 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2024

Paper 4

The spring length is $a+x$, its tension is $kx$, and the orbit radius is
$$
r=L+(a+x)\sin\phi_2.
$$
Vertical balance first gives
$$
kx\cos\phi_2=mg,
\qquad
\boxed{x=\frac{mg}{k\cos\phi_2}}.
$$
Radial balance is
$$
kx\sin\phi_2=m\omega^2r.
$$
Using the vertical equation,
$$
\boxed{
\omega=\left[
\frac{g\tan\phi_2}
{L+\left(a+\dfrac{mg}{k\cos\phi_2}\right)\sin\phi_2}
\right]^{1/2}}.
$$
Unlike the rigid-rod result, this depends on $m$: a larger mass stretches the spring farther and changes the radius of the orbit.


Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 9C / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 9C / b / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 9C / b / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)