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What ratio m/M maximizes the magnitude of the gravitational force between the parts? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154796

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A spaceship is on a straightline path between Earth and its moon. At what distance from Earth is the net gravitational force on the spaceship zero?
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Subject: Physics  Topic: Mechanics  ID: 154797

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How far from Earth must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances Earth's pull? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154798

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Three 5.0 kg spheres are located in the xy plane as shown in Fig.148.
What is the magnitude of the net gravitational force on the sphere at the origin due to the other two spheres? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154800

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In Fig.149 (a), four spheres form the corners of a square whose side is 2.0 cm long.
What are the magnitude and direction of the net gravitational force from them on a central sphere with mass M_5 = 250 kg? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154802

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In Fig.1410 , two spheres of mass m and a third sphere of mass M form an equilateral triangle, and a fourth sphere of mass m_4 is at the center of the triangle. The net gravitational force on that central sphere from the three other spheres is zero.
(a) What is M in terms of m?
(b) If we double the value of m_4 , what then is the magnitude of the net gravitational force on the central sphere? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154804

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The masses and coordinates of three spheres are as follows: 20 kg, x = 0.50 m, у = 1.0 m; 40 kg, x = 1.0 m, у = 1.0 m; 60 kg, x = 0 m, у = 0.50 m.
What is the magnitude of the gravitational force on a 20 kg sphere located at the origin due to the other spheres? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154805

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Four uniform spheres, with masses m_A = 400 kg, m_B =350 kg, m_C = 2000 kg, and m_D = 500 kg, have (x, y) coordinates of (0, 50 cm), (0, 0), (80 cm, 0), and (40 cm, 0), respectively.
What is the net gravitational force on sphere В due to the other spheres?
...MORE
Subject: Physics  Topic: Mechanics  ID: 154806

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Figure 1413 shows a spherical hollow inside a lead sphere of radius R; the surface of the hollow passes through the center of the sphere and "touches" the right side of the sphere. The mass of the sphere before hollowing was M.
With what gravitational force does the hollowedout lead sphere attract a small sphere of mass m that lies at a distance d from the center of the lead sphere,on the straight line connecting the centers of the spheres and ofthe hollow?
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Subject: Physics  Topic: Mechanics  ID: 154808

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You weigh 530 N at sidewalk level outside the World Trade Center in New York City. Suppose that you ride from this level to the top of one of its 410 m towers.
Ignoring Earth's rotation, how much less would you weigh there (because you are slightly farther from the center of Earth)? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154809

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At what altitude above Earth's surface would the gravitational acceleration be 4.9 m/s^2? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154810

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(a) What will an object weigh on the Moon's surface if it weighs 100 N on Earth's surface? (b) How many Earth radii must this same object be from the center of Earth if it is to weigh the same as it does on the Moon? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154811

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The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just barely provides the centripetal force needed for the rotation. (Why?) (a) Show that the corresponding shortest period of rotation is
T = SQRT(3*Pi/(G*Ro)
where Ro is the uniform density of the spherical planet, (b) Calculate the rotation period assuming a density of 3.0 g/cm3, typical of many planets, satellites, and asteroids. No astronomical object has ever been found to be spinning with a period shorter than that determined by this analysis, ...MORE
Subject: Physics  Topic: Mechanics  ID: 154812

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One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M = 4.1 x 10^24 kg and R = 6.0 x 10^6 m,
what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154813

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A body is suspended from a spring scale in a ship sailing along the equator with speed v.
(a) Show that the scale reading will be very close to W_0(l ± 2*Omega*v/g), where Omega is the angular speed of Earth and W_0 is the scale reading when the ship is at rest.
(b) Explain the ± sign.
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Subject: Physics  Topic: Mechanics  ID: 154814

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The radius R_h and mass M_h of a black hole are related by R_h = 2GM_h/c^2, where с is the speed of light. Assume that the gravitational acceleration a_g of an object at a distance r_0 =1.001Rh from the center of a black hole is given by Eq. a(g) = GM/r^2 (it is, for large black holes),
(a) Find an expression for a_g at r_a in terms of M_h.
(b) Does a_g at r_0 increase or decrease with an increase of M_h?
(c) What is ag at r_0 for a very large black hole whose mass is 1.55 x 10^12 times the solar mass of 1.99 x 10^10 kg?
(d) If the astronaut is at r_0 with her feet toward this black hole, what is the difference in gravitational acceleration between her head and her feet?
(e) Is the tendency to stretch the astronaut severe? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154836

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Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation? ...MORE
Subject: Physics  Topic: Mechanics  ID: 154837

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Two concentric shells of uniform density having masses M_1 and M_2 are situated as shown in Fig.1422.
Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at
(a) point A, at distance r = a from the center,
(b) point В at r = b, and
(c) point С at r = c. The distance г is measured from the center of the shells. ...MORE
Subject: Physics  Topic: Mechanics  ID: 154839

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A solid sphere of uniform density has a mass of 1.0 x 10^4 kg and a radius of 1.0 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass m located at a distance of
(a) 1.5 m and
(b) 0.50 m from the center of the sphere?
(c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r < 1.0 m from the center of the sphere. ...MORE
Subject: Physics  Topic: Mechanics  ID: 154840

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A uniform solid sphere of radius R produces a gravitational acceleration of a(g) on its surface.
At what two distances from the center of the sphere is the gravitational acceleration a_g/3?
(Hint: Consider distances both inside and outside the sphere.) ...MORE
Subject: Physics  Topic: Mechanics  ID: 154841

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