Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 11, Problem 97P
To determine
To Find:The speed of rotation.
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IIIIIIIty (11ee nom the pull of gravity)
surface of the earth
An object would have to have enough kinetic energy to equal the
potential energy at infinity.
Ek = Epg
1/2 m v2 = G m¡m2r
rearranging for v:
v = /2 Gmr
ex. The escape velocity at the surface of the earth is approximately
8 km/s. What is the escape velocity for a planet whose radius is 4
times and whose mass is 100 times that of earth?
(a) Evaluate the gravitational potential energy (in J) between two 9.00 kg spherical steel balls separated by a center-to-center distance of 23.0 cm.
-2.349E-8
J
(b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast (in m/s) will they each be traveling upon impact. Each sphere has a radius of 5.50 cm.
10.90
X m/s
Plz
Chapter 11 Solutions
Physics for Scientists and Engineers
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- A Molniya orbit is a highly eccentric orbit of a communication satellite so as to provide continuous communications coverage for Scandinavian countries and adjacent Russia. The orbit is positioned so that these countries have the satellite in view for extended periods in time (see below). If a satellite in such an orbit has an apogee at 40,000.0 km as measured from the center of Earth and a velocity of 3.0 km/s, what would be its velocity at perigee measured at 200.0 km altitude?arrow_forwardCheck Your Understanding If we send a probe out of the solar system starting form Earth’s surface, do we only have to escape the Sun?arrow_forwardThe perihelion of Halley’s comet is 0.586 AU and the aphelion is 17.8 AU. Given that its speed at perihelion is 55 km/s, what is the speed at aphelion ( IAU=1.4961011m )? (Hint: You may use either conservation of energy or angular momentum, but the latter is much easier.)arrow_forward
- The Sun’s mass is 2.01030kg , its radius is 7.0105km , and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius 3.5103km , what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?arrow_forward13-62 Comets move around the sun in very elliptical orbits. At its closest approach, in 1986 Comet Halley was 8.79 x 10' km from the sun and moving with a speed of 54.6 km/s. What was the comet's speed when it crossed Neptune's orbit in 2006? (Neptune: mean distance fromn the sun 4.50 x 102 m; Mass 1.03 x 1026 kg)arrow_forward19-77/ A satellite in a circular orbit 1000 km above Earth's surface has total mechanical energy U. Find (A) kinetic anergy, (B) mass and (C) speed. [Data: U = -1.8 GJ ; ] Post Discussion Send Feedbackarrow_forward
- a) Derive the escape speed vII (sometimes called the second cosmic speed) from the surface of body of radius R and mass M, using energy conservation. Assume that the planet does not move or spin, so that the total mechanical energy E of a test particle both on the surface and at infinity is equal to zero, and the speed at infinity is zero. Use the formula come up in the last part, Compute this escape speed (in km/s) from Venus, Mars, Jupiter and Neptune. b) Evaluate vIII from the heliocentric orbit of the 4 planets (Venus, Mars, Jupiter and Neptune) mentioned above, assuming circularity of their orbits. Compare the computed speeds with the escape speeds from their surfaces (vII). Notice a big difference in the situation around the inner and the outer planets. What is it due to? A fly-by’s of small bodies near a planet can result in the small particle being accelerated to a final speed close to vII w.r.t. the planet. Draw conclusions as to which planets are able to accelerate small…arrow_forward(a) Calculate how much work is required to launch a spacecraft of mass m from the surface of the earth (mass mE, radius RE) and place it in a circular low earth orbit—that is, an orbit whose altitude above the earth’s surface is much less than RE. (As an example, the International Space Station is in low earth orbit at an altitude of about 400 km, much less than RE = 6370 km.) Ignore the kinetic energy that the spacecraft has on the ground due to the earth’s rotation. (b) Calculate the minimum amount of additional work required to move the spacecraft from low earth orbit to a very great distance from the earth. Ignore the gravitational effects of the sun, the moon, and the other planets. (c) Justify the statement “In terms of energy, low earth orbit is halfway to the edge of the universe.”arrow_forwardA satellite is in an elliptic orbit around the earth. Its sped at perigee A is 8650 m/s. Use conservation of energy to determine the speed at the apogee C. Radius of earth is 6380 km. Chapter 8 question 99 page 212 figure 8-46 in Giancoli Physics 4th editionarrow_forward
- 15-93. Disks A and B have a mass of 15 kg and 10 kg, respectively. If they are sliding on a smooth horizontal plane with the velocities shown, determine their speeds just after impact. The coefficient of restitution between them is e = 0.8. Line of impact 10 m/s 8 m/s B 15-107arrow_forwardConsider a distant planet that has twice the mass and twice the radius of the Earth.Is the escape speed on this planet greater than, less than, or equal to the escape speedon the Earth? Explainarrow_forwardIf an object collapses to a black hole, [problem 9-99 for studentb] then the escape velocity at the surface of the black hole is equal to the speed of light. Determine the radius of the black hole, if the mass is 4.1 times the mass of the sun. [radius in km = ]arrow_forward
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