A disk is mounted with its axis vertically. It has radius R and mass M. It is initially at rest. A bullet of mass m and velocity v is fired horizontally and tangential to the disk. It lodges in the perimeter of the disk. What angular velocity will the disk acquire? ( 2mv (M+2m)R'
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- An astronaut, of total mass 85.0 kg including her suit, stands on a spherical satellite of mass 375 kg, both at rest relative a nearby space station. She jumps at a speed of 2.56 m/s directly away from the satellite, as measured by an observer in the station. At what speed does that observer measure the satellite traveling in the opposite direction? (See Section 6.2.)A particle of mass m moving along the x-axis with a velocity component +u collides head-on and sticks to a particle of mass m/3 moving along the x-axis with the velocity component −u. What is the mass M of the resulting particle?(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.96 x 10“ m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) 354790 Your response differs from the correct answer by more than 100%. m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 x 10“ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 × 10“ m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume…
- A star with mass M and radius R collides head-on with another star of mass ¾*M and radius 4/5*R, and they coalesce to form a new start at rest whose radius is 6/5*R. Assume that initially the colliding stars had angular velocities with opposite directions but the same magnitude w. What is the magnitude and direction of the final’s stars angular velocity? (Express the magnitude as a fraction of w.)An object of mass is released from rest a distance 3.2R above the surface of a planet, which has no atmosphere, of mass and radius . It strikes the surface of the planet with a speed given by v=c (sqt GM/R) , where c is a constant What is the numerical value of ?C6M.9 Astar with mass M and radius R collides with another star of massM and radius R, and coalesce to form a new star at rest whose radius is R. Assume that initially the colliding stars had angular velocities with opposite direc- tions but the same magnitude | What is the magnitude and direction of the final star's angular velocity? (Express the magnitude as a fraction of )
- A mass mA = 50 kg moving with a velocity vA = (5.0i + 2.0j – 4.0k) m/s, collides with mass mB = 5.0 kg which is initially at rest. Immediately after the collision, mass mA is observed traveling at velocity (-3.0i - 2.0k) m/s. Calculate the magnitudes of vA and vA’. the velocity of B after impact (vB’}.A spaceship has length 120 m, diameter 25 m, and mass 4.0 x 103 kg as measured by its crew. As the spaceship moves parallel to its cylindrical axis and passes us, we measure its length to be 90 m. (a) What do we measure its diameter to be? (b) What do we measure the magnitude of its momentum to be?A binary-star system contains a visible star and a black hole moving around their center of mass in circular orbits with radii r1 and r2 , respectively. The visible star has an orbital speed of v=5.36x105 ms-1 and a mass of m1 =5Ms ,where Ms= 1.98x1030kg is the mass of our Sun. Moreover, the orbital period of the visible star is T = 30 hours.(a) What is the radius r1 of the orbit of the visible star?(b) Calculate the mass m2 of the black hole in terms of MS . [Hint: One root of the equation x3 = 20a(5a+x)2 , where a is a constant, is x = 28a .]
- Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has orbital speed v = 280 km/s, orbital period T = 22.5 days, and approximate mass m₁ = 6.2M5, where Ms is the Sun's mass, 1.99 x 1030 kg. Assume that the visible star and its companion star, which is dark and unseen, are both in circular orbits (see the figure). Find the ratio of the approximate mass m2 of the dark star to Ms. Number i 0.16 m₁ Units No units m₂Three disks A, B and C with same radius 5.0 cm are placed at coordinate (0,50 cm), (-15 cm, 0), and (15 cm, 0), respectively as shown as Figure 1. The masses of the three disks are ma 0.2 kg, mg = mc = 0.4 kg. They are connected by thin rods which has negligible masses. Find A(0, 50) MA = 0.2 B(-15,0) С(15, 0) тв 3 0.4 mc = 0.4 Figure 1 (a) the coordinate of the centre of mass of the system. (b) the rotational inertia about the axis perpendicular to the plane and passing through the centre of disk A.In a 2-body system, a space craft is in a circular orbit at a fixed radius B (450*10^8) around a central star of mass M (6*10^120) Determine the total energy and angular momentum of the circular orbit. (v/m = -E/m) and angular momentum (l/m) Both of these values are normalised by the mass of the spacecraft.