   Chapter 13, Problem 67AP

Chapter
Section
Textbook Problem

A 3.00-kg object is fastened to a light spring, with the intervening cord passing over a pulley (Fig. P13.67). The pulley is frictionless, and its inertia may be neglected. The object is released from rest when the spring is unstretchcd. If the object drops 10.0 cm before stopping, find (a) the spring constant of the spring and (b) the speed of the object when it is 5.00 cm below its starting point. Figure P13.67

(a)

To determine
The spring constant of the spring.

Explanation

Given info: The mass of the object is 3.00kg . The object drops 10.0cm before stopping.

The conservation of mechanical energy,

(KE+PEg+PEs)f=(KE+PEg+PEs)i (1)

• KE is the kinetic energy
• PEg is the gravitational potential energy
• PEs is the elastic potential energy

Consider the initial state to be when the object is in its initial state of rest and the spring is un-stretched. Choose PEg to be zero at that position. Hence the initial total energy will be zero.

(KE+PEg+PEs)i=0 (2)

Consider the final state when the object is in its final state of rest and the object has dropped 10.0cm ,

(KE+PEg+PEs)f=0+mg(10.0cm)+12k(10.0cm)2 (3)

From (1), (2) and (3),

0+mg(10

(b)

To determine
The speed of the object when it is 5.00cm below its starting point.

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