Problem 1 - Obstacle Course. On an obstacle course a woman of mass 54 kg starts

Question

Problem 1 - Obstacle Course.
On an obstacle course a woman of mass 54 kg starts from ground level at point A, climbs 9 m up a scramble net, drops from the top B to a mat C, 3.6 m below B. and then runs up a bar to D at a height of 8 m above the ground, as shown in figure (1)

I - Compute her potential energy relative to the ground at A and D.

II - What was her gain in potential energy between A and B.

III - What was her loss in potential energy between B and C.

IV - Compute the gain in potential energy between C and D.

V - Using the answers to parts II, III and IV find the potential energy at D, and check that this agrees with your answer to part I

Explanation / Answer

Mass of Women = 54 kg Height = h a. Point A is at Ground level : Now Potential Energy at Point A = mgh = mg(0) = 0 Potential Energy at Point D (at height 8 meters) = mgh = 54 x 9.8 x 8 = 4233.6 J b. Gain in potential energy between A and B = mgh = 54 x 9.8 x 9 = 4762.8 J c. Loss in potential energy between B and C = mgh' = 54 x 9.8 x 3.6 = 1905.12 J d. Gain in potential energy between C and D = mgh = 54 x 9.8 x (8-5.4) = 1375.92 J e . Potential Energy at D = Potential Energy at B -Gain in Potential Energy between B and C + gain in potential energy between C and D = 4762.8 J - 1905.12 J + 1375.92 J = 4233.6 Joules which is the same as the potential energy we get in part (a) . Hence verified .

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