Class 11 Physics Work Energy Power Potential energy of spring

Potential energy of spring

• The spring force is an example of a variable force, which is conservative.
• In an ideal spring, Fs = − kx , this force law for the spring is called Hooke’s law.
• The constant k is called the spring constant. Its unit is N m-1.
• The spring is said to be stiff if k is large and soft if k is small.
•  • Spring force is position dependent as first stated by Hooke, (Fs = − kx)
• Work done by spring force only depends on the initial and final positions. Thus, the spring force is a conservative force.
• We define the potential energy V(x) of the spring to be zero when block and spring system is in the equilibrium position.
• For an extension (or compression) x,  V(x) = kx2/2

If the block of mass m is extended to xm and released from rest, then its total mechanical energy at any arbitrary point x (where x lies between – xm and + xm) will be given by:    Example:  A car of mass M travelling with speed v, collides with a spring, having spring constant k. The car comes to rest (momentarily) when spring is compressed to a distance of xm . Find xm .