Question

PLEASE SHOW WORK AND ANSWER ALL PARTS. WHEN I ASKED THE SECTIONS SEPARATELY THE ANSWERS DID NOT MATCH, THANK YOU!!!

All of the questions on this concern a space station, consisting of a long thin uniform rod of mass 4.4 x 10⁶kg and length 171 meters, with two identical uniform hollow spheres, each of mass 1.3 x 10⁶ kg and radius 57 meters, attached at the ends of the rod, as shown below. Note that none of the diagrams shown is drawn to scale!

PART A:

a) Suppose that the station starts out at rest (not rotating). What we want is to get it spinning about an axis passing through its center of mass, at an angular velocity of 0.22 rad/s, which is just what’s needed to produce 1-g of artificial gravity at the endpoints. To achieve this, we use rocket motors to apply a constant force F = 1.9 x 10⁶ N to each sphere as shown, directed toward the centers of the spheres. How long must the motors fire in order to bring the station from rest up to an angular velocity of 0.22 rad/s? Answer: _________.___ minutes

PART B:

(b) Suppose once again that the space station begins at rest, not rotating. This time, instead of using rocket engines attached to the spherical end modules, we will have small probes periodically launched from two points on the rod-shaped part of the station as shown. The probes will launch in pairs in opposite directions, each individual probe of identical mass 3534 kg and launched at a speed 23900 m/s with respect to the space station. The launch points are each located at the same distance 64 meters from the center of the rod, on opposite sides of the rod. Each time a pair of probes are launched, some angular momentum is imparted to the station, increasing its spin rate. Question: how many such pairs of probes must be launched so that the station’s angular velocity will reach the required value of 0.22 rad/s? Answer: _____________.___ launched pairs

PART C:

(c) Now, another feature of this station is that the rod-shaped section can change its length (kind of like an old-fashioned telescope), without changing its overall mass and remaining uniform in its density. Suppose that, however it was accomplished, the station is now rotating at a constant angular velocity of 0.22 rad/s. If the length of the rod is reduced to 104 meters, what will be the new angular velocity of the space station? Answer: __________.___ rad/s

PART D:

(d) Let's start again with the station not rotating, and back to its original size, with the rod again at 171 meters long. This time, we would like to get the station rotating at a rate of 0.22 rad/s, but now about an axis that passes straight down the length of the rod. We will accomplish this by placing a pair of rocket engines as shown, each again with a thrust of 1.9 x 10⁶ N, on one of the spherical end modules. How long must these engines fire in order to get the stations angular velocity up to 0.22 rad/s? Answer: __________.___ minutes

axis launch point launch point xis axis axis 褂欒3 IS 90 degree perspective shift so you're looking straight along the new rotation axis

Answer 1

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