Problem 6-11 Dynamics with friction - Part 4 - 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.

Correct! \(\sum F_y = F_N - mg\; \cos \;25 = 0\)

Therefore \(F_N  = mg\; \cos \;25\) and \(f = \mu F_N  = (0.10)(m)(9.8) \cos \;25 = 0.888\;m\)

The correct expression in the \(x\)-direction is:

(A)   \(mg - f = ma\)

(B)   \(mg\; \cos \;25 - f = ma\)

(C)   \(mg\; \sin \;25 - f = ma\)