Falling Velocity Relative to Weight

In summary, a wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.490 kg clings to one end of the stick, and a mouse with mass 0.240 kg clings to the other end. When the system is released from rest, the animals will reach a speed of approximately 2.3 m/s as the rod swings through a vertical position. This can be calculated by taking into account the conservation of energy and calculating the change in gravitational potential energy for each animal separately. The total kinetic energy of the system is equal to the change in gravitational potential energy, which can be set equal to 1/2 of the total
  • #1
coolguy9
5
0

Homework Statement



A wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.490 kg clings to one end of the stick, and a mouse with mass 0.240 kg 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



free fall acceleration = 9.80 m/s^2.


The Attempt at a Solution



I would love to attempt at the solution, but I haven't even the slightest clue where to start, I'm quite confused :(
 
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  • #2
I would think about conservation of energy. The total kinetic energy of the unfortunate mammals is equal to the change in gravitational potential energy.
 
  • #3
I'm not making too much headway on this problem..

I've got

PE = change in mgh and
KE = change in 1/2mvf^2 - 1/2mvi^2

PE = 5.7232, assuming m = 0.490 kg + .240 kg, and g = 9.8, and h = .80m

but I don't really know where to go from there. and is that PE even correct? or do I have to do it separately for each animal, and add them? ahh, so confused
 
  • #4
Ok, so mouse goes up, rat goes down. PE=mgh. One h is positive and one is negative. Since one goes up and one goes down. Hence, don't add the masses. Calculate each one separately. Initial KE is zero.
 
  • #5
Alright, I'm still a little confused but I'm getting there, I think..

PE(mouse) = (9.8m/s)(.24kg)(0.8m) = 1.8816
PE(rat) = (9.8)(.49)(-0.8) = -3.8416

change in PE = 5.7232

5.7232 = 1/2 mv^2

v = 3.38?

Which is still wrong, so.. I'm doing something wrong hehe
 
  • #6
You have to ADD the PE's. If the mouse and the rat had the same mass there would be no change in PE.
 
  • #7
Ok, so..


Total PE = -1.96

-1.96 = (1/2) (0.49 + 0.24)(v^2)

Assume the negative sign is negligible?

v = 2.3?
 
  • #8
The minus sign isn't negligible. You just have to think about what it means relative to your choice of the sign of h. But yes, roughly 2.3m/s.
 
  • #9
The website is telling me 2.3 is incorrect.. I re-calculated, and it's coming up 2.3172, rounded to the tenths is 2.3..

Is there anything else we might not be accounting for?
 
  • #10
I don't think so. I worked it out again and agree with your number. Did you put correct units on it?
 

Related to Falling Velocity Relative to Weight

1. What is falling velocity relative to weight?

Falling velocity relative to weight is a measure of how quickly an object falls due to the force of gravity, taking into account the object's weight or mass. It is influenced by factors such as air resistance and the strength of the gravitational pull.

2. How is falling velocity relative to weight calculated?

Falling velocity relative to weight is calculated using the equation v = gt, where v is the velocity, g is the acceleration due to gravity (9.8 m/s^2 on Earth), and t is the time the object has been falling. This equation assumes that there is no air resistance.

3. How does air resistance affect falling velocity relative to weight?

Air resistance can significantly affect falling velocity relative to weight. As an object falls, air resistance increases and eventually balances out the force of gravity, causing the object to reach a constant velocity known as terminal velocity. This means that the falling velocity relative to weight will eventually stop increasing and remain constant.

4. How does weight affect falling velocity relative to weight?

Weight directly affects falling velocity relative to weight, as the gravitational force pulling the object towards the ground is directly proportional to its weight. Objects with greater weight will have a greater force of gravity acting on them, causing them to fall faster than lighter objects.

5. Does the medium through which an object is falling affect its falling velocity relative to weight?

Yes, the medium (such as air or water) through which an object is falling can greatly affect its falling velocity relative to weight. Different mediums have different levels of resistance, which can slow down or speed up the falling object. For example, falling in water will have a greater resistance than falling in air, resulting in a slower falling velocity relative to weight.

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