Translational Kinetic Energies + Plane

AI Thread Summary
The discussion focuses on finding the ratio of translational kinetic energies for a ring, a coin, and a solid sphere at the bottom of an inclined plane, assuming pure rolling without slipping. Participants clarify that the translational kinetic energy (T.K.) is influenced by the moment of inertia and the linear velocities of the objects. The correct approach involves using potential energy (PE) and relating it to kinetic energy (KE) for each object, noting that they all start from the same height and mass. The final ratio of translational kinetic energies is suggested to be 21:28:30, derived from the respective equations. Understanding the relationship between the center of mass velocity and the rolling object's edge velocity is emphasized as crucial for solving the problem.
Kishor Bhat
Messages
21
Reaction score
0

Homework Statement


Find the ratio of the translational kinetic energies of a ring, a coin, and a solid sphere at the bottom of an inclined plane. The bodies have been released from rest at the top. Assume pure rolling without any slipping.


The Attempt at a Solution



Well, I'm really not sure. Since T.K.=1/2 m*v^2, we need to look at linear velocities v at the bottom of the plane for each object. Obviously the rotation will influence this, and I've tried obtaining final ω and using v=ωr at the bottom, but I'm not getting the answer. Which, by the way, is 21:28:30.
 
Physics news on Phys.org
Perhaps you are confusing the linear velocity from v=ωr, which is the instantaneous velocity of the edge of the rolling object, with the linear velocity of the center of mass of the object.

Beside that, are you using the correct moments of inertia for the different objects? I'm assuming the masses and radii are all the same.
 
The MI's are correct, and yes, they are all of same mass and radius. One question: can we find the acceleration of c.o.m and then use the equations of motion to find final velocity? I haven't tried that.
 
PICsmith said:
Perhaps you are confusing the linear velocity from v=ωr, which is the instantaneous velocity of the edge of the rolling object, with the linear velocity of the center of mass of the object.

Nevermind this statement...while yes they are different things, in this case they are the same velocity (the center of mass velocity in the frame at rest w.r.t. the ramp is of course the same as the linear velocity of the edge in the co-moving frame, since there is no slipping).

You don't have to calculate any velocites. Here's how you go about it. For example, for the ring you have KE = PE-RE = PE-(1/2)Iω^2 = PE-(1/2)mv^2 = PE-KE, and so you have KE=PE/2. Obtain the KE in terms of PE for the other two objects, and then you can take the ratios between them.

Edit: Keep in mind that the PE for each object is the same since they all start at the same height and have the same mass.
 
Last edited:
Gracias.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

A cylinder rotating on a plane with friction and then moving across a frictionless plane to a collision
Replies
1
Views
754
Kinetic Energy of a Cylinder Rolling Without Slipping
Replies
21
Views
4K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Which sphere reaches the bottom of the inclined plane first
Replies
19
Views
4K
Average Translational Kinetic Energy: P & V Given
Replies
1
Views
2K
Possible to use work-energy theorem from a non-inertial frame?
Replies
1
Views
2K
Translational and rotational kinetic energy-Mass Unknown
Replies
3
Views
2K
What fraction of its total kinetic energy is rotational kinetic energy
Replies
20
Views
21K
A ball climbing a ramp while "rolling the wrong way"
Replies
32
Views
3K
Solid sphere and hollow sphere rolled down an inclined plane
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top