Calculating Force on a Rat Attached to a Spinning Rod: Physics Homework Solution

In summary, a wooden rod with a white rat and a mouse attached to its ends is released from rest with the rod horizontal. The question asks for the magnitude of the force on the rat as the rod swings through a vertical position. The tangential acceleration of the rat at that location is zero, so the force on the rat is also zero. The attempt at solving the problem involved finding the speed of the rat and mouse, and using the equation f=ma to calculate the force. However, this was incorrect and further attempts using the distance traveled were also incorrect.
  • #1
mybrohshi5
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Homework Statement



A wooden rod of negligible mass and length 77.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.480 kg clings to one end of the stick and a mouse with mass 0.180 kg is placed at the other end of the rod (the end away from the rat), and the system is released from rest with the rod horizontal.

what is the magnitude of the force on the rat by the rod as the rod swings through a vertical position?

Since the spin rate of the rod will be maximum as it swings through a vertical position, therefore the tangential acceleration of the rat (at that location) will be zero.

Homework Equations



f=ma
conservation of energy

The Attempt at a Solution



First off i thought since it is the force when it is swinging through the vertical it should be 0, but that is incorrect :(

From an early part of the question i had to find the speed of the mouse and the rat.
v = 1.85 m/s

so i thought maybe i should use this to find acceleration and then use f=ma

vf2=2ad

1.852=2a(.77/2)

a = 4.445 m/s2

then...

f = 0.480(4.445)

f = 2.1335 N

I have a feeling this is wrong though. Can anyone confirm that this is right or tell me where i am going wrong?

Thank you
 
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  • #2
I just checked and that is wrong :(

I thought maybe the distance traveled instead of .77/2 was 1/4 the circumference of a circle so i tried using 1/2pi(.77/2) but that does not work either.

any suggestions?
 

1. How do you calculate the force on a rat attached to a spinning rod?

To calculate the force on a rat attached to a spinning rod, you need to consider two main factors: the rotational force (or torque) exerted by the rod and the centripetal force acting on the rat. The formula for calculating torque is torque = force x distance, and the formula for centripetal force is centripetal force = mass x velocity^2 / radius. By plugging in the appropriate values and using vector addition to combine the forces, you can determine the total force on the rat.

2. What is the role of the radius in calculating the force on a rat attached to a spinning rod?

The radius plays a crucial role in calculating the force on a rat attached to a spinning rod because it determines the distance from the axis of rotation to the rat. This distance is used in the formula for torque and also affects the centripetal force calculation. A longer radius will result in a greater torque and a smaller centripetal force, while a shorter radius will have the opposite effect.

3. How does the mass of the rat impact the force calculation?

The mass of the rat is a key factor in calculating the force on a rat attached to a spinning rod because it affects the centripetal force calculation. A heavier rat will require a greater centripetal force to keep it moving in a circular path, while a lighter rat will require a smaller centripetal force. However, the mass of the rat does not directly impact the torque calculation.

4. Is there a maximum safe force that a rat can withstand while attached to a spinning rod?

Yes, there is a maximum safe force that a rat can withstand while attached to a spinning rod. This limit is determined by the rat's body mass, size, and strength, as well as the speed of the rotation and the duration of the experiment. It is important to carefully consider these factors and ensure that the force exerted on the rat does not exceed its physical limitations.

5. How can this concept be applied to other animals or objects attached to a spinning rod?

This concept can be applied to other animals or objects attached to a spinning rod by using the same principles and formulas. The only difference would be in the values used for mass, size, and strength of the object being rotated. Additionally, it is important to note that different animals or objects may have different physical limitations, so the maximum safe force may vary.

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