   Chapter 5, Problem 45P

Chapter
Section
Textbook Problem

# A 2.1 × 103-kg car starts from rest at the top of a 5.0-m-long driveway that is inclined at 20.0° with the horizontal. If an average friction force of 4.0 × 103 N impedes the motion, find the speed of the car at the bottom of the driveway.

To determine
The speed of the car at the bottom of the driveway.

Explanation

Given Info:

The mass of the car is 2.1×103kg .

The length of the driveway is 5.0m .

The inclination of the driveway with the horizontal is 20.0° .

The average frictional force is 4.0×103N .

Since the frictional force acting on the car is non-conservative force, the mechanical energy will not be conserved.

Since the frictional force is acting opposites to the speed of the car, the angle between them is 180.0° .

The work done by the non-conservative force is,

Wnc=(fcos180°)s      (I)

• f is the frictional force
• s is the length of the driveway

Using mechanical energy, the change in kinetic energy will be equal to the total work done by the non-conservative force.

Wnc=(KEf+PEg,f)(KEi+PEg,i)       (II)

Substitute equation (I) in (II),

(fcos180°)s=(KEf+PEg,f)(KEi+PEg,i)       (III)

Consider PEg is zero at the bottom of the driveway

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