Mouse Jumps Onto An Exercise Wheel

In summary, the vertical exercise wheel in a mouse cage, with a moment of inertia of 0.0004kg m2 and a radius of 0.06m, is initially at rest but can rotate without friction around a horizontal axis through its center. A mouse of mass 0.03kg and initial speed of 2m/s jumps onto the edge of the wheel and rotates with it. The angular velocity of the "wheel plus mouse turning together" is 7.09 rad/s. To determine the maximum height of the mouse while riding the wheel, the equation 1/2Iω2 = mgh is used where I is the moment of inertia, ω is the angular velocity, m is the mass of
  • #1
burnst14
53
2

Homework Statement


The vertical exercise wheel in a mouse cage is initially at rest, but can turn without friction around a horizontal axis through the center of the wheel. The wheel has a moment of inertia I=0.0004kg m2 and radius R = 0.06m An extremely smart pet mouse of mass m = 0.03 kg runs across her cage with initial speed v = 2 m/s, jumps onto the edge of her exercise wheel, holds on tightly, and rotates together with the wheel.

  1. Determine the angular velocity of the "wheel plus mouse turning together" immediately after she jumps on.
  2. Determine the maximum height of the mouse as she rides the wheel.

Homework Equations

The Attempt at a Solution


I solved the first one and got 7.09 rad/s by:
L = Rmv = Iω
0.06*0.03*2 = (0.0004+0.03*0.062
ω = 7.09 rad/s

However part 2, I can't wrap my head around. I have an answer packet, but it has already had a couple incorrect solutions in it so I'm not quick to trust it.
I tried 1/2Iω2 = mgh

KE = 1/2(5.08E-4)(7.09)2 = 0.03*9.81*h

where h is the maximum height and 0.03 kg is the mass of only the mouse because the wheel is a homogenous cylinder and has equal mass on all "sides".

I feel like I'm missing torque though.
Any ideas?

Thanks guys
 
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  • #2
The approach via energy conservation is good. Torque will vary along the ride, but you don't have to worry about that as energy is conserved and you can calculate it both before and after.
 
  • #3
So my answer is correct then? Or is my formula missing a piece?

Thanks!
 
  • #4
I don't see a final answer, but ω and the approach look good. You should add units, however.
 
  • #5


I would approach this problem by first identifying all the relevant variables and equations. The key variables in this problem are the moment of inertia (I), radius (R), mass (m), initial velocity (v), and angular velocity (ω). The relevant equations are L = Iω (angular momentum), KE = 1/2Iω^2 (rotational kinetic energy), and PE = mgh (gravitational potential energy).

For part 2, we want to find the maximum height of the mouse as it rides the wheel. To do this, we can use the conservation of energy principle, which states that the total energy of a system remains constant. Initially, the mouse has kinetic energy, KE = 1/2mv^2, and no potential energy. After jumping onto the wheel, the mouse has rotational kinetic energy, KE = 1/2Iω^2, and gravitational potential energy, PE = mgh. Therefore, we can set these two energies equal to each other and solve for h:

1/2mv^2 = 1/2Iω^2 + mgh

Solving for h, we get:

h = (1/2mv^2 - 1/2Iω^2)/mg

Substituting in the values given in the problem, we get:

h = (1/2*0.03*2^2 - 1/2*0.0004*7.09^2)/(0.03*9.81) = 0.063 m

Therefore, the maximum height of the mouse as it rides the wheel is 0.063 m. This makes intuitive sense, as the mouse would reach its maximum height when it is at the top of the wheel, where it has the most potential energy.

Overall, this problem demonstrates the principles of rotational motion and conservation of energy. By identifying the relevant variables and using the appropriate equations, we can solve for the unknown quantities and gain a better understanding of the physical phenomenon at hand.
 

FAQ: Mouse Jumps Onto An Exercise Wheel

1. How does a mouse learn to use an exercise wheel?

Mice are naturally curious and exploratory animals, so they will often investigate and try out new objects in their environment. When a mouse first encounters an exercise wheel, it may take some time for them to figure out how to use it. However, with consistent exposure and practice, they will learn how to jump onto the wheel and start running.

2. Why do mice use exercise wheels?

Mice use exercise wheels for physical activity and mental stimulation. In the wild, mice are constantly on the move, running and exploring their surroundings. In captivity, they do not have as much space to roam, so an exercise wheel provides them with an outlet for their natural instincts to run and play.

3. Is it safe for mice to use exercise wheels?

Yes, exercise wheels are generally safe for mice to use as long as they are the appropriate size and type for the mouse. It is important to choose a wheel that is large enough for the mouse to run comfortably without arching their back. Wire wheels should be avoided, as they can cause injuries to the mouse's feet.

4. How long should a mouse use an exercise wheel?

Mice should have access to an exercise wheel at all times, as they are active animals and enjoy running for extended periods. However, it is important to monitor their use and ensure they are not overexerting themselves. If a mouse seems tired or is panting excessively, it is a sign that they should take a break from the wheel.

5. Can exercise wheels help keep mice healthy?

Yes, exercise wheels can contribute to a mouse's overall health and well-being. Regular use of an exercise wheel can help prevent obesity and promote cardiovascular health in mice. It also provides them with mental stimulation and can help reduce stress and boredom in captivity.

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