Problem 6-11 Dynamics with friction - Part 5 - C

A child is sliding down a water slide inclined at \(25^\circ\) to the horizontal. The coefficient of kinetic friction between the child and the slide is \(0.10\). What is the magnitude of the acceleration of the child? (Hint: \(F_N\) is not equal to \(mg\).)

Accumulated Solution

FBD with all forces, directions and angles indicated.

\(f = \sum F_N = 0.888\;m\)

Correct!

\(\sum F_x = mg\; \sin \;25 - f = ma\)

Substituting the value of \(f\)

\(m(9.8) \sin 25 - 0.888\;m = ma \\ a = 3.3 \;m/s^2\)

(Notice that as in all cases where the forces derive solely from the force of gravity, the acceleration is independent of the mass as for free-falling objects.)

 

You have completed this problem.