   Chapter 15, Problem 14P

Chapter
Section
Textbook Problem

Two identical metal blocks resting on a frictionless horizontal surface are connected by a light metal spring having constant k = 100 N/m and unstretched length Li = 0.400 m as in Figure P15.14a. A charge Q is slowly placed on each block causing the spring to stretch to an equilibrium length L = 0.500 m as in Figure P15.14b. Determine the value of Q, modeling the blocks as charged particles. To determine
The value of Q.

Explanation

Given info: The spring constant (x) is 100 N/m. The unstretched length ( Li ) is 0.400m. The equilibrium length (L) is 0.500 m.

Formula to calculate the spring force is,

F=k(LLi) (I)

• k is the spring constant.

From Coulomb’s Law,

F=keQ2L2 (II)

• ke is the Coulomb constant.
• Q is the charge.

The spring force equals the Coulomb force at equilibrium.

From Equations (I) and (II)

k(LLi)=keQ2L2

On Re-arranging,

Q=Lk(LLi)ke

Substitute 8

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