Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Question
Chapter 8, Problem 46P
To determine
The speed of the canister as it dropped from the rest.
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I keep getting this wrong despite working it out many times. Can I please get some insight on the right approach?
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ?esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ?=3.32×106 g/m3 and volume ?=2.40×1012 m3 . Recall that the universal gravitational constant is ?=6.67×10−11 N·m2/kg2 .
Answer in m/s
A meteor of mass m is approaching earth as
shown on the sketch. The distance h on the
sketch below is called the impact parameter.
The radius of the earth is Re
6400km . The
6x1024 kg
mass of the earth is me =
Suppose the meteor has an initial speed of
vo = 30km/s. Assume that the meteor
started very far away from the earth. Suppose
the meteor just passes earth at a distance of
2.5 Re from the earth's center. You may ignore
all other gravitational forces except the earth.
Find the moment arm h in km (called the
impact parameter).
G
-11
6.673x10-"Nm²kg
%3D
meteor very far away
Vo
h impact parameter
planet
In 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?
Chapter 8 Solutions
Essential University Physics (3rd Edition)
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 - Find the energy necessary to put 1 kg, initially...Ch. 8 - Whats the total mechanical energy associated with...Ch. 8 - Prob. 30ECh. 8 - Determine escape speeds from (a) Jupiters moon...Ch. 8 - Prob. 32ECh. 8 - The gravitational acceleration at a planets...Ch. 8 - One of the longest-standing athletic records is...Ch. 8 - Prob. 35PCh. 8 - If youre standing on the ground 15 m directly...Ch. 8 - Given the Moons orbital radius of 384,400 km and...Ch. 8 - Equation 7.9 relates force to the derivative of...Ch. 8 - During the Apollo Moon landings, one astronaut...Ch. 8 - Prob. 40PCh. 8 - Prob. 41PCh. 8 - Youre preparing an exhibit for the Golf Hall of...Ch. 8 - Prob. 43PCh. 8 - Satellites A and B are in circular orbits, with A...Ch. 8 - The asteroid that exploded over Chelyabinsk,...Ch. 8 - Prob. 46PCh. 8 - Prob. 47PCh. 8 - Neglecting air resistance, to what height would...Ch. 8 - Show that an object released from rest very far...Ch. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - Prob. 55PCh. 8 - Two meteoroids are 160,000 km from Earths center...Ch. 8 - Two rockets are launched from Earths surface, one...Ch. 8 - Prob. 58PCh. 8 - A missiles trajectory takes it to a maximum...Ch. 8 - Prob. 60PCh. 8 - Mercurys orbital speed varies from 38.8 km/s at...Ch. 8 - Prob. 62PCh. 8 - Two satellites are in geostationary orbit but in...Ch. 8 - Prob. 64PCh. 8 - Prob. 65PCh. 8 - We derived Equation 8.4 on the assumption that the...Ch. 8 - Prob. 67PCh. 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. 72PPCh. 8 - Prob. 73PPCh. 8 - Prob. 74PPCh. 8 - The Global Positioning System (GPS) uses a...
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- What is the escape speed from a planet of mass M = 3.1 x 1023 kg and radius R = 2.6 x 106 m? Write the answer in terms of km/s.arrow_forwardA satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. First, find an expression for the gravitational potential energy PE in terms of G, M, m, and R. a)Calculate the value of PE in joules. b)Enter an expression for the total energy E of the satellite in terms of m and v. c)Calculate the value of the total energy E in joules.arrow_forwardYou are on a space station, in a circular orbit h = 475 km above the surface of the Earth. You complete your tasks several days early and must wait for the next mission from the surface to bring you home. After days of boredom, you decide to play some golf. Walking on the space station surface with magnetic shoes, you tee up a golf ball. You hit it with all of your might, sending it off with speed vrel relative to the space station, in a direction parallel to the velocity vector of the space station at the moment the ball is hit. You notice that you then orbit the Earth exactly n = 2.00 times and you reach up and catch the golf ball as it returns to the space station. With what speed vrel (in m/s) was the golf ball hit? Note: Your result will be unrealistically high-much higher than it is possible for a human to hit a golf ball. m/sarrow_forward
- A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.01 x 10* m/s. The mass of the planet is M = 6.02 x 1024 kg. The mass of the satellite is m= 3.2 × 103 kg. Enter an expression for the kinetic energy KE of the satellite in terms of m and v. Calculate the value of KE in joules. Enter an expression for the magnitude of the gravitational force F in terms of M, R, m and the gravitational constant G. Enter an expression for the centripetal acceleration of the satellite a, in terms of the speed of the satellite, v, and R. Enter an expression for the radius R in terms of G, M and v. Calculate the value of R in meters. Enter an expression for the gravitational potential energy PE in terms of G, M, m, and R. Calculate the value of PE in joules. Enter an expression for the total energy E of the satellite in terms of m and v. Calculate the value of the total energy E in joules.arrow_forwardEuropa orbits Jupiter at a distance of 6.7 x 108 m from Jupiter's cloudtops (the surface of the planet). If Jupiter's mass is 1.9 x 1027 kg and radius is 6.8 x 107 m, what is the speed of Europa as it orbits in m/s? Round to the nearest hundredth. Don't worry about putting units, just put the number.arrow_forwardA satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. a)Enter an expression for the kinetic energy KE of the satellite in terms of m and v. Calculate the value of KE in joules. b)Enter an expression for the magnitude of the gravitational force F in terms of M, R, m and the gravitational constant G. c)Enter an expression for the centripetal acceleration of the satellite ac in terms of the speed of the satellite, v, and R.arrow_forward
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