You have been provided with a retort stand, clamp and boss, a set of masses, a spiral spring, stopwatch, split cork, and other necessary apparatus. Using the diagram above as a guide, carry out the following instructions;
(b)i. Define Young modulus and force constant.
ii. A force of magnitude 500N is applied to the free end of a spiral spring of force constant 1.0 x 10\(^{4}\) Nm\(^{-1}\). Calculate the energy stored in the stretched spring.
Table of values/observation
Number of oscillations (n) = 20
S/N | M(g) | t\(_{1}\)(s) | t\(_{2}\)(s) | t = \(\frac{t_{1}+t_{2}}{2(s)}\) | T = \(\frac{t}{n}\) | T\(^{2}\)(sec\(^{2}\)) | T\(^{2}\)(sec\(^{2}\))x10\(^{-3}\) |
1 | 50.0 | 5.80 | 5.80 | 5.80 | 0.290 | 0.084 | 84 |
2 | 70.0 | 6.70 | 6.90 | 6.80 | 0.340 | 0.116 | 116 |
3 | 90.0 | 7.70 | 7.90 | 7.80 | 0.395 | 0.156 | 156 |
4 | 110.0 | 8.50 | 8.70 | 8.60 | 0.430 | 0.185 | 185 |
5 | 130.0 | 9.20 | 9.20 | 9.20 | 0.460 | 0.212 | 212 |
(7)The graph of T\(^{2}\)(sec\(^{2}\)) Vs m(g) axis
Scale: T\(^{2}\)(sec\(^{2}\)) axis: 2cm = 20 units
m(g) axis: 2cm = 20 units
(8) Slope/gradient = \(\frac{\bigtriangleup {T}^{2}(sec^{2})}{\bigtriangleup {m(s)}}\)
\(\frac{234-10}{140-6} = \frac{224}{134}\)
= 1.672 sec\(^{2}\)/g
l on the vertical axis is (0)
(9) K = \(\frac{4\pi ^{2}}{s} = \frac{4 \times ({\frac{22}{7})^{2}}}{1.672}\)
= \(\frac{4 \times (22)^{2}}{7^{2} \times 1.672} = \frac{4 \times 484}{49 \times 1.672}\)
= \(\frac{1936}{81.928}\) = 23.61 g/sec\(^{2}\)
Precautions are:
(b)i. Young modulus is defined as the ratio of tensile or Compressive stress to tensile or compressive strain. It is denoted by E and measured in N/m\(^{2}\). Thus,
Young modulus = \(\frac{\text {tensile/compressive stress}}{\text{tensile/compressive strain}}\)
E = \(\frac{F/A}{e/L} =\frac{FL}{Ae}\)
Force constant is defined as the amount of force that causes a unit extension of an elastic material or the ratio of F/e of an elastic material. It is denoted by K and measured in N/m or N/m\(^{-1}\). Thus,
F = Ke, K = \(\frac{f}{e}\)
ii. F = 500N, K = 1.0 x 10\(^{4}\) Nm\(^{-1}\), F = ke
500 = 1 x 10\(^{4}\) x e
e = \(\frac{500}{1 \times 10^{4}} = \frac{5 \times 10^{2}}{1 \times 10^{4}}\) = 5 x 10\(^{2-4}\)
= 5 x 10\(^{-2}\) (0.05)m
W = ½Fe = ½ x 500 x 0.05 = 12.5J
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