Essential University Physics
4th Edition
ISBN: 9780134988559
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 8, Problem 50P
To determine
The speed of the canister as it dropped from the rest.
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You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of 630 km above the planet's surface, the ship's orbital speed is 5500 m/s. By observing the planet, you determine its radius to be 4.48×106m. You then land on the surface and, at a place where the ground is level, launch a small projectile with initial speed 12.6 m/s at an angle of 30.8∘ above the horizontal.
If resistance due to the planet's atmosphere is negligible, what is the horizontal range of the projectile?
You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of ?o=2.45 km/s�o=2.45 km/s . The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth.
With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is ?E=6370000 m�E=6370000 m, the mass of the Earth is ?E=5.98×1024 kg�E=5.98×1024 kg , the acceleration due to gravity on the surface of the Earth is ?=9.81…
Consider an object that is in an elliptical orbit with semimajor axis a = 7.9×106 m about a planet of mass M = 1.0×1023 kg.
(a) What is the speed of the object when it is closest to the planet at r = a/4?
(b) What is the speed of the object when it is furthest from the planet?
Chapter 8 Solutions
Essential University Physics
Ch. 8.2 - Suppose the distance between two objects is cut in...Ch. 8.3 - Suppose the paths in Fig. 8.8 are the paths of...Ch. 8.4 - Prob. 8.3GICh. 8 - What do Newtons apple and the Moon have in common?Ch. 8 - Prob. 2FTDCh. 8 - When you stand on Earth, the distance between you...Ch. 8 - The force of gravity on an object is proportional...Ch. 8 - A friend who knows nothing about physics asks what...Ch. 8 - Could you put a satellite in an orbit that keeps...Ch. 8 - Why are satellites generally launched eastward and...
Ch. 8 - Given Earths mass, the Moons distance and orbital...Ch. 8 - How should a satellite be launched so that its...Ch. 8 - Does the gravitational force of the Sun do work on...Ch. 8 - Space explorers land on a planet with the same...Ch. 8 - Use data for the Moons orbit from Appendix E to...Ch. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Two identical lead spheres with their centers 14...Ch. 8 - Whats the approximate value of the gravitational...Ch. 8 - A sensitive gravimeter is carried to the top of...Ch. 8 - Prob. 18ECh. 8 - Find the speed of a satellite in geostationary...Ch. 8 - Marss orbit has a diameter 1.52 times that of...Ch. 8 - Calculate the orbital period for Jupiters moon Io,...Ch. 8 - An astronaut hits a golf ball horizontally from...Ch. 8 - The Mars Reconnaissance Orbiter circles the red...Ch. 8 - Earths distance from the Sun varies from 147 Gm at...Ch. 8 - Prob. 25ECh. 8 - A rocket is launched vertically upward from Earths...Ch. 8 - What vertical launch speed is necessary to get a...Ch. 8 - Prob. 28ECh. 8 - Determine escape speeds from (a) Jupiters moon...Ch. 8 - Prob. 30ECh. 8 - Prob. 31ECh. 8 - Prob. 32ECh. 8 - Example 8.2: Find the altitude and speed of a...Ch. 8 - Prob. 34ECh. 8 - Prob. 35ECh. 8 - Example 8.4: A coronal mass ejection (CME) is an...Ch. 8 - Example 8.4: In September 2017, the Cassini...Ch. 8 - The gravitational acceleration at a planets...Ch. 8 - Prob. 39PCh. 8 - If youre standing on the ground 15 m directly...Ch. 8 -
On January 1, 2019, the450-kg New Horizons...Ch. 8 - Equation 7.9 relates force to the derivative of...Ch. 8 - During the Apollo Moon landings, one astronaut...Ch. 8 - Prob. 44PCh. 8 - Prob. 45PCh. 8 - Prob. 46PCh. 8 - Prob. 47PCh. 8 - Satellites A and B are in circular orbits, with A...Ch. 8 - The asteroid that exploded over Chelyabinsk,...Ch. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Neglecting air resistance, to what height would...Ch. 8 - Show that an object released from rest very far...Ch. 8 - Prob. 54PCh. 8 -
In 2017 North Korea developed ballistic missile...Ch. 8 - Prob. 56PCh. 8 - Prob. 57PCh. 8 - Prob. 58PCh. 8 - Prob. 59PCh. 8 - Two meteoroids are 160,000 km from Earths center...Ch. 8 - Prob. 62PCh. 8 - A missiles trajectory takes it to a maximum...Ch. 8 - Prob. 64PCh. 8 - Mercurys orbital speed varies from 38.8 km/s at...Ch. 8 - Prob. 66PCh. 8 - Two satellites are in geostationary orbit but in...Ch. 8 - Prob. 68PCh. 8 - Prob. 69PCh. 8 - We derived Equation 8.4 on the assumption that the...Ch. 8 - Prob. 71PCh. 8 - As a member of the 2040 Olympic committee, youre...Ch. 8 - The Olympic Committee is keeping you busy! Youre...Ch. 8 - Tidal forces are proportional to the variation in...Ch. 8 - Spacecraft that study the Sun are often placed at...Ch. 8 - Prob. 76PPCh. 8 - Prob. 77PPCh. 8 - Prob. 78PPCh. 8 - The Global Positioning System (GPS) uses a...
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- Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forwardFor many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?arrow_forwardModel the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forward
- What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?arrow_forwardWhat would be the minimum Earth-Moon distance at which the center-of-mass of the Earth-Moon system would lie outside the Earth’s surface?arrow_forwardMiranda, a satellite of Uranus, is as shown. It can be modeled as a sphere of radius 242 km and mass 6.68 × 1019 kg. (a) Find the free-fall acceleration on its surface. (b) A cliff on Miranda is 5.00 km high. It appears on the limb at the 11 o’clock position as shown and is magnified as shown. If a devotee of extreme sports runs horizontally off the top of the cliff at 8.50 m/s, for what time interval is he in flight? (c) How far from the base of the vertical cliff does he strike the icy surface of Miranda? (d) What will be his vector impact velocity?arrow_forward
- A rocket is launched straight up from the earth's surface at a speed of 1.90×10^4 m/s. What is its speed when it is very far away from the earth?arrow_forwardWhat are (a) the speed and (b) the period of a 220 kg satellite in an approximately circular orbit 640 km above the surface of Earth? Suppose the satellite loses mechanical energy at the average rate of 1.4 * 105 J per orbital revolution. Adopting the reasonable approximation that the satellite’s orbit becomes a “circle of slowly diminishing radius,” determine the satellite’s (c) altitude, (d) speed, and (e) period at the end of its 1500th revolution. (f ) What is the magnitude of the average retarding force on the satellite? Is angular momentum around Earth’s center conserved for (g) the satellite and (h) the satellite–Earth system (assuming that system is isolated)?arrow_forwardA girl, having a mass of 15 kg, sits motionless relative to the surface of a horizontal platform at a distance of 5 m from the platform's center. If the girl speed is 2 m/s. What is the normal force that affects the girl?arrow_forward
- A satellite of mass 1250 kg is to be placed in a circular orbit at a height h=210 km above the Earth’s surface, where g=9.2 m/s2. (a) What is the weight of the satellite at this altitude? (b) With what tangential speed must it be inserted into its orbit? The Earth’s radius is R= 6370 km.arrow_forwardCommunications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The altitude of a geosynchronous orbit is 3.58×107m(≈22,000miles)3.58×107m(≈22,000miles). What is the period of a satellite in a geosynchronous orbit? Express your answer to three significant figures and include the appropriate units. Find the value of gg at this altitude. Express your answer to three significant figures and include the appropriate units. What is the weight of a 2000 kg satellite in a geosynchronous orbit? Express your answer as an integer and include the appropriate units.arrow_forwardA projectile is fired straight upward from the Earth's surface at the south pole with an initial speed equal to one third the escape speed. Ignoring air resistance, determine how far from the center of the earth the projectile travels before stopping momentarily.arrow_forward
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