Outside the space shuttle, you
Outside the space shuttle, you and a friend pull on two ropes todock a satellite whose mass is 800 kg. The satellite is initiallyat position < 3.0, -1.6, 3.0 > m and has a speed of 6 m/s.You exert a force < -400, 400, 250 > N. When the satellitereaches the position < 1.7, 2.6, 4.8 > m, its speed is 7.11m/s. How much work did your friend do?
Answer:
Solution:Let us go to the basics first.
Letr1 = initial position,r2 = final position,i,j,k = unit vectors along x,y,z axes respectivelyF1 = force by me,W1 = work done by me,W2 = work done by my friendr1 = (3 i – 1.6 j + 3 k)mr2 = (1.7 i + 2.6 j + 4.8 k) mF1 = (-400 i + 400 j + 250 k)NW1 = F1.(r2 – r1)Or W1 = (-400 i + 400 j + 250 k).{(1.7 i + 2.6 j + 4.8 k) – (3 i -1.6 j + 3 k)}Or W1 = (-400 i + 400 j + 250 k).(1.7 i + 2.6 j + 4.8 k – 3 i + 1.6j – 3 k)Or W1 = (-400 i + 400 j + 250 k).(-1.3 i + 4.2 j +1.8 k)Or W1 = -400 * (-1.3) + 400 * 4.2 + 250 *1.8Or W1 = 2650 JMass m = 800 kgInitial speed u = 6 m/sInitial kinetic energy K1 = 1/2 mu^2Or K1 = 1/2 * 800 * 6^2Or K1 = 14400 JFinal speed v = 7.11 m/sFinal kinetic energy K2 = 1/2 mv^2Or K2 = 1/2 * 800 * 7.11^2Or K2 = 20220.84 JTotal work done = change in kinetic energy=> W1 + W2 = K2 – K1=>2650 J + W2 = 20220.84 J – 14400 J=> W2 = 3170.84 J (Answer)
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