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1. A car is accelerating when it is: Answer: C) going around a circular track at a steady 100 miles per hour. Explanation: Answer C is correct because acceleration is equal to a change in velocity over time, and C is the only instance of a change in either direction or speed. 2. Compared to their values on Earth, on another planet your… Answer: B) mass would be the same but your weight would be different. Explanation: Mass would remain the same, but weight is the measure of mass and the force that mass exerts on the scale, which is dependent on gravity. Because gravity changes from planet to planet, your weight would also change. 3. Which person is weightless? Answer: A) A child in the air as she plays on a trampoline. Explanation: All objects falling back to Earth experience the same acceleration due to gravity. Because gravity is the only force acting on an object when it is in a continued state of “free fall”, the absence of our usual normal force acting upwards gives a feeling of weightlessness. 4. Consider the statement “There’s no gravity in space.” This statement is: Answer: A) completely false. Explanation: This statement is false because gravity is a force generated by any object with mass. The effects of gravity diminish as the distance between objects increases, but it does not cease to exist. 5. To make a rocket turn left, you need to… Answer: B) fire an engine that shoots out gas to the right. Explanation: Because of the conservation of momentum, objects exchange momentum through equal and opposite forces. This means that to move in one direction, the rocket must exchange momentum in the opposite direction. 6. Compared to its angular momentum when it is farthest from the Sun, Earth’s angular momentum when it is nearest to the Sun is: Answer: C) the same. Explanation: Angular momentum does not change if there is no external torque acting upon it. Earth has no torque causing it’s angular momentum to change in this situation . 7. The gravitational potential energy of a contracting interstellar cloud: Answer: B) gradually transforms into other forms of energy. Explanation: As an interstellar cloud shrinks, it’s gravitational potential energy is converted to the kinetic energy of gas particles falling inwards. 8. If Earth were twice as far from the Sun, the force of gravity attracting Earth to the Sun would be: Answer: C) one quarter as strong.

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Explanation: If the distance between the Earth and the Sun doubled, it would decrease the force of gravity by (¼) because the two are inversely proportional according to Newton’s Universal Law of Gravity. 9. According to the universal law of gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass? Answer: C) Earth’s orbit would not change. Explanation: Because both masses, the gravitational constant, and the distance from center do not change because of the Black Hole, Earth cannot build up the energy to reach escape velocity and change it’s orbit. 10. If the Moon were closer to Earth, high tides would… Answer: A) be higher than they are now. Explanation: If the moon were nearer to the “near side” of Earth, it’s gravity would pull even harder, causing an even greater bulge in the ocean along the direction of the moon.

ASTRO 102: Stars, Galaxies, and the Universe Winter 2024 Homework 3. Due: Thursday, 02/08 Name: Uniqename: Section Number or GSI name: • We request that you do your homework on paper or a tablet (the sheet you are reading can be printed and you can use it). We recommend that you write out any math by hand (neatly). If you need more space just add a sheet of paper and make it clear what is going on. Alternatively, using a tablet also works quite well. • Scan the pages into a pdf document using your phone (or other method of your choice). Upload to Gradescope, via the Canvas site. Videos on how how to scan into a pdf and upload to Gradescope are available on the Canvas site. • Make sure to mark the pages your answer to specific questions appear on in Gradescope. If you are unsure how to do this, please look at the gradescope video/website or ask your GSI. If you do not tag the pages that questions are answered on, this significantly increases the time it takes to grade the HWs and we will begin deducing points after HW 1. • We suggest you keep your original paper homework or the pdf you submitted to Gradescope for your own records. In the event that there is a computer error associated with Gradescope software your own records or paper copy will help to clarify the problem and secure your credit. • Homework will be graded based on correctness and clarity. Make sure that your work is easy to read and show all the work necessary to complete each quantitative problem, including units and conversions between units at each step. Simply stating the answer is not sufficient for credit, even if the answer is correct. When appropriate, use scientific notation and round your numerical result to a reasonable number of significant figures. • Do not use generative AI (such as ChatGPT or UM GPT) to produce your solutions. 3-1 Harper Johnston harpjohn Robert Frasier

3-2 Homework 3. Due: Thursday, 02/08 Problem 1 Take two pages of notes on Chapter 4 of the textbook/lecture. (hint: the Big Picture and Summary of Key Concepts sections at the end of the chapter may be useful.) 20 points

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Homework 3. Due: Thursday, 02/08 3-3 continued

3-4 Homework 3. Due: Thursday, 02/08 Problem 2 Answer all ten Quick Quiz Questions from Chapter 4. Write out the question and your answer selection. Justify your answer in no more than 2 sentences. Make sure to give the number of the question you are answering. 20 points

Homework 3. Due: Thursday, 02/08 3-5 (continued)

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3-6 Homework 3. Due: Thursday, 02/08 Problem 3 Quantitative problems from 4.1-4.3 (20 points) Problem 3.1 10 points : A typical candy bar has ⇡ 250 Calories of metabolically accessible chemical potential energy (note: one Calorie with a capitalized “C” is 1 kilocalorie or 1000 calories with a lower case “c”). Convert this to Joules. Assuming the candy bar’s mass is 0.25 kg, use the formula for kinetic energy to calculate the velocity a candy bar would have to have in order to have kinetic energy equal to this. Give your answer in km/s. Problem 3.2 10 points : No one has yet succeeded in creating a commercially viable way to produce energy through nuclear fusion. However, suppose we could build fusion power plants using the hydrogen in water as a fuel. Based on the data in Table 4.1, how much water would we need each minute to meet U.S. energy needs? Could such a reactor power the entire United States with the hydrogen in the water flowing from your kitchen faucet? Explain. (Hint: Use the annual U.S. energy consumption to find the energy consumption per minute, and then divide by the energy yield from fusing the hydrogen in 1 liter of water to figure out how many liters would be needed each minute.)

Homework 3. Due: Thursday, 02/08 3-7 Problem 4 Quantitative questions on 4.4-4.5 (30 points total) Problem 4.1 10 points : We see a very low mass star in orbit around an unseen star. We can assume that we have additional informa- tion that tells us the unseen star has almost all of the mass in the system. The star we see has a period of 5 years and a semi-major axis of about 5 ⇥ 10 8 km. What is the mass of the unseen star? Problem 4.2 10 points : Calculate the escape velocities from the surface of Mars and the surface of Io (one of Jupiter’s moons). Ignoring atmospheric drag, how many times more kinetic energy does it take to escape from the surface of the Earth than Mars? Use the data from Appendix E in the textbook.

3-8 Homework 3. Due: Thursday, 02/08 Problem 4.3 10 points : Find the orbital period for a planet with 3.5 times the Earth’s mass orbiting a star at a distance of 3 AU. The star is 2.5 times the mass of the Sun.

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Homework 3. Due: Thursday, 02/08 3-9 Problem 5 Drawing the tides 10 points : Make a diagram showing the two arrangement of the Earth, Moon, and Sun that leads to the highest possible high tides. Make sure to label the Sun, Earth, and Moon and note the phase of the moon during each of the two arrangements. newoo Earth ( Moon Sun A A Full

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