**Problem Statement:**A veterinarian uses a spring scale to weigh a cat. He records the cat's weight as 2 kilograms and notices the spring stretches 4 centimeters.Which expression represents the spring constant? \( (1 \, \text{kg} = 9.8 \, \text{N}) \)**Options:**- ⭘ \( \dfrac{-19.6 \, \text{N}}{4} \)- ⭘ \( \dfrac{-4 \, \text{cm}}{k} \)- ⭘ \( \dfrac{-4}{19.6 \, \text{N}} \)- ⭘ \( \dfrac{-4 \, k}{\text{cm}} \)**Explanation:**From the given information, we know:- Weight (\( F \)): 2 kg, which converts to \( 19.6 \, \text{N} \) (using \( 1 \, \text{kg} = 9.8 \, \text{N} \))- Extension of the spring (\( x \)): 4 cmHooke's Law for spring constant ( \( k \) ) is given by the formula:\[ F = -kx \]Rearranging this formula to solve for \( k \):\[ k = -\dfrac{F}{x} \]Substitute the given values:\[ k = -\dfrac{19.6 \, \text{N}}{4 \, \text{cm}} \]Thus, the correct representation of the spring constant \( k \) is:\( \dfrac{-19.6 \, \text{N}}{4} \).

Here Weigh of cat = W = 2 × 9.8 N = 19.6 N Elongation in spring = x = 4cmWe have to find the correct…

A veterinarian uses a spring scale to weigh a cat. He records the cat's weight as 2 kilograms and notices the spring stretches 4 centimeters. Which expression represents the spring constant? (1 kg = 9.8 N) O -19.6 N/4 O -4 cm/k O-4/19.6 N -4 k/cm

A veterinarian uses a spring scale to weigh a cat. He records the cat's weight as 2 kilograms and notices the spring stretches 4 centimeters. Which expression represents the spring constant? (1 kg = 9.8 N) O -19.6 N/4 O -4 cm/k O-4/19.6 N -4 k/cm

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

**Problem Statement:**

A veterinarian uses a spring scale to weigh a cat. He records the cat's weight as 2 kilograms and notices the spring stretches 4 centimeters.

Which expression represents the spring constant? \( (1 \, \text{kg} = 9.8 \, \text{N}) \)

**Options:**

- ⭘ \( \dfrac{-19.6 \, \text{N}}{4} \)
- ⭘ \( \dfrac{-4 \, \text{cm}}{k} \)
- ⭘ \( \dfrac{-4}{19.6 \, \text{N}} \)
- ⭘ \( \dfrac{-4 \, k}{\text{cm}} \)

**Explanation:**

From the given information, we know:
- Weight (\( F \)): 2 kg, which converts to \( 19.6 \, \text{N} \) (using \( 1 \, \text{kg} = 9.8 \, \text{N} \))
- Extension of the spring (\( x \)): 4 cm

Hooke's Law for spring constant ( \( k \) ) is given by the formula:
\[ F = -kx \]

Rearranging this formula to solve for \( k \):
\[ k = -\dfrac{F}{x} \]

Substitute the given values:
\[ k = -\dfrac{19.6 \, \text{N}}{4 \, \text{cm}} \]

Thus, the correct representation of the spring constant \( k \) is:
\( \dfrac{-19.6 \, \text{N}}{4} \).

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