Calculating Inertia Ratios of Carts on a Low-Friction Track

In summary: The vx(t) curves for two carts, A and B, that collide on a low-friction track are shown below:The ratio of the carts' inertias is 1/2.
  • #1
emily081715
208
4

Homework Statement



The vx(t) curves for two carts, A and B, that collide on a low-friction track are shown below:
Mazur1e.ch4.p10.jpg

What is the ratio of their inertias?

Homework Equations


the ratio i am looking for is mB/mA

The Attempt at a Solution


I believed that the ration was 1/2 however that is not correct and i do not see how there can be another ratio
 
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  • #2
How did you get the value 1/2?
Which mass is larger?
 
  • #3
mfb said:
How did you get the value 1/2?
Which mass is larger?
is the cart of mass B not larger because it had a smaller change is speed, meaning it has a larger inertia and greater mass. i got the 1/2 ratio because the mass of cart A is double the mass of cart B
 
  • #4
emily081715 said:
is the cart of mass B not larger because it had a smaller change is speed, meaning it has a larger inertia and greater mass.
Correct, cart B has a larger mass.
emily081715 said:
because the mass of cart A is double the mass of cart B
This is in contradiction to what you said immediately before that.
 
  • #5
I meant cart B is double the mass of cart A. But the ratio isn't 2/1
 
  • #6
emily081715 said:
But the ratio isn't 2/1
Why not?
You can try to estimate the changes a bit better from the diagram, that will give a value very close to 2/1, but usually you are not supposed to measure individual pixels on problems like this.
 
  • #7
mfb said:
Why not?
You can try to estimate the changes a bit better from the diagram, that will give a value very close to 2/1, but usually you are not supposed to measure individual pixels on problems like this.
i already tried the ratio and it was wrong which is why I'm confused for the question
 
  • #8
emily081715 said:
i already tried the ratio and it was wrong which is why I'm confused for the question
turns out the answer was 2.1
 
  • #9
Okay, bad problem statement. Giving something that is so close to 2 and then expecting students to count pixels is a very bad style.
 

1. What is inertia?

Inertia is the resistance of an object to change in its state of motion. It is a physical property that depends on the mass of the object.

2. How is inertia related to calculating inertia ratios of carts on a low-friction track?

Inertia ratios are used to compare the amount of inertia between two or more objects. In the case of carts on a low-friction track, the inertia ratio is used to compare the mass of the carts and their resistance to changes in motion.

3. What is a low-friction track?

A low-friction track is a surface that has minimal resistance to the movement of objects. This allows for more accurate measurements of inertia as it reduces external forces that can affect the motion of the carts.

4. How do you calculate inertia ratios of carts on a low-friction track?

The inertia ratio is calculated by dividing the mass of one cart by the mass of the other cart. This can be done by using a balance scale or by measuring the mass of each cart individually.

5. Why is it important to calculate inertia ratios of carts on a low-friction track?

Calculating inertia ratios allows for a better understanding of the relationship between mass and inertia. It also helps in making predictions about the motion of objects and can be used to design experiments to test other factors that may affect motion, such as friction or force.

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