A wedge with angle as shown, of mass m₂ is in contact with two equal masses m₁. All the contacts are frictionless. Find the initial accelerations of the masses. вт M2 m, M₁
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- An astronaut out on a spacewalk to construct a new section of the International Space Station walks with a constant velocity of 2.00 m/s on a flat sheet of metal placed on a flat, frictionless, horizontal honeycomb surface linking the two parts of the station. The mass of the astronaut is 75.0 kg, and the mass of the sheet of metal is 245 kg. a. What is the velocity of the metal sheet relative to the honeycomb surface? b. What is the speed of the astronaut relative to the honeycomb surface?ll Problem Three. Consider two planets: Neptune with a mass of m, × 1.02×10% kg and Uranus with a mass of m, = 8.68 x10*kg. The planets are a distance of d =1.62×10°km apart. Let Neptune be at the origin of a coordinate system, and Uranus be along the positive x-axis. (See the diagram below.) m2 X Find the location "x" where a test particle would accelerate toward the two planets with a force that is half due to Neptune, and half due to Uranus. Give an answer in 1010 km. 7.) (A) 5.6 B) 3.6 (C) 9.4 (D) 2.1 (E) 8.9 Consider if a large asteroid of mass m =1.00×10²ºkg is a distance d above m. Find the magnitude of the gravitational force the asteroid experiences due to both planets. Give an answer in units of 1010 N. 8.) (A) 35 (B) 83 (C) 71 (D) 53 (E) 98An 8.00-kg point mass and a 15.0-kg point mass are held in place 50.0 cm apart. A particle of mass m is released from a point between the two masses 20.0 cm from the 8.00-kg mass along the line connecting the two fixed masses. Find the magnitude and direction of the acceleration of the particle.
- A hockey puck with mass 0.160kg is at rest at the origin on the horizontal, frictionless surfaceof the rink. At t = 0, a player applies a force of 0.250N to the puck parallel to the surface. Hecontinues to apply the force until t = 2.00s. What are the position and speed of the puck at t =2.00?Chapter 13, Problem 055 In 1610, Galileo used his telescope to discover four prominent moons around Jupiter. Their mean orbital radii a and periods T are as follows (a) Io has a mean orbital radius of 4.22 x 108 m and a period of 1.77 days. Find the mass of Jupiter from this information. (b) Europa has a mean orbital radius of 6.71 x 108 m and a period of 3.55 days. Find the mass of Jupiter from this information. (c) Ganymede has a mean orbital radius of 10.7 x 108 m and a period of 7.16 days. Find the mass of Jupiter from this information. (d) Callisto has a mean orbital radius of 18.8 x 108 m and a period of 16.7 days. Find the mass of Jupiter from this information. Units (a) Number Units (b) Number Units (c) Number Units (d) Number Click if you would like to Show Work for this question: Open Show WorkA binary star consist of two stars of the same mass m revolving in a circle of radius R about their common centre of mass. Suppose that a meteorite passes through the centre of mass of the binary star in a direction perpendicular to the orbital plane. What is the minimum speed that the meteorite must have at the centre of mass in order for it to escape from the gravitational attraction of the binary star? ANSW: 4Gm R w
- Problem One newly discovered light particle has a mass of m and property q. Suppose it moves within the vicinity of an extremely heavy (fixed in place) particle with a property Q and mass M. When the light particle is xi distance from the heavy particle, it is moving directly away from the heavy particle with a speed of vi. a) What is the lighter particle's speed when it is xf away from the heavy particle? Am,m2 where A is a constant, m, and m, are the masses of the two Consider a new expression for gravitation potential energy as: PE grav objects, and r is the distance between them. Moreover, the new particle has an additional interaction with the heavy particle through the following force expression Fnew 4TE0 where En is a constant that is read as epsilon subscript 0, q and Q are their new properties.r is the distance between the new particle and the heavy particle. Solution: We may solve this using two approaches. One involves the Newton's Laws and the other involving Work-Energy…Two asteroids collide and stick together, with initial and final states as shown. If the velocity v1i = 13 m/s, what is the magnitude of the initial velocity v2i of the second asteroid?Question 2: An OSU-branded squishy moon ball has a mass of 25 g and a diameter of 60 mm. Consider two squishy moons located in deep space far from the Sun or any other massive body. The two squishy moons form a binary system with their centers separated by 0.5 meters, and they are in circular orbits around their common center of mass. a. Draw a sketch of the squishy moon system and correctly label the dimensions and orbits. b. What is the orbital period of the two squishy moons about their center of mass? c. What is their orbital speed? d. If the squishy moon binary system is 5au from the Sun, what is the Hill radius of the system in the tidal field of the Sun? Compare the Hill radius to the semi-major axis of the squishy moon binary orbit radius and comment on whether this binary squishy moon system is stable when it is 5au from the Sun. e. Follow-up your answer to part d and estimate the distance from the Sun where the squishy moons in this binary system are exactly twice their Hill…
- An 8.50 kg point mass and a 15.0 kg point mass are held in place 50.0 cm apart.A particle of mass m is released from a point between the two masses 12.0 cm from the 8.50 kg mass along the line connecting the two fixed masses. Part A Find the magnitude of the acceleration of the particle.An object is dropped from an altitude of one Earth radius above Earth's surface. If M is the mass of Earth and R is its radius, the speed of the object just before it hits Earth is given by: GM R 0 GM 2R O GM V2R 0 GM VR 2GM RA rod of length 3 meters with density 8(x) = 1.1 + 1.1x4grams/meter is positioned along the positive x-axis, with its left end at the origin. Find the total mass and the center of mass of the rod. Round your answers to four decimal places. The total mass of the rod is i The center of mass of the rod is i grams. meters.
