2 One end of a light spring is attached to a fixed point. A mass of 2 kg is attached to the other end of the spring.
The spring hangs vertically in equilibrium. The extension of the spring is 0.05 m .
- Find the stiffness of the spring.
- Find the energy stored in the spring.
- Find the dimensions of stiffness of a spring.
A particle P of mass \(m\) is performing complete oscillations with amplitude \(a\) on the end of a light spring with stiffness \(k\). The spring hangs vertically and the maximum speed \(v\) of P is given by the formula
\(\mathrm { v } = \mathrm { Cm } ^ { \alpha } \mathrm { a } ^ { \beta } \mathrm { k } ^ { \gamma }\),
where \(C\) is a dimensionless constant. - Use dimensional analysis to determine \(\alpha , \beta\), and \(\gamma\).
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A circular hole with centre C and radius \(r \mathrm {~m}\), where \(r < 0.5\), is cut in a uniform circular disc with centre O and radius 0.5 m . The hole touches the rim of the disc at A (see diagram).
The centre of mass, G , of the remainder of the disc is on the rim of the hole.
Determine the value of \(r\).