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syang9
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the starship enterprise is cruising along at constant speed v when it encounters a mysterious space station. (enterprise = x, space station = S)
http://x402.putfile.com/4/11618084116.jpg
the enterprise is headed such that it will pass the space station at a distance d, as shown above. the question states:
argue that angular momentum conservation does not allow the tractor beam to make the enterprise reach the space station if we treat them both as point particles. given, v_enterprise, d.
so.. here's what i tried.
system = ship + station; no external torques, so angular momentum is conserved.
let l = the top side of the triangle (distance that enterprise would travel if not being pulled by tractor beam)
let r = hypotenuse
L_i = r X p
|r| = sqrt(l^2 + d^2); |p| = mv
let the space station be at the origin, therefore
L_f = 0
so..
sqrt(l^2 + d^2)*(mv)*sin(phi) = 0; sin(phi) = L/r
sqrt(l^2 + d^2)*(mv)*(L/r) = 0
now.. i have absolutely no idea what to do.. could i get a hint, anyone?
http://x402.putfile.com/4/11618084116.jpg
the enterprise is headed such that it will pass the space station at a distance d, as shown above. the question states:
argue that angular momentum conservation does not allow the tractor beam to make the enterprise reach the space station if we treat them both as point particles. given, v_enterprise, d.
so.. here's what i tried.
system = ship + station; no external torques, so angular momentum is conserved.
let l = the top side of the triangle (distance that enterprise would travel if not being pulled by tractor beam)
let r = hypotenuse
L_i = r X p
|r| = sqrt(l^2 + d^2); |p| = mv
let the space station be at the origin, therefore
L_f = 0
so..
sqrt(l^2 + d^2)*(mv)*sin(phi) = 0; sin(phi) = L/r
sqrt(l^2 + d^2)*(mv)*(L/r) = 0
now.. i have absolutely no idea what to do.. could i get a hint, anyone?
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