   Chapter 4, Problem 22P

Chapter
Section
Textbook Problem

A student of mass 60.0 kg, starting at rest, slides down a slide 20.0 m long, tilted at an angle of 30.0° with respect to the horizontal. If the coefficient of kinetic friction between the student and the slide is 0.120, find (a) the force of kinetic friction, (b) the acceleration, and (c) the speed she is traveling when she reaches the bottom of the slide.

(a)

To determine
The force of kinetic friction.

Explanation

Given Info: Length of the incline is 20 m. Mass of the student is 60.0 kg. Angle of inclination is 30ο . The co-efficient of kinetic friction is 0.120.

Formula for kinetic friction is,

Fk=μkN                                                       (I)

• μk is co-efficient of kinetic friction.
• N is the normal force.

The free body diagram is given below.

From the above diagram,

N=mgcosθ

• m is the mass of the student.
• g is the acceleration due to gravity.
• θ is the angle of inclination.

Substitute mgcosθ for N in Equation (I) to get the expression for Fk .

Fk=μkmgcosθ

Substitute 0

(b)

To determine
The acceleration of the student of mass 60 kg.

(c)

To determine
The speed of the student when she reaches the bottom.

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