In 2021, Linden Hall became the first Australian woman in history to break four - minutes in the 1500m running race. Briefly describe the forces acting on Linden as she runs the last 100 metres on the final straight towards the finish line. Hint: In your answer, make sure that the explanation is related to a physics principle covered in this unit.
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- Check Your Understanding The U.S. Air Force uses “10gs” (an acceleration equal to 109.8m/s2 ) as the maximum acceleration a human can withstand (but only tot several seconds) aid survive. How much time must the Enterprise spend accelerating if the humans on board are to experience an average at most 10gs of acceleration? (Assume the inertial dampeners are offline.)The radius Rhand mass Mh of a black hole are related by Rh = 2GMh/c2, where c is the speed of light. Assume that the gravitational acceleration agof an object at a distance ro= 1.001Rh from the center of a black hole is given by ag = G M / r2 (it is, for large black holes).(a) In terms of Mh, find ag at ro.(c) What is ag at rofor a very large black hole whose mass is 1.69 × 1015 times the solar mass of 1.99 × 1030 kg?(d) If an astronaut with a height of 1.73 m is at rowith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet?Imagine an anti-yravily fuice lhal acts just like Newtonian gravity, but repels. So in the 5. M, M2 = M = M diagram, M1 repels the little mass, m, with a force magnitude of Fanti-grav = GM,m/r12, where G still -12 +a -a equals 6.674 x 1011 m3kg-1s2, 'x(t) The system shown in the diagram is isolated. M1 and M2 each repel m. No other forces act on m. And M, and M2 are held in place att a. sho an expression for the restoring force exerted onto m. The expression should be in terms of G, M, m, a and x(t). b. Is the motion of the little mass, m, simple harmonic motion? Explain why or why not. c. Determine the period for small amplitude (x << a) oscillations of m. Leave your answer in terms of G, M and a.
- A 2400-kg satellite is ina arcuar motion around a A planet.The satellite travels witha constant speed ofa Lele70 m/s. Radio us or tne circlar orbit is 8.92 x 10*M, w Determine Hthe magnitude of the gravitational force exerted on the satellite by the planet.In a science-fiction TV show, the hero spent the entire 30 min fretting about running out offuel before he could pilot his spaceship back to base. Several times in the sequence thecamera cut from his worried face to the blasting rockets, to the fuel gauge, and back to hisworried expression as the engines roared and the fuel amount keeps decreasing. Whatshould he have done and what you would say about the writers of the show?What is the strength of the weak nuclear force relativeto the strong nuclear force? (b) What is the strength of theweak nuclear force relative to the electromagnetic force?Since the weak nuclear force acts at only very shortdistances, such as inside nuclei, where the strong andelectromagnetic forces also act, it might seem surprising thatwe have any knowledge of it at all. We have such knowledgebecause the weak nuclear force is responsible for beta decay,a type of nuclear decay not explained by other forces
- Check Your Understanding Suppose that Balto in Example 2.10 leaves the game to attend to more important matter, but Astro Clifford and Dug continue playing. Astro and Clifford’s pull on the toy does not change, but Dug rims around and bites on the toy in a different place. With how big a force and in what direction must Dug pull on the toy now to balance out the combined pulls from Clifford and Astro? Illustrate this situation by drawing a vector diagram indicating all forces involved.Check Your Understanding Consider the density required to make Earth a black hole compared to that required for the Sun. What conclusion can you draw from this comparison abut what would be required to create a black hole? Would you expect the Universe to have many black holes with small mass?Some of the most spectacular objects in the universe are fairly small: neutron stars are spheres with a diameter that'sabout 10km (they are remnants of old stars). Their spectacular nature is indicated by the fact that they are about asmassive as the sun, i.e. 2 x 1030kg. What is the gravitational acceleration on the surface of such an object? Expressyour result as a multiple of g.
- The radius Rhand mass Mh of a black hole are related by R₁ = 2GM₁/c², where c is the speed of light. Assume that the gravitational acceleration as of an object at a distance r= 1.001Rh from the center of a black hole is given by ag = GM/r² (it is, for large black holes). (a) In terms of Mh, find ag at ro. (b) Does sag at ro increase or decrease as M₁ increases? (c) What is ag at ro for a very large black hole whose mass is 1.54 × 10¹3 times the solar mass of 1.99 × 10³⁰ kg? (d) If an astronaut with a height of 1.66 m is at råwith her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet ahead-afeet? (e) Is the tendency to stretch the astronaut severe?After consuming all of its nuclear fuel, a massive star can collapse to form a black hole, which is an immensely dense object whose escape speed is greater than the speed of light. Newton's law of universal gravitation still describes the froce that a black hole exerts on objects outside it. A spacecraft in the shape of a long cylinder has a length of 100m, and its mass with occupants is 1000kg. It has strayed too close to a black hole having a mass 100 times that of the sun. If the nose of the spacecraft points toward the center of the black hole, and if the distance between the nose of the spacecraft and the black hole's center is 10km (a) determine the total force on the spacecraft. (b) What is the difference in the force per kilogram of mass felt by the occupants in the nose of the ship versus those in the rear of the ship farthest from the black hole?A Princeton prof. (mass = 70.0 kg), surprised by the large stopping force he calculates for jumping flat footed from a height of 0.12 m, decides to try the experiment. Calculate he deceleration (in g′s) if he stops in a distance of 0.36 cm. (Do not try this. You could easily break an ankle!)