Physics Coursera Tests Week 3 [PDF]

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PHYSICS COURSERA TESTS WEEK 3 WEEK 3 PRACTICE QUIZ: PROJECTILES, FALLING VERTICALLY UNDER GRAVITY 1. You are sitting in a plane, in straight horizontal flight at constant speed of 250m.s−1, when you drop your pen from height 0.30 m above your leg. How long does it take the pen to hit your leg? Time = _____ seconds. (Hint: remember significant figures.) ANS: 0.25

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2. You are sitting in a plane, in straight horizontal flight at constant speed of 250 m.s−1, when you drop your pen from height 0.30 m above your leg. You've just shown that it hits your leg after 0.25 s. How far does the plane travel in that time? Distance = _____ m. ANS: 62

3. The pen lands: ANS: Directly below where your hand was, with respect to the plane, when it dropped the pen 4. NASA astronaut Alan Shepard fitted the head of a golf club onto the shaft of a lunar sample collector. He then hit three golf balls (they are still there). During the flight of a golf ball on the moon, which if any of the following is/are constant? ANS: horizontal component of velocity

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horizontal component of acceleration

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vertical component of acceleration

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PHYSICS COURSERA TESTS WEEK 3 Remember the string in the last movie, with masses at n2L, where L = 0.15 m. Suppose that some astronauts took the string and masses we've just used to the moon, where the gravitational acceleration is gmoon =1.6 m⋅s−2. If we let it drop, as before, what would be the tempo (i.e. the rate in bangs per minute) of masses hitting the ground? ANS: 140 beats per minute 6. How fast would you have to launch a ball vertically upwards (on the earth) to give you 5.0 s before it returned to the same height? Neglect air resistance and use g = 9.8 m⋅s–2. Velocity = _____ m/s upwards. ANS: 25

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7. In the previous problem, the ball was in the air for 5.0 s and we saw that that required a vertical take-off speed of 25 m⋅s–1. How high above the launch site would the ball go? Height = _____ m. ANS: 31

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PHYSICS COURSERA TESTS WEEK 3 WEEK 3 PRACTICE QUIZ: COMBINING VERTICAL AND HORIZONTAL MOTION

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A ball rolls off a table. The table is 92 cm high and the ball travels 63 cm horizontally, before bouncing. (The illustration is a montage of 3 screen grabs.) How fast was the ball rolling when it left the table? We've put the origin for the x and y axes on the floor as shown. (Hint: we've seen that the x and y motion are independent. Here, try thinking about them independently.) The ball was rolling on the table at _____ m.s−1. ANS: 1.5

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I launch this ball approximately vertically from a height of 0.90 m above the floor. It takes 30 frames on my video camera for the ball to reach the floor, and my camera records at 25 frames per second. From these data, calculate the ball's launch velocity. (Hint: you know the time of flight. What are the initial and final heights? What is the acceleration?) Launch velocity = _____ m.s −1 up. ANS: 5.1 m.s−1 upwards 3. For the previous problem, I tossed the ball upwards at 5.1 m.s−1 from an initial height of 0.90 m above the floor. What is the maximum height of the ball above the floor? Height = _____ m. ANS: 2.2

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PHYSICS COURSERA TESTS WEEK 3

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4. For the previous problem, the initial velocity was 5.1 m.s−1 and the direction was up. How long does it take the ball to reach its maximum height? Time = _____ s. ANS: 0.52 s

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Here is a plot of y(t) for the previous questions. Five points are marked with a, b, c, d, e; take each to identify the point on the purple curve closest to the letter. Indicate which point is identified as: (i) y0 (ii) 0.52 s (iii) maximum height Separate your answers with commas. Example: if you think the answer is (i) = a, (ii) = b, (iii) = c, then write: a, b, c ANS: a, b, b 6. If the initial velocity v0 has magnitude v0 and direction at an angle of θ above the horizontal, what is the expression for the x component of the velocity? vx0 = _____ . ANS: v0 cos θ 7. If the initial velocity v0 has magnitude v0 and direction at an angle of \thetaθ above the horizontal, what is the expression for the yy component of the velocity? vy0 = _____ . ANS: v0 sin θ

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PHYSICS COURSERA TESTS WEEK 3 WEEK 3 PRACTICE QUIZ: TRAJECTORIES AND RANGE

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1. For a projectile with no air resistance, launched and landing at the same height, we saw that the maximum range is achieved with an angle of 45∘. If we keep the launch speed constant, what fraction of that range do we achieve with angles 15∘ and 30∘? For a launch angle of 15∘, we find: Range(θ)/Range(45∘ ) = _________. Please give your answer to two significant figures. ANS: 0.50

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2. For a launch angle of 30∘, we find: Range(θ)/Range(45∘)= _________. Please give your answer to two significant figures. ANS: 0.87

3. NASA's plane, the 'Vomit Comet', flies in a parabola (sketch) to allow astronauts to experience free fall for 25 s. During this parabolic section, the plane is first ascending then descending, and at all times the engines produce only just enough thrust to overcome air resistance. What is the height of the parabolic section? In other words, how much higher is the top of the parabolic section than the bottom of the parabolic section? (Hints: The astronauts are projectiles without air resistance for 25 s. Can you remember a simple way we did a related problem? How many significant figures?) Maximum height above the starting point: _____ m. This study source was downloaded by 100000831796066 from CourseHero.com on 10-03-2021 22:05:53 GMT -05:00 ANS: 770 https://www.coursehero.com/file/92886419/PHYSICS-COURSERA-TESTS-WEEK-3docx/

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PHYSICS COURSERA TESTS WEEK 3

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PHYSICS COURSERA TESTS WEEK 3 WEEK 3 PRACTICE QUIZ: UNIFORM CIRCULAR MOTION

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A car goes over a hill whose crest has a radius of curvature of 30 m (two significant figures). It's travelling at constant speed and we shall neglect aerodynamic forces. Treat the car as a particle. (i.e. neglect the size of the car in comparison with the size of the hill.) At the very highest point, how fast does it have to travel so that it becomes airborne at that point? (Hints: what shaped path? and what is the maximum downwards acceleration it can have? BTW, the photo does not represent the shape of a real hill.) Important: Answer this question theoretically, not experimentally! Speed to become airborne: _____ kph. ANS: 62

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(The above illustration shows the UNSW Foucault pendulum.) What is the direction of the acceleration of a pendulum at the lowest point of its swing? Neglect air resistance. ANS: upwards

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PHYSICS COURSERA TESTS WEEK 3 WEEK 3 QUIZ 1. A juggler throws balls almost vertically upwards, with time Δt=0.23 s between each throw. (Yes, pretty amazing.) The balls are all thrown to the same height, and in repeated succession (e.g. 1, 2, 3, 1, 2, 3 etc.). Let's simplify: neglect air resistance, neglect the time between catching and throwing a ball and assume that balls are thrown and caught at the same height. Calculate the minimum height he must throw the balls if he is to juggle 3 balls? _____ m (Hints: How many throws before the same ball gets thrown again? How does the time for the ball to go up compare with the time to go down?) ANS: 0.58 2. Using the information from question #361a above: Calculate the minimum height he must throw the balls if he is to juggle 5 balls? _____ m (Hints: How many throws before the same ball gets thrown again? How does the time for the ball to go up compare with the time to go down?) ANS: 1.6

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3. Suppose that an astronaut, wearing a space suit on Earth, can kick a ball a distance of 25 m (have you tried kicking in a space suit?). Using the datum gravitational acceleration is gmoon =1.6 m.s−2, estimate how far he could kick the ball on the moon, using the same action and kicking at the same angle. (Remember significant figures and neglect air resistance. Assume that the launch and landing heights are the same. Do not use exponent notation.) _____ m ANS: 153.125

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You've made it to the top deck on the diving tower, 10 m above both the ground level deck and the water, and 3 m wide, as in the diagram above (not to scale). Your friend has dared you to run and jump horizontally, so as to go as far forwards as you can before hitting the water. But you see that the far side of the pool is only 10 m from the edge of your platform. a) Treating yourself as a projectile (something only recommended in theory) travelling horizontally as you leave the platform. How fast would you have to run in order to travel 10 metres horizontally before hitting the water? Give your answer to only one significant figure. Speed v= _____ m.s−1. Do not try to answer this question experimentally. ANS: 7

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5. Using the information from question #363a above; b) What horizontal acceleration do you need to achieve the speed calculated in (a)? Acceleration a = _____ m.s−2. c) Not for marks, only for you to think about: Can you accelerate this fast in this situation? ANS: 8

6. Here, I am swinging a ball around in a horizontal circle with a radius of 0.60 \text{ m}0.60 m a) What is its vertical component of acceleration? _____ m.s−2 ANS: 9.81, 10, 9.8 7. Using the information from question #364a above: b) At what constant speed must it travel so that the horizontal component of its acceleration is 3.5 m.s−2? This study source was downloaded by 100000831796066 from CourseHero.com on 10-03-2021 22:05:54 GMT -05:00 _____ m.s−1 https://www.coursehero.com/file/92886419/PHYSICS-COURSERA-TESTS-WEEK-3docx/

PHYSICS COURSERA TESTS WEEK 3 ANS: 1.45, 1.5, 1

8. (Image from NASA http://settlement.arc.nasa.gov/70sArtHiRes/70sArt/Torus_Cutaway_AC75-10861_900.jpg ) This artist's conception imagines a 'wheel-shaped' space station. The idea is that the 'wheel' would turn on its axis at a rate such that the acceleration in the rim of the wheel would be 9.8 m.s −2. (This would make inhabitants feel as though they had their normal weight.) Suppose that the radius of the wheel is 1.0×102 m.

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What is the required period of rotation of the space station about its axis?

Period of rotation = _____ s. (Enter the number without using exponent notation.)

[Interesting. In the movies 2001 and The Martian, the living areas of the spacecraft are rotating wheels, for the same reason. Being subjected to normal forces is healthier for astronauts, though it sometimes creates difficulties for special effects crews: https://www.youtube.com/watch?v=1wJQ5UrAsIY ] ANS: 0.64, 20.07

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9. Give one plausible reason why are there no sunflowers on the space station described above. ANS: The direction of the sun changes too rapidly.

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