Use the worked example above to help you solve this problem. Waterslides are nea

Question

Use the worked example above to help you solve this problem. Waterslides are nearly frictionless, hence can provide bored students with high-speed thrills (see the figure). One such slide, Der Stuka, named for the terrifying German dive bombers of World War II, is 72.0 feet high (21.9 m), found at Six Flags in Dallas, Texas, and at Wet'n Wild in Orlando, Florida. (a) Determine the speed of a 61.6-kg woman at the bottom of such a slide, assuming no friction is present. (Assume her initial speed vi = 0,) m/s (b) If the woman is clocked at 17.6 m/s at the bottom of the slide, find the work done on the woman by friction. EXERCISE HINTS: GETTING STARTED I I'M STUCK! Suppose a slide similar to Der Stuka is 35.8 meters high, but is a straight slope, inclined at 45.0 with respect to the horizontal. (a) Find the speed of a 61.6-kg woman at the bottom of the slide, assuming no friction. (Enter your answer to at least one decimal place.) m/s (b) If the woman has a speed of 22.8 m/s at the bottom, find the change in mechanical energy due to friction. (c) Find the magnitude of the force of friction, assumed constant.

Explanation / Answer

(A) Applying work - energy theorem,

total work done= change in KE

work done by gravity + work done by normal = Kf - Ki

m g h + 0 = m v^2 /2 - 0

v = sqrt(2 x 9.8 x 21.9) = 20.7 m/s .....Ans

(B) Work done by gravity + work doneby friction = Kf - Ki

(61.6 x 9.8 x 21.9) + W = (61.6 x 17.6^2 / 2) - 0

W = - 3680 J ...Ans

EXERCISE:

(A) v = sqrt(2 g h) = 26.5 m/s

(B) (61.6 x9.8 x 35.8) + W = (61.6 x 22.8^2 / 2) - 0

W = - 5600 J  

change in thermal energy = 5600 J

(C) W = - f.d

d = h/sin45 = 35.8 / sin45 = 50.63 m

-5600 = f(50.63 )

f = 110.6 N

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