Question

A 5.0 kg Foucalt Pendulum swings at the end of a 4.0 m long cable. The pendulum is released from a height of 1.5 m above the lowest position of its swing. What is the maximum tension in the cable?

Answer 1

Hi there!

We can begin by solving for the pendulum's velocity at the bottom of its trajectory using the work-energy theorem.

Recall:

`E_i = E_f`

Initially, we just have Potential Energy. At the bottom, there is just Kinetic Energy.

`PE = KE\\\\`

Working equation:

`\large\boxed{mgh = (1)/(2)mv^2}`

Rearrange to solve for velocity:

`gh = (1)/(2)v^2\\\\v = √(2gh)\\\\v = √(2(9.8)(1.5)) = 5.42 (m)/(s)`

Now, we can do a summation of forces:

`\Sigma F = T - W`

The net force is the centripetal force, so:

`(mv^2)/(r) = T - W`

Rearrange to solve for tension:

`T = (mv^2)/(r) + W\\\\T = (5(5.42^2))/(4) + 5(9.8) = \boxed{85.75 N}`