   Chapter 5, Problem 48P

Chapter
Section
Textbook Problem

In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 4.0 m/s up a 20.0° inclined track. The combined mass of monkey and sled is 20. kg, and the coefficient of kinetic friction between sled and incline is 0.20. How far up the incline do the monkey and sled move?

To determine
How far up the incline do the monkey and sled move.

Explanation

Given Info:

The combined mass of monkey and sled is 20.0kg .

Initial speed of the combined system is 4.0m/s .

The inclination of the track is 20.0° .

The coefficient of kinetic friction between the sled and the track is 0.20 .

Since the frictional force is a non-conservative force, the work done by the non-conservative force is,

Wnc=(KEf+PEg,f)(KEi+PEg,i)       (I)

The frictional force is,

fk=μkn       (II)

• μk is the coefficient of kinetic friction
• n is the normal force exerted don the sled

Since the normal force exerted on the shed is,

n=mgcosθ       (III)

Apply equation (III) in (II),

fk=μk(mgcosθ)

Suppose x is the length measured on the track that the sled travels,

From equation (I), for the entire trip

[μk(mgcosθ)cos180°]x=[0+mgx(sinθ

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