In the figure, identical blocks with identical masses m = 2.11 kg hang from strings of different lengths on a balance at Earth's surface. The strings have negligible mass and differ in length by h = 5.38 cm. Assume Earth is spherical with a uniform density p=5.50 g/cm³. What is the difference in the weight of the blocks due to one being closer to Earth than the other?
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- A stick with a mass of 0.224 kg and a length of 0.416 m rests in contact with a bowling ball and a rough floor, as shown in the figure(Figure 1). The bowling ball has a diameter of 20.6 cm , and the angle the stick makes with the horizontal is 30.0 ∘∘. You may assume there is no friction between the stick and the bowling ball, though friction with the floor must be taken into account. Find the magnitude of the force exerted on the stick by the bowling ball. Find the horizontal component of the force exerted on the stick by the floor. Repeat part B for the vertical component of the forceTwo blocks, which can be modeled as point masses, are connected by a massless string which passes through a hole in a frictionless table. A tube extends out of the hole in the table so that the portion of the string between the hole and M1 remains parallel to the top of the table. The blocks have masses M1= 1.9 kg and M2= 2.8 kg. Block 1 is a distance r= 0.35 m from the center of the frictionless surface. Block 2 hangs vertically underneath. How much time, in seconds, does it take for block one, M1, to make one revolution? Assume that block two, M2, does not move relative to the table and that block one, M1, is rotating around the table.A rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the pulsar is 5.00 × 10−4 times the radius of the star before collapse. There is no change in mass. In both cases, the mass of the star is uniformly distributed in a spherical shape. If the period of the star’s rotation before collapse is 4.00 × 104 s, what is its period after collapse?
- The Cavendish balance shown in the figure below has two large lead balls, each of mass M = 1.5 kg,and two smaller lead balls, each of mass m = 0.8 kg. The lengths of the suspended rod to which the twosmaller balls are attached and the fixed rod to which the larger balls are attached are both 40 cm asmeasured from the center of each lead ball. If the angle between the centers of the large and smallballs is = 22 degrees with respect to the rotational axis established by the quartz fiber, find the force ofgravitational attraction between each pair of large and small balls.A meteoroid is moving towards a planet. It has mass m = 0.18×109 kg and speed v1 = 3.8×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.26×107 m. The mass of the planet is M = 10×1025 kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.Consider a planet that has two layers. There is a core, which has density 9.9 x 103 kg/m3 and radius 3.9 x 106 m, and then there is a crust, which has density 4.9 x 103 kg/m3 and sits on top of the core. The planet has a total radius of 16.9 x 106 m. Calculate the acceleration due to gravity at the surface of this planet, in N/kg. Use G = 6.7 x 10-11 N m2/ kg2. (Please answer to the fourth decimal place - i.e 14.3225)
- A meteoroid is moving towards a planet. It has mass m = 0.22×109 kg and speed v1 = 3.5×107 m/s at distance R1 = 2.9×107 m from the center of the planet. The radius of the planet is R = 0.46×107 m. The mass of the planet is M = 3.2×1025 kg. There is no air around the. Calculate the value of v in meters per second.A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.Two blocks, which can be modeled as point masses, are connected by a massless string which passes through a hole in a frictionless table. A tube extends out of the hole in the table so that the portion of the string between the hole and M1 remains parallel to the top of the table. The blocks have masses M1 = 1.4 kg and M2 = 2.1 kg. Block 1 is a distance r = 0.85 m from the center of the frictionless surface. Block 2 hangs vertically underneath. a) Assume that block two, M2, does not move relative to the table and that block one, M1, is rotating around the table. What is the speed of block one, M1, in meters per second? b) How much time, in seconds, does it take for block one, M1, to make one revolution?
- A mass m is suspended from a massless spring of natural length 90 cm with the spring constant k = 10 Nm and causes the spring to extend by 7.9 cm. Assuming the gravitational field strength g = 9.8 ms², calculate the value of the mass on the spring. Give your answer in Sl units. Answer: Choose... +Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object–Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.Two blocks, which can be modeled as point masses are connected by a massless string which passes through a hole in a frictionless table. A tube extends out of the hole in the table so that the portion of the string between the hole and M1 remains parallel to the top of the table l. The blocks have masses M1 = 1.2 kg and M2 = 2.5 kg. Block 1 is a distance r = 0.85 m from the center of the frictionless surface. Block 2 hangs vertically underneath Assume that block two, M2 does not move relative to the table and that the block one M1 is rotating around the table. What is the speed of block one, M1, in meters per second?