   Chapter 11.3, Problem 60E

Chapter
Section
Textbook Problem

# Braking LoadA 5400-pound sport utility vehicle is parked on an 18° slope. Assume the only force to overcome is that due to gravity. Find (a) the force required to keep the vehicle from rolling down the hill and (b) the force perpendicular to the hill.

(a)

To determine

To calculate: The amount of force required to keep a 5400-pound sports utility vehicle on a 18° slope from rolling down the hill.

Explanation

Given:

A 5400-pound sports utility vehicle is parked on a 18° slope and the only force to overcome is that due to gravity.

Formula used:

The work W done by a constant force F as along the vector v is given by W=(Fvv2)v.

Calculation:

Gravitational force vector F=5400j.

The unit vector to the sports utility vehicle position can be written as;

v=cos(18°)i+sin(18°)j

To find the force to keep it from rolling down the hill, it is required to find the gravitational force component along the slope, or the component of F along v.

W=(Fvv2)v=(Fv)v=5400sin(18°)[sin(18°)i+sin(18°)j]=1668

(b)

To determine

To calculate: The amount of force perpendicular to the hill when a 5400-pound sports utility

vehicle on a 18° slope from rolling down the hill.

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