An elastic string has natural length \(l\) and modulus of elasticity \(\lambda\). The string is stretched from length \(l\) to length \(l + e\).
Show, by integration, that the work done in stretching the string is \(\frac { \lambda e ^ { 2 } } { 2 l }\).
A particle, of mass 5 kg , is attached to one end of a light elastic string. The other end of the string is attached to a fixed point \(O\).
The string has natural length 1.6 m and modulus of elasticity 392 N .
Find the extension of the string when the particle hangs in equilibrium.
The particle is pulled down to a point \(A\), which is 2.2 m below the point \(O\).
Calculate the elastic potential energy in the string.
The particle is released when it is at rest at the point \(A\).
Calculate the distance of the particle from the point \(A\) when its speed first reaches \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).