Question

A wooden rod of negligible mass and length 80.0cm is pivoted about a horizontal axis through its center. A white rat with mass 0.450kg clings to one end of the stick, and a mouse with mass 0.220kg clings to the other end. The system is released from rest with the rod horizontal

Part A
If the animals can manage to hold on, what are their speeds as the rod swings through a vertical position?
Take free fall acceleration to be 9.80m/s2 .

Answer 1

The speed of the animals is 1.64m/s.

Step-by-step explanation:

Let us work with variables and call the mass of the two rats
`m_1` and
`m_2`, and the length of the rod
`L`.

Using the law of conservation of energy, which says the potential energies of the rats must equal their kinetic energies, we know that when the rod swings to the vertical position,

`$m_1(L)/(2)g -m_2(L)/(2)g = (1)/(2)m_1v^2+(1)/(2)m_2v^2$`

`$(m_1 -m_2)g(L)/(2) = (1)/(2)(m_1+m_2)v^2$`,

solving for
`v`, we get:

`$\boxed{v = \sqrt{((m_1 -m_2)gL)/((m_1+m_2))} }$`

Putting in the values for
`m_1`,
`m_2`,
`g`, and
`L` we get:

`$v = \sqrt{((0.450kg -0.220kg)(9.8m/s^2)(0.8m))/((0.450kg+0.220kg))} $`

`\boxed{ v= 1.64m/s}`

Therefore, as the rod swings through the vertical position , the speed of the rats is 1.64 m/s.