A 55-kg teenager at a water park slides down a long, winding waterslide of varyi

Question

A 55-kg teenager at a water park slides down a long, winding waterslide of varying slope. The slide has a height difference of 17 m (roughly four stories) from start to finish. The teenager takes a running start, launching himself with an initial speed of 3.5 m/s. If the slide were frictionless, find both the teenager's kinetic energy and speed at the end (bottom) of the slide. Suppose that, despite all the attempts to minimize friction with rushing water, there still remains substantial friction between the teenager and the slide, and he arrives at the end of the slide with a speed of 6.5 m/s instead of the speed you found above in part (a). What percentage of the teenager's initial mechanical energy was dissipated by friction on his way down? Assume zero gravitational potential energy at the bottom of the slide.

Explanation / Answer

mass = 55 kg

initial speed = u = 3.5 m/s

height = h = 17 m

a) Applying conservation of energy

0.5 m u^2 + m g h = 0.5 m v^2

Therefore, v = sqrt( u^2 + 2 g h ) = sqrt( 3.5^2 + 2 * 9.81 * 17 ) = 18.59 m/s

kinetic energy = 0.5 m u^2 + m g h = 0.5 * 55 * 3.5^2 + 55 * 9.81 * 17 = 9509.22 J

speed = 18.59 m/s

b) If final speed = v = 6.5 m/s

Energy lost in friction = 0.5 * 55 * ( 18.59^2 - 6.5^2 ) = 8341.79 J

percentage of initial mechanical energy dissipated as friction = 8341.79 * 100 / 9509.22 = 87.72 %

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