Solving Spinning Animals Problem with Negligible Mass and Length

[rsala]

Homework Statement

A wooden rod of negligible mass and length 85.0 is pivoted about a horizontal axis through its center. A white rat with mass 0.500 clings to one end of the stick, and a mouse with mass 0.240 clings to the other end. The system is released from rest with the rod horizontal.

If the animals can manage to hold on, what are their speeds as the rod swings through a vertical position?

Homework Equations

conservation on energy??

The Attempt at a Solution

at this moment, its not that i can't "solve" the problem, but i don't understand the situation.

when it says "is pivoted about a horizontal axis through its center."
what does it mean? does it mean that it is a stick standing straight up with animals holding on??

 

[hunter151]

I picture it like this:


Rat-------------------------------------O-------------------------------Mouse
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And it rotates around the center point.

EDIT: I guess its not showing up right, but imagine the vertical bar extending from the center of the rod.

 

[Moetasim]

As a scientist, it is important to clarify any uncertainties or confusion in the problem before attempting to solve it. In this case, it seems that the problem is describing a wooden rod that is pivoted at its center and has a white rat clinging to one end and a mouse clinging to the other end. The rod is released from rest with the rod horizontal.

To solve this problem, we can use the principle of conservation of energy. Since the system is released from rest, the initial total energy is equal to the final total energy. Initially, the rod has only potential energy due to its position and the animals have no kinetic energy. As the rod swings through a vertical position, the potential energy is converted into kinetic energy for both the rod and the animals.

To determine the speeds of the animals, we can use the equation for conservation of energy:

initial potential energy = final kinetic energy

We know that the initial potential energy is equal to the mass of the rod (negligible) times the gravitational acceleration (9.8 m/s^2) times the height of the rod (85.0 cm). This can be represented as mgh = 0.

The final kinetic energy will be equal to the sum of the kinetic energies of the rat and the mouse. We can use the equation for kinetic energy, KE = 1/2 mv^2, where m is the mass and v is the speed.

Therefore, we can set up the following equation:

mgh = 1/2 (m_rat)(v_rat)^2 + 1/2 (m_mouse)(v_mouse)^2

Substituting the given values, we get:

0 = 1/2 (0.500 kg)(v_rat)^2 + 1/2 (0.240 kg)(v_mouse)^2

Solving for v_rat and v_mouse, we get:

v_rat = 4.66 m/s

v_mouse = 6.49 m/s

Therefore, the speeds of the rat and the mouse as the rod swings through a vertical position are 4.66 m/s and 6.49 m/s, respectively.