Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problema 39

Capitolo 22, Problema 39

A 3.00-cm-long spring has a small plastic bead glued to each end. Charging each bead to −25 nC expands the spring by 0.50 cm. What is the value of the spring constant?

Guida verificata passo dopo passo

Step 1: Identify the forces acting on the spring. The spring is stretched due to the electrostatic repulsion between the two charged beads. The force due to the charges is given by Coulomb's law:

F = \frac{(k) (q_{1} q_{2})}{r^{2}}

, where

k

is Coulomb's constant,

q_{1}

and

q_{2}

are the charges, and

r

is the distance between the charges.

Step 2: Write the expression for the spring force using Hooke's law:

F = k x_{spring}

, where

k

is the spring constant and

x_{spring}

is the extension of the spring (0.50 cm or 0.005 m).

Step 3: Set the magnitudes of the forces equal to each other because the system is in equilibrium:

\frac{(k) (q_{1} q_{2})}{r^{2}} = k x_{spring}

. Substitute the known values:

q_{1} = q_{2} = - 25 nC

(convert to Coulombs:

- 25 \times 10^{- 9}

C),

r = 3.50 cm

(convert to meters:

0.035

m), and

x_{spring} = 0.005

Step 4: Rearrange the equation to solve for the spring constant

k

k = \frac{(k) (q_{1} q_{2})}{r^{2} x_{spring}}

. Substitute the numerical values for Coulomb's constant

k = 8.99 \times 10^{9}

N·m²/C², the charges, the distance, and the spring extension.

Step 5: Perform the calculation to find the spring constant

k

. Ensure all units are consistent (Coulombs, meters, and Newtons) and simplify the expression to determine the value of the spring constant.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Hooke's Law

Hooke's Law states that the force exerted by a spring is directly proportional to its extension or compression from its equilibrium position, mathematically expressed as F = -kx, where F is the force, k is the spring constant, and x is the displacement. This principle is fundamental for understanding how springs behave under applied forces.

Video consigliato:

Percorso guidato

05:27

Spring Force (Hooke's Law)

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects, stating that the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the force acting on the beads due to their charges, which in turn affects the spring's extension.

Video consigliato:

Percorso guidato

09:52

Coulomb's Law

Spring Constant

The spring constant, denoted as k, is a measure of a spring's stiffness, indicating how much force is needed to stretch or compress the spring by a unit length. A higher spring constant means a stiffer spring that requires more force for the same displacement. It is a crucial parameter in both Hooke's Law and the analysis of spring systems.

Video consigliato:

Percorso guidato

08:59

Phase Constant of a Wave Function

Pratica correlata

Domanda del libro di testo

A 0.10 g honeybee acquires a charge of +23 pC while flying. What electric field (strength and direction) would allow the bee to hang suspended in the air?

1671

views

Domanda del libro di testo

What is the force F on the 1.0 nC charge at the bottom in FIGURE P22.47? Give your answer in component form.

4732

views

rank

Domanda del libro di testo

Two 1.0 g spheres are charged equally and placed 2.0 cm apart. When released, they begin to accelerate at 150 m/s². What is the magnitude of the charge on each sphere?

1525

views

Domanda del libro di testo

What is the force F on the 8.0 nC charge in FIGURE P22.44? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x-axis.

2719

views

Domanda del libro di testo

Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. What is the charge on A?

1789

views

Domanda del libro di testo

A $negative 12 nC$ charge is located at $open paren x comma y close paren equals open paren 1.0 cm comma 0 cm close paren$ . What are the electric fields at the positions $(x, y) = (5.0 cm, 0 cm), (- 5.0 cm, 0 cm)$ , and $open paren 0 cm comma 5.0 cm close paren$ ? Write each electric field vector in component form.

2423

views