# Helical Spring Experiment (Class 11) Readings

**Helical Spring Experiment with Readings (Class 11)**

**Experiment - 1**

**Aim:** To find the spring constant k of a helical
spring by measuring time period of vertical oscillations of a known load.

**Apparatus:** A helical spring, a rigid support, metre
scale, weight hanger, a set of equal weights (20 g or 50 gm slotted weights), a
fine pointer, stop watch, etc.

**Procedure:** The helical spring is balanced vertically
from a rigid support. The pointer is attached horizontally at the free end of
the spring. A 20 g (or 50 g) weight hanger is suspended from the hook at the
free end of the spring. The weight m of the hanger should be enough to keep the
spring vertical and stretched. Now the load M at the end of the spring is lm.
The metre scale is set aside vertically such that its tip of the pointer comes
over the divisions on the scale; also confirm that it is not touched the scale.
The weight hanger is pulled a bit downwards and left free. The load moves up
and down executing vertical oscillations. Time t for, say; 20 oscillations is
determined. From this, the period of oscillations, T = t/20, of the spring is
calculated. Then (M/T^{2}) is calculated.

A slotted weight of mass m is placed on the weight hanger.
Now the load M at the end of the spring is 2m. As before, (M/T^{2}) is
calculated. The experiment is repeated for the load M equals to 3m, 4m, etc.
The average value of (M/T^{2}) is determined. The spring constant k is
calculated from the equation,

k = 4π^{2}(M/T^{2})

The spring constant can also be calculated graphically as mentioned
below. A graph is plotted with load M (1m, 2m, 3m, etc.) in kg along the X-axis
and T^{2} along the Y-axis. The graph is a straight line. The
reciprocal of the slope of the graph i.e., (M/T^{2}) is determined. The
spring constant of the spiral spring is calculated from the equation, k = 4π^{2}(M/T^{2})

**Observations and Readings**

**To find k by Vertical Oscillations,**

Slotted weight, m = 20 gwt

Load M x 10 |
Time for 20 Oscillations |
Period, T(s), t/20 |
T |
M/T |
||

1 |
2 |
Mean t(s) |
||||

30 x 10 |
13 |
12 |
12.5 |
0.62 |
0.38 |
0.078 |

40 x 10 |
14 |
14 |
14 |
0.7 |
0.49 |
0.081 |

50 x 10 |
15 |
15 |
15 |
0.75 |
0.56 |
0.089 |

60 x 10 |
15 |
15 |
15 |
0.75 |
0.56 |
0.107 |

70 x 10 |
16 |
16 |
16 |
0.8 |
0.64 |
0.109 |

Mean (M/T^{2}) = 0.092 kg/s^{2}

K = 4π^{2}(M/T^{2}) = 3.86 Nm^{-1}

**From the graph,**

AB = 27.5 x 10^{-2}; BC = 0.30

Therefore, M/T^{2} = AB/BC = 0.092

K = 4π^{2}(M/T^{2}) = 3.62 Nm^{-1}

Mean K = 3.62 Nm^{-1}

**Result **

Spring constant, k, by vertical oscillations = 3.62 Nm^{-1}

**Experiment 2:**

**Aim:** To find the spring constant k of a helical
spring from load-extension graph.

**Observations and Readings:**

Reading of the pointer for the dead load W_{0} m

(i) Loading = 24.7 cm

(ii) Unloading = 24.7 cm

Mean r_{0} = 24.7 cm

Load, M x 10 |
Reading of the pointer |
Extension e (cm) |
Extension e (m) |
M/e = K (Kg/m) |
||

Loading |
Unloading |
Mean |
||||

10 x 10 |
23.7 |
23.7 |
23.7 |
1 |
1 x 10 |
10 x 10 |

20 x 10 |
22.6 |
22.6 |
22.6 |
2.1 |
2.1 x 10 |
9.52 x 10 |

30 x 10 |
21.6 |
21.6 |
21.6 |
3.1 |
3.1 x 10 |
9.57 x 10 |

40 x 10 |
20.8 |
20.8 |
20.8 |
3.9 |
3.9 x 10 |
10.25 x 10 |

50 x 10 |
19.7 |
19.7 |
19.7 |
5 |
5 x 10 |
10 x 10 |

60 x 10 |
18.6 |
18.6 |
18.6 |
6.1 |
6.1 x 10 |
9.83 x 10 |

70 x 10 |
17.5 |
17.5 |
17.5 |
7.2 |
7.2 x 10 |
9.72 x 10 |

**a) Spring Constant K**

by Calculation,

K = (M/e) = 0.98 kgwt/m = 9.604 N/m^{-1}

**b) From the Graph,**

AB = 40 x 10^{-3} kgwt

BC = 0.040 m

K = AB/BC = 1 Kgwt m^{-1} = 1 x 9.8 = 9.8 Nm^{-1}

**Result**

Spring constant (a) by calculation = 9.604 N/m^{-1}

(b) k, from load-extension graph = 9.8 Nm^{-1}

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