   Chapter 4, Problem 44P

Chapter
Section
Textbook Problem

A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 80.0 N at an angle of 25.0° above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and floor is 0.300. (a) Find the acceleration of the box. (b) The student now starts moving the box up a 10.0° incline, keeping her 80.0 N force directed at 25.0° above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?

(a)

To determine
The acceleration of the box.

Explanation

Given Info: The force with which the box is pulled is 80.0 N. Angle of inclination is 25ο . Mass of the box is 25.0 kg. The co-efficient of kinetic friction ( μk ) is 0.300.

The free body diagram is given below.

From the above diagram,

N=mgFsin25ο (I)

Fcos25οFk=ma (II)

• Fk is the friction force.
• N is the normal force.
• g is the acceleration due to gravity.
• a is the acceleration.
• m is the mass of the box.

The friction force is expressed as,

Fk=μkN (III)

From equation (I), (II) and (III), the formula for acceleration is,

a=Fm(cos25ο+μksin25ο)μkg

Substitute 80 N for F, 25

(b)

To determine
The new acceleration of the box.

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