Answer to Question #238185 in Molecular Physics | Thermodynamics for Kelani

Question

A student of mass 59.4 kg, starting at rest, slides down a slide 24.2 m long, tilted at an angle of 20.1° with respect to the horizontal. If the coefficient of kinetic friction between the student and the slide is 0.108, find the force of kinetic friction, the acceleration, and the speed she is traveling when she reaches the bottom of the slide. (Enter the magnitudes.)

(a) the force of kinetic friction (in N) __ N

(b) the acceleration (in m/s²) ___m/s²

(c) the speed she is traveling (in m/s) ___ m/s

Answer 1

(a) The force of kinetic friction is

$$f=\mu N,\\ N=mg\cos\theta,\\ f=\mu mg\cos\theta=59\text{ N}.$$

(b) The acceleration is

$$a=\frac{F_\text{net}}{m}=\frac{mg\sin\theta-f}{m}=g\sin\theta-\frac fm=2.37\text{ m/s}^2.$$

(c) The speed at the bottom is

$$v=\sqrt{2ad}=10.7\text{ m/s}.$$