Two springs P and Q are identical except that P is stiffer than Q. If they are stretched by the

Name: Problem 99, Chapter 1: IIT JEE Super Course in Physics: Mechanics II
Uploaded: 2021-06-11T02:21:08-08:00
Duration: 2 min 16 s
Channel: Suman Saurav Thakur
Description: Two springs P and Q are identical except that P is stiffer than Q. If they are stretched by the same amount and Wp and WQ represent the work expended on the springs then (a) Wp>WQ

step 1 we have problem 99 in which there are two springs p and q two springs p and q this is p this is

Question

Two springs $\mathrm{P}$ and $\mathrm{Q}$ are identical except that $\mathrm{P}$ is stiffer than $\mathrm{Q}$. If they are stretched by the same amount and $\mathrm{W}_{\mathrm{p}}$ and $\mathrm{W}_{\mathrm{Q}}$ represent the work expended on the springs then (a) $\mathrm{W}_{\mathrm{p}}>\mathrm{W}_{\mathrm{Q}}$

   Two springs $\mathrm{P}$ and $\mathrm{Q}$ are identical except that $\mathrm{P}$ is stiffer than $\mathrm{Q}$. If they are stretched by the same amount and $\mathrm{W}_{\mathrm{p}}$ and
$\mathrm{W}_{\mathrm{Q}}$ represent the work expended on the springs then
(a) $\mathrm{W}_{\mathrm{p}}>\mathrm{W}_{\mathrm{Q}}$

IIT JEE Super Course in Physics: Mechanics II

Trishna Knowledge… 1st Edition

Chapter 1, Problem 99

Instant Answer

Solved by Expert Suman Saurav Thakur

06/11/2021

Step 1

They are identical except that P is stiffer than Q. This means that the spring constant of P (denoted as $K_P$) is greater than the spring constant of Q (denoted as $K_Q$). This is because the spring constant is directly proportional to the stiffness of the Show more…

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Two springs $\mathrm{P}$ and $\mathrm{Q}$ are identical except that $\mathrm{P}$ is stiffer than $\mathrm{Q}$. If they are stretched by the same amount and $\mathrm{W}_{\mathrm{p}}$ and $\mathrm{W}_{\mathrm{Q}}$ represent the work expended on the springs then (a) $\mathrm{W}_{\mathrm{p}}>\mathrm{W}_{\mathrm{Q}}$

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Key Concepts

Spring Constant

The spring constant is a measure of a spring's stiffness, indicating how much force is needed to produce a unit change in its length. A larger spring constant means that the spring is stiffer and requires more force to achieve the same displacement as a spring with a smaller constant.

Hooke's Law

Hooke's law relates the force exerted by a spring to its displacement from equilibrium, typically stated as F = kx. This law is fundamental in describing the linear elastic behavior of springs within their elastic limit.

Elastic Potential Energy

Elastic potential energy is the energy stored in a deformed spring, calculated using the formula U = 1/2 k x^2. This expression shows that the energy stored in a spring increases with both the stiffness of the spring (k) and the square of the displacement (x), which is key to understanding the work done in stretching different springs.

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