Which Mass Reaches the Bottom First When Rolling Down an Incline?

[hatingphysics]

The five masses below all have the same radius and a cylindrically symmetric mass distribution. They start to roll down an inclined plane, starting from rest, at the same time and from the same height. Give their order of arrival at the bottom.

Icm=684 g*cm2, M = 47g

Icm=373 g*cm2, M = 41g

Icm=415 g*cm2, M = 44g

Icm=600 g*cm2, M = 50g

I found the ratio by dividing inertia/mass. I thought it was the one with the lowest ratio reaches the bottom first...but why am I not getting the right answers?!

 

[Nate810]

The correct order is: Icm=373 g*cm2, M = 41g, Icm=415 g*cm2, M = 44g, Icm=600 g*cm2, M = 50g, Icm=684 g*cm2, M = 47g. The order of arrival is determined by the moment of inertia of each mass. The lower the moment of inertia, the faster the mass will reach the bottom. Moment of inertia is calculated by dividing the mass by the radius of the cylindrical body. Therefore, the mass with the lowest moment of inertia (Icm=373 g*cm2, M = 41g) will arrive first, followed by the mass with the second lowest moment of inertia (Icm=415 g*cm2, M = 44g), and so on.

 

[kyle8921]

I would first like to clarify that the order of arrival at the bottom of the inclined plane is not solely determined by the ratio of inertia to mass. Other factors such as the slope and length of the incline, as well as external forces such as friction, can also affect the rolling motion.

That being said, let's look at the given information and see if we can determine the order of arrival at the bottom. The given data shows that all five masses have the same radius and start from the same height and at the same time. This means that the initial potential energy and starting conditions are the same for all five masses.

Now, let's consider the ratio of inertia to mass for each mass. The one with the lowest ratio is the third one, with an Icm/M ratio of 9.43 g*cm^2/g. This means that this mass has the lowest resistance to rotation and should theoretically reach the bottom first. However, as mentioned earlier, other factors such as the slope and length of the incline can also affect the motion.

In order to accurately determine the order of arrival, we would need more information such as the slope and length of the incline, as well as the presence of any external forces. It is also important to note that in real-world scenarios, there will always be slight variations and uncertainties, making it difficult to predict the exact order of arrival. Therefore, it is important to conduct experiments and collect data to verify and validate any theoretical predictions.