A 17 kg girl slides down a playground slide that is 2.7 m high. When she reaches the bottom of the slide, her speed is 1.3 m/s. What is the coefficient of friction? Use energy theorem

Answer 1

Potential energy at start = m g h
Kinetic energy at finish = (1/2) m v^2

energy turned into heat = mgh - (1/2) m v^2
that is friction force times distance down slide
if angle of inclination of slide it T
distance down slide = h/sin T
normal force on slide = m g sin T
friction force = mu m g sin T
so energy to friction = mu m g sin T * h/sin T = mu m g h (remarkable)
so
mu m g h = m g h - (1/2) m v^2
note that m does not matter :)