define potential energy. write the expression potential energy of a spring. plote a graph
Answers
Explanation:
An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational-potential energy. This gravitational-potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.
An object of mass m, when raised through a height h from the ground, then work done by this object will be
W = force x displacement = mg x h = mgh k
The characteristic of a spring is that the force needed to stretch or compress a spring by an amount x is equal to k x and is in the direction opposite to the extension or compression. Here k is called the spring constant.
Restoration Force of the spring (compression or tensile) Fs = - k x = - external force F
Work done by the external force in compressing the spring from x = 0 to x = L can be obtained by:
\begin{gathered}W = \int\limits^L_0 {F .} \, ds = \int\limits^L_0 {( k x)} \, dx,\ \ \ \ as\ displacement\ s= x\\ \\ W = k\int\limits^L_0 {x} \, dx = \frac{1}{2}k [x^2 ]_0^L = \frac{1}{2}k\ L^2 =\frac{1}{2}k x^2\\\end{gathered}
W=
0
∫
L
F.ds=
0
∫
L
(kx)dx, as displacement s=x
W=k
0
∫
L
xdx=
2
1
k[x
2
]
0
L
=
2
1
k L
2
=
2
1
kx
2
is the energy given by the external force to the spring with an extension x.
This energy is stored as potential energy in the spring.