In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.40 kg and 14.0 g whose centers are separated by about 6.10 cm. Calculate the gravitational force between these spheres, treating each as a particle located at the center of the sphere.
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- In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.40 kg and 14.0 g whose centers are separated by about 6.10 cm. Calculate the gravitational force between these spheres, treating each as a particle located at the center of the sphere.
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- 7 of 16 (a) Number 0.37/1 A solid sphere of uniform density has a mass of 9.3 × 104 kg and a radius of 3.4 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 7.5 kg located at a distance of (a) 12 m and (b) 2.7 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 ≤ 3.4 m from the center of the sphere. 3.23 (b) Number i 1.4 Units Units E (c) |Fon m = k·r, where k = i N N > <Suppose a cylindrical habitat in space 7.90 km in diameter and 45.0 km long has been proposed. Such a habitat would have cities, land, and lakes on the inside surface and air and clouds in the center. They would all be held in place by rotation of the cylinder about its long axis. How fast would the cylinder have to rotate to imitate the Earth's gravitational field at the walls of the cylinder?Q11 In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.20 kg and 12.0 g whose centers are separated by about 5.80 cm. Calculate the gravitational force between these spheres, treating each as a particle located at the center of the sphere.
- Assuming that the Earth has a uniform density ?=5540.0 kg/m^3, what is the value of the gravitational acceleration ?? at a distance ?=5900.0 km from the Earth's center?A satellite m = 500 kg orbits the earth at a distance d = 213 km, above the surface of the planet. The radius of the earth is re = 6.38 × 106 m and the gravitational constant G = 6.67 × 10-11 N m2/kg2 and the Earth's mass is me = 5.98 × 1024 kg. What is the speed of the satellite in m/s? v =A ring of radius 7 m lies in the x,y plane, centered on the origin. The portions of the ring in the first and third quadrants have a mass density of 8 kg/m, while the portions of the ring in the second and fourth quadrants have a mass denisty of 11.3 kg/m. Find the z-component of the gravitational field due to the ring at a point P on the z-axis at a distance 5 m from the origin. Use G = 6.673e-11 N*m^2/kg^2 9z =
- The gravitational constant G was first measured accurately by Henry Cavendish in 1798. He used an exquisitely sensitive balance to measure the force between two lead spheres whose centers were 0.27 m apart. One of the spheres had a mass of 168 kg, while the mass of the other sphere was 0.73 kg. What was the ratio of the gravitational force between these spheres to the weight of the lighter sphere?Two masses m, = 100 kg and m, = 8100 kg are held 1 m apart. (a) At what point on the line joining them is the gravitational field equal to zero? Find the gravi- tational potential at that point. (b) Find the gravitational potential energy of the system. Given G = 6.67 × 10-" Nm? kg.A satellite m = 500 kg orbits the earth at a distance d = 199 km, above the surface of the planet. The radius of the earth is re=6.38×106 m and the gravitational constant G =6.67×10-11 N m2/kg2 and the Earth's mass is me=5.98×1024 kg. What is the speed of the satellite in m/s?
- The figure below shows a spherical hollow inside a lead sphere of radius R = 4.00 cm. 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 = 2.50 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 0.459 kg that lies at a distance d = 9.00 cm from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?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 = 4.07 × 1024 kg and R = 5.79 x 106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number i Units (b) Number i UnitsA ring of radius 7 m lies in the x-y plane, centered on the origin. The portions of the ring in the first and third quadrants have a mass density of 7.4 kg/m, while the portions of the ring in the second and forth quadrants have a mass density of 7.3 kg/m. Find the z component of the gravitational field due to the ring at a point P on the z axis a distance 6 meters from the origin. Use G = 6.673E-11 N m2/kg2.