Cambridge Maths Academy

Further mechanics 1 Table of contents Hooke's law Units Modulus of elasticity ($\lambda$) Examples Exercise 3A 1. Hooke's law When an elastic string or spring is stretched, the tension, $T$, produced is proportional to the extension, $x$. $$ \begin{align} T \propto x \\ \\ \Rightarrow \qquad T = kx \end{align} $$ where $k$ is a constant. The constant $k$ depends on the unstretched length of the ..

수학 모음 (Maths collection) 전체보기 To find the surface area of a circular cone, we need to consider the area of the circular sector and the area of the circle. The area of the circular sector: We find the angle $\theta$ by considering the arc length, i.e. $$ \begin{align} L=2\pi\ell\times\frac{\theta}{360}&=2\pi r \\ \Rightarrow\quad \ell\times\frac{\theta}{360}&=r \end{align} $$ The area is then $$ ..