What is the Speed v2 of the Mouse and the 0.25-kg Cart?

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In summary, a 0.038-kg pet lab mouse sitting on a 0.35-kg air-track cart jumps to a second cart with a mass of 0.25 kg. The first cart is initially at rest and after the jump, it has a speed of v1=0.86m/s. The goal is to find the speed v2 of the mouse and the 0.25-kg cart. The relevant equation for this scenario expresses the conservation of kinetic energy. However, since the mouse "sticks" to the second cart, the collision is not an elastic one. Therefore, another conservation law, which applies to a system with no external forces acting in the direction of interest, must be used.
  • #1
Angela_vaal
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Homework Statement


A 0.038-kg pet lab mouse sits on a 0.35-kg air-track cart, as shown in (Figure 1) . The cart is at rest, as is a second cart with a mass of 0.25 kg. The lab mouse now jumps to the second cart. After the jump, the 0.35-kg cart has a speed of v1=0.86m/s.

What is the speed v2 of the mouse and the 0.25-kg cart?
fig_9-27.png


Homework Equations


1/2m1v02=1/2m1v1,f2+1/2m2v2,f2

The Attempt at a Solution


I don't know where to start. I am assuming this is an elastic collision since the carts don't stick together after the collision. Would I use the equation listed above? I just don't know how to start
 
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  • #2
I don't know if 'not sticking together' ensures an elastic collision ...

And if the speeds beforehand were zero, then afterwards they must be zero too ?
Do you think there is conservation of kinetic energy in this case ?
What about the work mickey mouse does when kicking away the 0.35 kg block ?

Know any other conservation laws ? (in fact, one other is already enough...:smile: )
 
  • #3
The mouse "sticks" to the second cart, so at least part of the scenario involves a collision that is not an elastic one.

What conservation law does your relevant equation express? Is there another quantity that's conserved that might be a better choice for the overall scenario?Edit: Ah! BvU got there before me!
 
  • #4
gneill said:
The mouse "sticks" to the second cart, so at least part of the scenario involves a collision that is not an elastic one.

What conservation law does your relevant equation express? Is there another quantity that's conserved that might be a better choice for the overall scenario?Edit: Ah! BvU got there before me!

Is the collision inelastic then?
 
  • #5
I'm confused.
 
  • #6
Angela_vaal said:
Is the collision inelastic then?
It's not a single collision scenario. The mouse pushes off the first cart with what might be interpreted as an inelastic collision in reverse (separation instead of joining) and then collides with and sticks to the second cart in another inelastic collision.

The good news is that one conservation law covers the whole process from start to finish.
 
  • #7
And what is this conservation law?
 
  • #8
Angela_vaal said:
Is the collision inelastic then?
You should never assume collisions are elastic without good reason. If you can solve without that assumption, do so.
As others have told you, there is another conservation law available. You must have been taught it. It applies to a system (two carts plus mouse in this case) provided there are no external forces acting on the system in the direction of interest. Since the track is frictionless, there are no external horizontal forces on that system, so the law applies in that direction.
 

FAQ: What is the Speed v2 of the Mouse and the 0.25-kg Cart?

1. What is the elastic equation?

The elastic equation is a mathematical formula used to calculate the change in length or deformation of an object when a force is applied to it. It is commonly used to study the behavior of materials such as springs, rubber bands, and other elastic materials.

2. How do you find V2 in an elastic equation?

To find V2 in an elastic equation, you need to know the initial length (L0) of the object, the elastic modulus (E) of the material, and the force (F) applied to the object. The formula for finding V2 is V2 = (F/E) * (L0 + V1), where V1 is the initial displacement of the object.

3. What is the unit of measurement for V2 in an elastic equation?

The unit of measurement for V2 in an elastic equation is meters (m) or any other unit of length, as it represents the change in length of the object due to the applied force.

4. Can the elastic equation be used for any material?

No, the elastic equation can only be used for materials that exhibit elastic behavior, meaning they return to their original shape after the applied force is removed. Materials such as plastic and glass do not follow this behavior and therefore, cannot be analyzed using the elastic equation.

5. Are there any limitations to the elastic equation?

Yes, the elastic equation assumes that the material being studied is linearly elastic, meaning that the relationship between the applied force and the resulting displacement is linear. It also assumes that the material is isotropic, meaning that it has the same properties in all directions. If these conditions are not met, the results obtained from the elastic equation may not be accurate.

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