A spring is kept horizontal by attaching it to points A and B, as shown in the figure.
Point A is on a movable slider and point B is on a fixed support. A cart of mass 
has horizontal velocity 
towards the slider. The cart collides with the slider. The spring is compressed as the cart comes to rest. The variation of compression 
of the spring with force 
exerted on the spring is shown in the figure below.
The figure above shows the compression of the spring for 
to 
. The cart comes to rest when is 
.
Use the figure above to
show that the compression of the spring obeys Hooke’s law,
determine the spring constant of the spring,
determine the elastic potential energy 
stored in the spring due to the cart being brought to rest.
is the same for two different sets of co-ordinates.
.
.
