(D) Given: Natural length $L_0 = 10 \ cm$,extension $x_1 = 2 \ cm = 0.02 \ m$,mass $m = 20 \ g = 0.02 \ kg$,$g = 10 \ m/s^2$.At equilibrium,the spring

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(D) Given: Natural length $L_0 = 10 \ cm$,extension $x_1 = 2 \ cm = 0.02 \ m$,mass $m = 20 \ g = 0.02 \ kg$,$g = 10 \ m/s^2$.At equilibrium,the spring force equals the gravitational force: $k x_1 = mg$.$k(0.02) = 0.02 \times 10 \implies k = 10 \ N/m$.The total length becomes $14 \ cm$,so the new extension is $x_2 = 14 \ cm - 10 \ cm = 4 \ cm = 0.04 \ m$.The elastic potential energy stored in the spring is given by $U = \frac{1}{2} k x_2^2$.$U = \frac{1}{2} \times 10 \times (0.04)^2 = 5 \times 0.0016 = 0.008 \ J = 8 \times 10^{-3} \ J$.

Class 11 Physics Work, Energy, Power and Collision Work Done by Spring and Potential Energy of Spring

Medium

$A$ light spring of length $10 \ cm$ is stretched by $2 \ cm$ when a mass of $20 \ g$ is attached to its end. The mass is pulled until the total length of the spring becomes $14 \ cm$. What is the elastic potential energy stored in the spring (in Joules)?

A
$4 \times 10^{-2}$
B
$4 \times 10^{-3}$
C
$8 \times 10^{-2}$
D
$8 \times 10^{-3}$

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Work, Energy, Power and Collision

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Work Done by Spring and Potential Energy of Spring

Two springs with spring constants $K_1 = 1500 \, N/m$ and $K_2 = 3000 \, N/m$ are stretched by the same force. The ratio of potential energy stored in the springs will be

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$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

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When a spring is stretched by $2 \ cm$,the potential energy stored is $U$. If it is stretched by $10 \ cm$,the potential energy stored will be:

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$A$ block of mass $m=25 \ kg$ sliding on a smooth horizontal surface with a velocity $v=3 \ ms^{-1}$ meets a spring of spring constant $k=100 \ N/m$ fixed at one end as shown in the figure. The maximum compression of the spring and the velocity of the block as it returns to the original position are, respectively:

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Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force $F$,which of the following statements is true regarding the work done?

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$A$ light spring of length $10 \ cm$ is stretched by $2 \ cm$ when a mass of $20 \ g$ is attached to its end. The mass is pulled until the total length of the spring becomes $14 \ cm$. What is the elastic potential energy stored in the spring (in Joules)?

Similar Questions

Two springs with spring constants $K_1 = 1500 \, N/m$ and $K_2 = 3000 \, N/m$ are stretched by the same force. The ratio of potential energy stored in the springs will be

$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

When a spring is stretched by $2 \ cm$,the potential energy stored is $U$. If it is stretched by $10 \ cm$,the potential energy stored will be:

Two springs have their force constants as $k_1$ and $k_2$ $(k_1 > k_2)$. When they are stretched by the same force $F$,which of the following statements is true regarding the work done?

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