This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 9.63 x 10^6 kg and length 1266 meters. Small probes of mass 8244 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 3919 m/s with respect to the launch points, which are each located 356 m from the center of the rod. After 14 pairs of probes have launched, how fast will the station be spinning? 1 3.59 rpm 1.00 rpm 3 2.39 rpm 4 1.67 rpm
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- In the figure below, three point particles are fixed in place in an xy plane. Particle A has mass mA, particle B has mass 2.35mA, and particle C has mass 3.45mA. A fourth particle D, with mass 4.40mA, is to be placed near the other three particles. In terms of distance d, at what coordinates should particle D be placed so that the net gravitational force on particle A from particles B, C, and D is zero? (a) C 1.5d x coordinate d (b) y coordinate Bo A d xA disk with velocity v= 10m/s, mass m=5 kg, and radius r=2 m. Find the total kinetic energy.Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.
- 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.This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 4.07 x 10^6 kg and length 1052 meters. Small probes of mass 9923 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 4148 m/s with respect to the launch points, which are each located 357 m from the center of the rod. After 10 pairs of probes have launched, how fast will the station be spinning? 7.48 rpm 2.99 rpm 8.98 rpm 2.09 rpmIn the figure, two satellites, A and B, both of mass m = 49.1 kg, move in the same circular orbit of radius r = 7410 km around Earth (mass ME = 5.98×1024 kg) but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy EA+ EB of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth’s center or orbiting around Earth?
- You are a visitor aboard the New International Space Station, which is in a circular orbit around the Earth with an orbital speed of vo = 2.72 km/s. The station is equipped with a high velocity projectile launcher, which can be used to launch small projectiles in various directions at high speeds. Most of the time, the projectiles either enter new orbits around the Earth or eventually fall down and hit the Earth. However, as you know from your physics courses at the Academy, projectiles launched with a sufficiently great initial speed can travel away from the Earth indefinitely, always slowing down but never falling back to Earth. With what minimum total speed, relative to the Earth, would projectiles need to be launched from the station in order to "escape" in this way? For reference, recall that the radius of the Earth is RE = 6370000 m, the mass of the Earth is MẸ = 5.98 × 1024 kg, the acceleration due to gravity on the surface of the Earth is g = 9.81 m/s and the universal…Three point particles are fixed in position in an xy plane. Two of them, particle A of mass 5 g and particle B of mass 11 g, are shown in the figure with a separation of dAB = 0.579 m at angle = 30°. Particle C, with mass 8 g, is not shown. The net gravitational force acting on particle A due to particles B and C is 2.02 x 10-¹4 N at an angle of -163.8��. from the positive x axis. What are (a) the x coordinate and (b) the y coordinate of particle C? B dAB 0 AIn the figure, two satellites, A and B, both of mass m = 36.1 kg, move in the same circular orbit of radius r = 7240 km around Earth (mass ME = 5.98×1024 kg) but in opposite senses of rotation and therefore on a collision course. (a) Find the total mechanical energy Е+ ЕÅ of the two satellites + Earth system before the collision. (b) If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass = 2m), find the total mechanical energy immediately after the collision. (c) Just after the collision, is the wreckage falling directly toward Earth's center or orbiting around Earth? (a) Number Units (b) Number (c) Units A B Earth
- This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 8.40 x 10^6 kg and length 1137 meters. Small probes of mass 8057 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 2897 m/s with respect to the launch points, which are each located 400 m from the center of the rod. After 10 pairs of probes have launched, how fast will the station be spinning? (1) 2.36 rpm 2 1.11 rpm 3) 1.97 rpm 4 1.58 rpmWe have a non-rotating space station in the shape of a long thin uniform rod of mass 2.60 x 10^6 kg and length 769 meters. Small probes of mass 8303 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 2888 m/s with respect to the launch points, which are each located 196 m from the center of the rod. After 11 pairs of probes have launched, how fast will the station be spinning? 3.70 rpm 7.71 rpm 4.63 rpm 10.02 rpm