Question

It has been proposed that extending a long conducting wire from a spacecraft (a "tether") could be used for a variety of applications, from navigation to power generation. One of the first such experiments involving this technique was an August 1992 space shuttle flight, but the tether failed and only only 250 m of the conducting wire could be let out. A 40.0 V motional emf was generated in the Earth's 5.0 x 10-T field, while the shuttle and tether were moving at 7.80 x 10 m/s. What was the angle (in degrees) between the shuttle's velocity and the Earth's field?

Answer 1

Complete Question

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Answer:

The angle between shuttle's velocity and the Earth's field is  $\theta = 24.2^o$

Explanation:

From the question we are told that

     The length of eire let out is  $L = 250 \ m$

      The emf generated is $\epsilon = 40 V$

      The earth magnetic field is $B = 5.0 *10^{-5} T$

     The speed of the shuttle and tether is $v = 7.80 * 10^3 \ m/s$

The emf generated is mathematically represented as

                             $\epsilon = L\ v\ B\ sin \ \theta$

making $\theta$  the subject of the formula

                        $\theta = sin ^{-1}[ \frac{\epsilon}{L * B *v} ]$

substituting values

                        $\theta = sin ^{-1}[ \frac{40}{250 * (5*10^{-5}) *(7.80 *10^{3})} ]$

                        $\theta = 24.2^o$