Question

Two springs are identical except for their force constants, $k_{2}>k_{1}$. If the same force is used to stretch the springs, (a) spring 1 will be stretched farther than spring 2 (b) spring 2 will be stretched farther than spring 1 , (c) both will be stretched the same distance.

Name: Problem 17, Chapter 5: College Physics
Uploaded: 2021-05-08T23:21:29-08:00
Duration: 1 min 48 s
Channel: Sachin Rao
Description: Two springs are identical except for their force constants, k2>k1. If the same force is used to stretch the springs, (a) spring 1 will be stretched farther than spring 2 (b) spring 2 will be stretched farther than spring 1 , (c) both will be stretched the same distance.

   Two springs are identical except for their force constants, $k_{2}>k_{1}$. If the same force is used to stretch the springs,
(a) spring 1 will be stretched farther than spring 2
(b) spring 2 will be stretched farther than spring 1 ,
(c) both will be stretched the same distance.

College Physics

Jerry D. Wilson,… 7th Edition

Chapter 5, Problem 17

Instant Answer

Solved by Expert Sachin Rao

05/08/2021

Step 1

Mathematically, this is represented as $F=kx$, where $F$ is the force, $k$ is the spring constant, and $x$ is the distance the spring is stretched or compressed. Show more…

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Two springs are identical except for their force constants, $k_{2}>k_{1}$. If the same force is used to stretch the springs, (a) spring 1 will be stretched farther than spring 2 (b) spring 2 will be stretched farther than spring 1 , (c) both will be stretched the same distance.

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Key Concepts

Hooke's Law

Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement from its rest position, mathematically expressed as F = kx. This principle underlies the behavior of springs in mechanical systems, allowing for the determination of displacement when a force is applied, given the spring's force constant.

Force Constant (Spring Constant)

The force constant, denoted as k, quantifies a spring's stiffness. A higher force constant means the spring is stiffer and will stretch less under a given force, whereas a lower force constant means the spring is less stiff and will stretch more. This relationship directly impacts how different springs behave under equal applied forces.

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