Question

The figure below shows the same ideal spring in three different situations.
First, without a mass hanging, the spring is unstretched.
Next with the blue mass hanging, the spring stretches.
Finally, with the red mass hanging, the spring stretches twice as much as it did with blue mass.
How much energy does the hanging red mass store in the spring-mass system, compared to the amount of energy the hanging blue mass stores in the spring-mass system?

• A. The red mass stores twice as much energy as the blue mass
• B. The red mass stores fours times as much energy as the blue mass
• C. The red mass stores half as much energy as the blue mass
• D. The red mass stores about $1.4$ times as much energy as the blue mass
• E. We cannot determined how much energy the red mass stores compared to the blue mass, because we do not know the unstretched length of the spring

Answer 1

Answer: (B)

The red mass stores fours times as much energy as the blue mass

The energy stored in a spring-mass system is given by ,

$E=1/2k{x}^2$ ,

for blue mass system ,

$E_B=1/2k{x}_B^2$

for red mass system ,

$E_R=1/2k{x}_R^2$ ,

or $E_R=1/2k(2x_B{)}^2=4/2k{x}_B^2$ (because given $x_R=2x_B$)

now dividing $E_R$ by $E_B$ , we get

$E_R/E_B=4$

or $E_R=4E_B$