Show all work and explain please A 50.-kg teenager at a water park slides down a
ID: 1553421 • Letter: S
Question
Show all work and explain please
A 50.-kg teenager at a water park slides down a long, winding waterslide of varying slope. The slide has a height difference of 20. m (roughly five stories) from start to finish. The teenager takes a running start, launching himself with an initial speed of 4.0 m/s. a. If the slide were frictionless, find both the teenager's kinetic energy and speed at the end (bottom) of the slide. Show your work completely. 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 7.5 m/s instead of the speed you found above in part (a). b. 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. Show your work completely. Thought questions [not for credit]: Do any of the above final answers depend on the steepness or shape of the slide? Which of the answers would be the same for the case of a sheer drop - if the teenager simply freefalls straight down? Do any of the above final answers depend on the teenager's mass? How so?Explanation / Answer
a) Use energy conservation
Energy on the top= energy at the bottom
(Kinetic + Gravitational PE)top= (KE+GPE)bottom
0.5*50*4^2+50*g*20= KE
KE at the bottom= 10200 J
10200=0.5*50*v^2
v=20.2 m/s
b) Velocity at the bottom is 7.5 m/s so KE at the bottom= 0.5*50*7.5^2= 1406.25 J
Loss= 10200-1406.25=8793.75 J
So fractional loss= 8793.75/10200 = 0.86 or 86 % is lost
For last parts
Steepness doesn't matter ,all these depend on the vertical height, Loss may change if length is longer so loss may depend on the Steepness so b answer will change if steepness or shape is different
Only KE at the bottom depends on the mass, otherwise mass is common everywhere so gets cancelled .