4. 1 points HRIW10 7.P.022 ty Notes Ask Your The lift is performed in throc stag

Question

4. 1 points HRIW10 7.P.022 ty Notes Ask Your The lift is performed in throc stages, A cwc escuc toam lifts an i ] rod spelunker drectly upward and out of ?5inkhole by means of motor driven cabl . cach equ ring a verticol distance of 11.6 m, 1 First, the nit ally stationary spclunker is accclerated to o spocd of 5,20 rnys. (2) He is then lifted at the constant speed of 3.20 m/s. (3) Finally he is decclcrated to zero spced. How much work is done on the 90.0 kg rescuce by the force lifting him during cach stoga? stage (I) stage (2) stage (3) kl kl Additional Materials Ll Sertinn 73

Explanation / Answer

We use d to denote the magnitude of the spelunker’s displacement during each stage. The
mass of the spelunker is
m = 90.0 kg. The work done by the lifting force is denoted Wi
where i = 1, 2, 3 for the three stages. We apply the work-energy theorem, Kf-Ki=Wa+Wg

(a) for stage 1, W1 - mgd = ?K1 = 1/2 mv^2 where v1 = 5.20m/s this gives

W1 = mgd + 1/2*mv^2 = (90.0kg)*(9.81)*(11.6m)+1/2*(90)(5.20)^2 = 11458 = 11.458KJ

(b) For stage 2, W2 - mgd = ?K2 = 0 which leads to

W2 = mgd = (90)(9.81)(11.6) = 10.24K J

(c) For stage 3 W3 - mgd = ?K3 = -1/2mv1^2 we obtain

W3 = mgd - 1/2mv1^2

= (90)(9.81)(11.6)-1/2(90)(5.20)^2 = 9.024KJ

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