Question

Spring A has a spring constant of 100 N/m and spring B has a spring constant of 200 N/m, and both have the same displacement of 0.20 m. The spring potential energy of spring A is _____ that of spring B.

Answer 1

Answer:

Explanation:

Given

Spring constant of spring A is $k_A=100\ N/m$

Spring constant of spring B is $k_B=200\ N/m$

If displacement in both the springs is $x=0.2\ m$

Potential Energy stored in the spring is given by

$U=\frac{1}{2}kx^2$

where k=spring constant

x=compression or extension

$U_A=\frac{1}{2}\times 100\times (0.2)^2----1$

$U_B=\frac{1}{2}\times 200\times (0.2)^2----2$

Divide 1 and 2

$\frac{U_B}{U_A}=\frac{200}{100}=2$

$U_A=\frac{U_B}{2}$

So Potential Energy Stored in Spring A is half of Spring B