Question

The energy stored in a stretched spring is \[36J\] and spring constant \[800N{m^{ - 1}}\], then the elongation in the spring is_____
A) \[300m\]
B) \[300cm\]
C) \[3cm\]
D) \[30cm\]

Answer 1

Hint : The potential energy stored in a spring (or any similar object) is known as the elastic potential energy. We can use the elastic potential energy of the spring to find the elongation in the spring. We can use the concept that the amount of an applied force is always directly proportional to the amount of stretch caused by the applied force.

Complete Step by step solution:
When a force is applied to an element, we know that it is pulling or compressing in response to the applied force. In mechanics, the force applied to the unit field is known as stress and is represented by the symbol by. The amount of material that is compressed or expanded is known as stress. Different materials respond differently to the applied pressure.
For certain springs, the amount of force is directly proportional to the amount of stretch or we can write
Potential energy\[ = \dfrac{1}{2}k{x^2}\]
Putting the values in the above equation.
\[
  36 = \dfrac{1}{2} \times 800 \times {x^2}
   \Rightarrow 36 = 400 \times {x^2}
   \Rightarrow {x^2} = 0.09m
   \Rightarrow x = 0.3m
   \Rightarrow x = 30cm
 \]

Thus, option D is correct
Hence, the elongation in the spring is $30cm$.

Additional information:
Elastic potential energy is the energy savings resulting from stretch or compression in an elastic material. Elastic potential energy can be stored in rubber bands, bungee cords, trampolines, springs, arrows drawn in bows, etc.
Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching. A force is required to compress a spring; the more compression there is, the more force that is required to compress it further.
Compression/Extension in spring is $x$ and the constant of proportionality is known as the spring constant $k$.
$F$ spring = $k \times x$
$x$ is positive if there is compression, and $x$ is negative if there is extension.

Such springs are said to follow Hooke's Law.
Hooke’s law states that the strain of the material is proportional to the applied stress within the elastic limit of that material.

Note- An object can store energy as a result of its position. For example, a demolition machine saves a lot of energy when it is placed in a high position. This stored energy of position is known as potential energy. Similarly, a drawn bow is able to store energy as a result of its position. The bow does not store any energy while operating its normal position (e.g., when not drawn).
Yet when its position changes from its normal state of equilibrium, the bow is able to store energy due to its position. This stored energy of position is known as potential energy. Potential energy is the stored energy of a position held by an object