The work done in stretching a spring of force constant from length and is
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A spring of spring constant is stretched initially by from the unstretched position. Then the work required to stretch it further by another is
.
A spring whose unstretched length is has a force constant . The spring is cut into two pieces of unstretched lengths and where, and is an integer. The ratio of the corresponding force constants, and will be:
and
As
The ....... energy of the spring is said to be zero when block and spring system is in the ... Y... position.
Here, and refer to
potential, equilibrium
mechanical, equilibrium
kinetic, equilibrium
vibrational, left
We define the potential energy of the spring to be zero when block and spring system is in the equilibrium position.
If stretch in a spring of force constant is tripled then the ratio of elastic potential energy in the two cases will be
For a given spring,
A particle is placed at the origin and a force is acting on it (where is positive constant). If , the graph of versus will be (where is the potential energy function) :
. It is correctly drawn in (a)
A mass of moving with a speed of on a horizontal smooth surface, collides with a nearly weightless spring of force constant . If the maximum compression of the spring is , the value of mass is
or
Two spring and of force constant and are stretched by applying forces of equal magnitude. If the energy stored in is , then the energy stored in is
Two springs have their force constant as and . When they are stretched by the same force
no work is done in case of both the springs.
equal work is done in case of both the springs
more work is done in case of second spring
more work is done in case of first spring.
From Hooke's law
., where is spring constant
Since force is same in stretching for both spring so
because
so work done in case of first spring is and work done in case of second spring is
so
It means that more work is done in case of second spring (work done on spring is equal to stored elastic potential energy of the spring)
One end of a light spring of spring constant is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work done by the spring is . The possible cases are
the spring was initially compressed by a distance , was finally in its natural length
it was initially stretched by a distance and was finally in its natural length
it was initially in its natural length and finally in a compressed position
it was initially in its natural length and finally in the stretched position
Stored elastic potential energy of spring . where is compression or elongation of spring from its natural length. In this position the spring can do work on the block tied to it, which is equal to , so both option (a) are correct.
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