Question

A spring is kept compressed by a small trolley of mass 0.5 kg lying on a smooth horizontal surface as shown in the below fig. When the trolley is released, it is found to move at a speed v= $2m{s^{ - 1}}$. What potential energy did the spring possess when compressed?

Answer 1

Hint: When the body is at rest after compressing the spring all the energy is stored in the form of potential energy and as soon as the trolley is released all of the potential energy will be converted into kinetic energy and the trolley will be moved by that energy.

Complete step by step answer:
When the trolley was kept at rest all the energy was stored in the form of kinetic potential energy and when the trolley is allowed to move all the potential energy stored in the spring will be converted into kinetic energy and the trolley will move
As the law of conservation of energy states that the energy can neither be created nor be destroyed only can be converted from one form to another hence here also the whole PE will be converted to kinetic energy
So, the potential energy will be equal to the kinetic energy of the trolley
As we know, \[K.E = \dfrac{1}{2}m{v^2}\]
Here mass the trolley (m) = 0.5kg
And the velocity of the trolley is given as \[v = 2m{s^{ - 1}}\]
Substituting the values, we get
$K.E = \dfrac{1}{2} \times 0.5 \times {2^2}$
$ \Rightarrow K.E = 1j$
Hence potential energy would also have been equal to 1 joule
Final answer: the amount of potential energy stored in the spring was 1 Joule.

Note:
-The whole P.E will be converted into K.E.
-The amount of energy will always remain the sum of K.E and potential energy at all positions except at the position when the trolley was held stationary at that position the K.E was zero.