Problem 7.48 A 27.0kg child plays on a swing having support ropes that are 220m

Question

Problem 7.48 A 27.0kg child plays on a swing having support ropes that are 220m long. A friend pulls her back until the ropes are 45.0 degree from the vertical and releases her from rest. art A What is the potential energy for the child just as she is released, compared with the potential energy at the bottom of the swing? art B How fast will she be moving at the bottom of the swing? art C How much work does the tension in the ropes do as the child swings from the initial position to the bottom?

Explanation / Answer

part A)

height should be h-hcostheta

PE = mg(h-hcostheta)

PE = 27*9.8(2.2-2.2cos45)

PE = 170.5 J

Part B )

at bottom all PE convert into KE

KE = 170.5 J

KE = 1/2mv^2

v = sqrt(2KE/m)

v = 3.55 m/s

Part C)

Work is Zero

W = F.d

rope displacement remain constant

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