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A spaceship of mass 270 kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 280 m/s and at an angle of φ0 = 51°, at a distance 11000 km from the center of the planet as shown in the figure.
Part (a) Give an expression for the
Part (b) If the spaceship whips around the planet to the other side so that the angle is φ = 31° and is moving at 85 m/s, how far, in kilometers, from the planet is it?
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- A spherical satellite of approximately uniform density with radius 6.3 m and mass 295 kg is originally moving with velocity (2600, 0, 0) m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 8.6 kg is initially moving toward the satellite with velocity (-2200, 0, 0) m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity (-1300, 480, 0) m/s. Both before and after the collision, the rotation of the space junk is negligible. Part 1 M.R.I Your answer is partially correct.The figure shows a device that can be used to measure the speed of a bullet. The device consists of two rotating disks, separated by a distance of d = 0.922 m, and rotating with an angular speed of 90.8 rad/s. The bullet first passes through the left disk and then through the right disk. It is found that the angular displacement between the two bullet holes is = 0.360 rad. From these data, determine the speed of the bullet. Number i Bullet Units 19 kd + MotorA 1500-kg satellite orbits a planet in a circular orbit of radius 6.2 × 106 m. What is the angular momentum, in kg m2/s, of the satellite in its orbit around the planet if the satellite completes one orbit every 1.5 × 104 s?
- Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. A star with a of mass of 2.0x1032 kg and radius 7.0x108 m is initially rotating at a rate of once every 30 days. The star collapses into a neutron star with the same mass but a new radius of 16,000 m. What is the angular speed of the star? (Give your answer in rotations per second.) Assume the star is a solid sphere: Isphere = 2/5 MR2. The Crab Nebula (shown below) formed from a nearby supernova (6000 light years away). Chinese astronomers observed the event in the year 1054 and since that time the nebula has been expanding into what it appears like today. The Crab Pulsar is a neutron star at the center of the nebula and the remains of the original supernova.A thin circular hoop made of tungsten is rotating about its axis.Two copper beads are gently attached to the opposite ends of adiameter of the tungsten hoop. Mass of tungsten hoop is m.Mass of each copper bead is M. The angular velocitiesbefore and after attachment of the copper beads are ω and ω',respectively. Find the final angular velocity ω'. (a)ω(m+2M)/m (b)ω(m-2M)/(m+2M) (c)ωm/(2m+M) (d)ωm/(m+2M).A spherical satellite of approximately uniform density with radius 4.8 m and mass 215 kg is originally moving with velocity (2600, 0, 0) m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 6.0 kg is initially moving toward the satellite with velocity (-2200, 0, 0) m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity ( 1300, 480, 0) m/s. Both before and after the collision, the rotation of the space junk is negligible. V3 L Part 1 Ux = Uy = @1 (a) Just after the collision, what are the components of the center-of-mass velocity of the satellite (v, and vy) and its rotational speed w? (For Ux, enter your answer to at least four significant figures.) Part 2 Mi @= i i Save for Later i M, R, 1 V2 m m/s m/s rad/s (b) Calculate the rise in the internal energy of the satellite and space junk combined. J Attempts: 0 of 10 used Submit Answer
- Three children are riding on the edge of a merry-go-round that is a disk of mass 102 kg, radius 1.3 m, and is spinning at 21 rpm. The children have masses of 20.4 kg, 26 kg, and 33.8 kg. If the child who has a mass of 26 kg moves to the center of the merry-go-round, what is the new magnitude of angular velocity in rpm?A man with a mass Of 80 kg runs at a speed of 4 m/s along the tangent to a disk shaped platform of mass 160 kg and radius of 2 m. The platform is initially at rest but can rotate freely about an axis through its center. For the platform, I = (1/2) M R². Treat the man as a point particle. (a) Find the angular velocity of the platform after the man jumps in. (2) He then walks slowly to the center. Find the new angular velocity.A spaceship of mass 110 kg is going to use a planet for a gravitational assist - that is, use the planet's gravity to change its direction of travel without expending any fuel. It is initially moving at a velocity of 230 m/s and at an angle of φ0 = 65°, at a distance 10200 km from the center of the planet as shown in the figure. Give an expression for the angular momentum of the spacecraft, using the coordinate system specified, in terms of m, r0, v0, φ0, and unit vectors i, j, and k. If the spaceship whips around the planet to the other side so that the angle is φ = 45° and is moving at 105 m/s, how far, in kilometers, from the planet is it?
- A particle of mass m moves in the xy plane with a velocity of v = vî + vj. Determine the angular momentum of the particle about the origin when its position vector is r = xî + vi.(Use the following as necessary: x, y, v, Vy, and m.)A planet is at a position of r→=3.0×10^12mx̂ − 4.0×10^12mŷ as it moves in an elliptical orbit around a large star at the origin (x=0, y=0). If the planet has a mass of 6.0 ×1026 kg and is moving with a velocity of v→=9.5km/sx̂, what is its angular momentum vector? (give magnitude and direction)Consider a spacecraft orbiting Earth. At an instant in time, the angular velocity of the spacecraft relative to Earth is = 1.9bh +0.82b2+0.34b3 (in rad/s) and the angular acceleration of the spacecraft relative to Earth is a = 0.0561 +0.19bz+0.22bg (in rad/s?). What is the moment (in N.m) being applied on the spacecraft in the b2. Assume the moment of inertia of the spacecraft is given by: Г5000 0.0 0.0 0.0 10000 0.0 kg.m? 0.0 13000 Note b1, b2, bz are unit vectors fixed in the spacecraft reference frame.