Experiment: Determination of Potential Energy of a Spring

Name of the experiment: Determination of potential energy of a spring

Theory: Let a weight of mass in be hanged at one end of a spring or the spring is expanded by an amount x due to application of force F. This displacement of the sprint is proportional to the applied force, i.e., F ∞ x

or, F = Kx [here, K = spring constant] … … … (1)

Now, work done by external force to expand the spring from position x₁ to x₂ is,

W = ^x2∫_x1 F dx

= ^x2∫_x1 Kx dx = K ^x2∫_x1 x dx

= K [x²/2]^x2_x1 = K/2 (x₂² – x₁²)

So, W = ½ K (x₂² – x₁²) … … … (2)

This work is positive work. This work remains in the spring as potential energy.

Let, x₁ = 0 and x₂ = x so,

W = ½ K (x² – 0)

or, W = ½ K x²

If a spring of mass m expands by ‘l’ and in this position if the spring is pulled by an amount x and released, then it executes simple harmonic motions. Its time period becomes, T = 2π √(m/K)

Apparatus:

(1) An experimental spring

(2) One metre scale

(3) Some suitable weights

(4) A hook to hang the spring

(5) A stop watch

Procedure

(1) The spring is to be hanged as per figure.

(2) At one end of the spring if a weight is hanged than the spring will be slightly elongated. Now unsure the distance between the stationary position and the changed position of the spring by a metre scale. This is gives the elongated length ‘l’.

(3) Then the weight is pulled downward by a distance x and released. Again, the expansion of length x is measured by the metre scale.

(4) The spring will continue moving ups and down. Time is recorded by a stop watch for 20 complete oscillations. Dividing this time by 20 time period T is to be measured.

(5) By changing weights the processes (3) and (4) are repeated for a few times.

Data Table- Table for the determination of T and x