is proportional to the acting force and inversely proportional to the mass. i.e. 𝐹 = 𝑚𝑎 The heavier the body, the more force must be applied to keep the acceleration the same. This explains you can kick a soccer ball further than you can a ball of lead. A Bit of Physics ·4−6· 4.2: Newton’s Laws of Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell Newton’s Third Law of Motion: If an object A exerts a force on object B, than object B will exert an equal but opposite force on object A. i.e. for every action there is an equal and opposite reaction. Is the force that Earth exerts on you larger, smaller, or the same as the force you exert on it? (a) The Earth exerts a larger force on you. (b) You exert a larger force on the Earth (c) The Earth and you exert equal and opposite forces on each other The black dot is a person spinning a ball on a string, clockwise. Where will the ball go if the string is cut when the ball is at point ⭐? (a) a (b) b (c) c (d) d Most of the time we are going to apply Newton’s Laws to astronomical situations, for example, circular motion. The linear motion terms we’ve learned so far have analogous terms for circular motion. A Bit of Physics ·4−7· 4.2: Newton’s Laws of Motion ASTR 1205 Unit 4 Dr. Bryan Rowsell Linear Term Circular Motion Analogue position → angle velocity → angular velocity acceleration → angular acceleration momentum → angular momentum force → torque Of all the above, angular momentum (L) is the most important term to understand for this course and will come up a lot in future topics. Momentum can be thought of as “mass in motion” and equals mass times velocity, or: 𝑝 = 𝑚𝑣 Angular momentum can be thought of as “mass in circular motion” and equals mass times velocity times distance from point of rotation, or: 𝐿 = 𝑚𝑣𝑟 4.3 Conservation Laws in Astronomy When objects interact with each other (such as during a collision), the total momentum of all objects in the system stays the same before and after the interaction. This is called the law of conservation of momentum. The total momentum before collision must be the same as after the collision (and during, for that matter!). − this is true for all types of momentum, linear or angular − this is also true for total energy of a system (called law of conservation of energy, or the first law of thermodynamics) A Bit of Physics ·4−8· 4.3: Conservation Laws in Astronomy ASTR 1205 Unit 4 Dr. Bryan Rowsell What is true of L, angular momentum? Momentum is conserved, that is both situations above have the same momentum. So what in the formula for L will change here? As a cloud of interstellar dust contracts, the cloud spins: (a) faster (b) slower (c) 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: (a) greater (b) less (c) equal A Bit of Physics ·4−9· 4.3: Conservation Laws in Astronomy ASTR 1205 Unit 4 Dr. Bryan Rowsell Types of Energy What is “energy”? The best and simplest definition of energy is: the capacity to cause change Most of the energy in the universe can be broken down into three major types: kinetic energy energy due to motion potential energy energy due to position and/or composition radiative energy energy from light, carried by photons These can interchange with each other, but the total energy in must equal the total energy out, law of conservation of energy. A subcategory of kinetic energy, the energy due to an object’s motion, is thermal energy, or sometimes called temperature. Thermal energy is the collective kinetic energy (or average kinetic energy) of the many particles that make up a substance/sample. In science, we use SI units, and the accepted unit for temperature isn’t Fahrenheit or Celsius, it’s called Kelvin. A Bit of Physics · 4 − 10 · 4.3: Conservation Laws in Astronomy ASTR 1205 Unit 4 Dr. Bryan Rowsell The nice thing is that a 1° change in Celsius is the same as a 1° change in Kelvin. Let’s not even talk about Fahrenheit. 0 K is where all motion stops and no atoms/particles are vibrating. This is impossible! 4.4 The Force of Gravity In chemistry and biology, most potential energy is due to composition, in physics and astronomy, most potential energy is due to position and how much stuff there is (as opposed to what that stuff is!). gravitational energy due to position in a gravitational field potential energy 𝐸 = 𝑚𝑔ℎ mass potential energy due to the raw amount of mass in an energy object, 𝐸 = 𝑚𝑐 2 A note on units: all types of energy are measured in Joules (J). 1 J = 1 kg·m2/s2. A Bit of Physics · 4 − 11 · 4.3: Conservation Laws in Astronomy ASTR 1205 Unit 4 Dr. Bryan Rowsell Now we can talk about gravity and the universal law of gravitation, which is summarized by the following: − every mass attracts every other mass through a force called gravity − the strength of this force is directly proportional to the product of the two masses − the strength of this force is inversely proportional to the distance between the centres of gravity of the two objects Gravitational Force follows an inverse square law. Light/heat intensity is also an inverse square law: G is a really small number. It’s called the gravitational constant. 𝐺 = 6.67 × 10−11 (𝑁 ⋅ 𝑚2 )/𝑘𝑔2 A Bit of Physics · 4 − 12 · 4.4: The Force of Gravity ASTR 1205 Unit 4 Dr. Bryan Rowsell A few interesting facts about the universal law of gravitation: Newton didn’t know the value of G. There is no (known) theoretical derivation of G. G can only be measured experimentally. In 1797 (110 years after Newton first introduced the Universal Law of Gravitation), Henry Cavendish made the first accurate measurement of G. How will the strength of the force of gravity change between two objects if one object’s mass quadruples and the other object’s mass doubles? 1 (a) the new force of gravity is of what it was before 4 1 (b) the new force of gravity is of what it was before 8 (c) the new force of gravity is 2× of what it was before (d) the new force of gravity is 4× of what it was before (e) the new force of gravity is 8× of what it was before How will the strength of the force of gravity change between two objects if the distance between them triples? 1 (a) the new force of gravity is of what it was before 3 1 (b) the new force of gravity is of what it was before 9 (c) the new force of gravity is 3× what it was before (d) the new force of gravity is 9× what it was before A Bit of Physics · 4 − 13 · 4.4: The Force of Gravity ASTR 1205 Unit 4 Dr. Bryan Rowsell Kepler's first two laws apply to all orbiting objects, not just planets orbiting the Sun. Ellipses are not the only allowed orbits. Orbits can be: − bound (circles and ellipses) − unbound (parabola and hyperbola) Total orbital energy (gravitational + kinetic) stays constant if there is no external force. Orbits cannot change spontaneously. Orbits are stable and cannot change spontaneously. An object’s orbit can change if it exchanges energy with another object in a gravitational encounter, such as a collision or near−collision with a massive object. A Bit of Physics · 4 − 14 · 4.4: The Force of Gravity ASTR 1205 Unit 4 Dr. Bryan Rowsell A comet passes close to Jupiter and loses so much energy that its orbit changes from unbound to bound. Jupiter gains the same amount of energy that the comet lost. Why? Law of Conservation of Energy The effect on Jupiter’s orbit is so small it can’t be measured…why? Jupiter’s much greater mass The reverse effect can be used to give a boost to a spacecraft so it can gain speed without having to spend fuel. If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit). Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr). Escape velocity does not depend on the mass of the escaping object. Tides The last gravitational effect we’ll discuss are tides. Tides happen because of the difference in the gravitational force of attraction between the Moon and different parts of the Earth. Remember: gravity is an inverse-square law so it gets weaker as the distance increases! A Bit of Physics · 4 − 15 · 4.4: The Force of Gravity ASTR 1205 Unit 4 Dr. Bryan Rowsell Spring tides and neap tides occur depending on the current position of the Moon. When the Moon is full, at what time is high tide on an island in the middle of the Pacific Ocean? (a) around sunset (b) around midnight (c) around sunrise (d) around noon (e) both midnight and noon A Bit of Physics · 4 − 16 · 4.4: The Force of Gravity ASTR 1205 Unit 4 Dr. Bryan Rowsell Why does the Sun not exhibit as much of a tidal effect on the Earth’s oceans as the moon does, despite the fact the Sun is MUCH more massive? Tides are about the difference in gravitational energy. The Earth−Moon distance is much smaller than the Earth−Sun distance. The tidal effect is essentially the difference between: − the diameter of the Earth (13,000 km) compared to the Earth/Moon distance (380,000 km) − the diameter of the Earth (13,000 km) compared to the Earth/Sun distance (s, about 150,00,000 km) In other words, the Earth is a “point” compared to the Sun, and each side of the Earth experiences roughly the same gravitational attraction to the Sun. There is much more of a difference between the attraction of the side of the Earth closest to the Moon than the side of the Earth furthest from the Moon. Thus the Moon has much more of a tidal effect on the Earth than the Sun does. A Bit of Physics · 4 − 17 · 4.4: The Force of Gravity ASTR 1205 Unit 4 Dr. Bryan Rowsell Chapter 4: The Essential Cosmic Perspective End−of−Chapter Questions: 1−34, 38−41, 43−46. Solutions are found on Bb. Extra Resources: Watch the following Crash Course Astronomy videos: The Gravity of the Situation [10 min]: https://www.youtube.com/watch?v=TRAbZxQHlVw Tides [10 min]: https://www.youtube.com/watch?v=KlWpFLfLFBI Watch the following Crash Course Physics videos: Newton's Laws [11 min]: https://www.youtube.com/watch?v=kKKM8Y-u7ds Newtonian Gravity [9 min]: https://www.youtube.com/watch?v=7gf6YpdvtE0 Explore concepts of position, velocity, and acceleration with the various simulations on this interactive website: https://ophysics.com/k.html Watch this video about Galileo's rolling ball experiment [5 min]: https://www.youtube.com/watch?v=ZBr8Q2ROX9s Watch as a feather and a bowling ball hit the ground together when released at the same time here on Earth... in a vacuum [5 min] https://www.youtube.com/watch?v=E43-CfukEgs Watch this video about artificial gravity in space [4 min]: https://www.youtube.com/watch?v=z6MmJAWjcZs Read more about free fall and orbital speed from the creator of xkcd comics: https://what- if.xkcd.com/58/ Play with orbital parameters on this interactive website: https://phet.colorado.edu/sims/html/gravity-and-orbits/latest/gravity-and- orbits_en.html Watch this video for an explanation of how gravity assists work and how they have successfully been used by spacecraft to explore our Solar System [3 min]: https://www.youtube.com/watch?v=0iAGrdITIiE Watch a spandex & marbles demo about gravity assists [3 min]: https://www.youtube.com/watch?v=-CqBP-CtM0c Watch this short video that explains Tidal Locking [2 min]: https://www.youtube.com/watch?v=6jUpX7J7ySo Watch this longer video that explains Tidal Locking and so much more (from metronomes to crazy chemistry to a wobbling bridge) [21 min]: https://www.youtube.com/watch?v=t- _VPRCtiUg Extra Physics Fun: Watch Chris Hadfield brush his teeth in space [3 min]: https://www.youtube.com/watch?v=3bCoGC532p8 Watch the 2016 movie, Hidden Figures [2h 7m] (I think it's on Disney+) Watch the 1995 movie, Apollo 13 [2h 20m] (I think it's on Amazon Prime Video) A Bit of Physics · 4 − 18 · Questions and Resources