Kinetic Energy in Rolling Motion

In summary, the problem involves a cylinder with a radius of 0.5m being pulled to the right by a 10N force. The question asks for the work done by the force when the cylinder has moved 5m. The solution involves finding the translational kinetic energy, which is equal to Fd, and the rotational kinetic energy, which is equal to 1/2Iw2. The rotational energy depends on whether the cylinder is full or hollow, with the full cylinder having rotational energy equal to half of the translational energy, and the hollow cylinder having rotational energy equal to the translational energy. The center of mass of the cylinder is at the center regardless of its fullness or hollowness, but
  • #1
scratchfish
6
0

Homework Statement


Upon application of the 10-N force F to the cord in Figure P5.3, the cylinder begins to roll to the right. After C has moved 5 m, how much work has been done by F?

do not have picture so let me decribe the picture: 1) cylinder with radius .5m is on the ground 2) the cord is attached on the very top of the cylinder (symmetrical to the center) and is pulled to the right at 10N force


Homework Equations


Translational KE: 1/2mv2
Rotational KE: 1/2Iw2


The Attempt at a Solution


I found translational KE, which is equal to Fd = (10N)(5m) = 50 joule
I don't know how to find the rotational energy of this problem.
The answer should be 100J.
Help me! I am prparing for the final
 
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  • #3
cylinder is full the mass of it is unknown. This seems to require more math than normal intro physics would require, where it briefly touches on the rotational motion
 
  • #4
scratchfish said:
cylinder is full the mass of it is unknown. This seems to require more math than normal intro physics would require, where it briefly touches on the rotational motion

Not really. I've only read the article. If full or hollow the difference is KErotational equals half or exactly the KEtranslational. Seems logical.
 
  • #5
uhm.., but how do you assume that it's exactly half? any work?
I mean how did you solve 1/2Iw^2??
How did you find w? where did this derive from?
By the way, this is dyanamics problem, which you take after physics2 and statics,,,,
It can't be that simple.
 
  • #6
oh that... well ... didn't work ... I assumed you would :P

If the Cyl is empty them you have KE of the whole Cyl as it gains speed after 5 m, that would be translational. And KE of the mass as it rotates with the same speed as the translational motion.( When I say the same speed then the rotational can be likened to translational and you get a result like 1/2mv2)

Same for a full Cylinder just that the outside has the trans speed and the middle has 0, so you get only half of it.

Basicaly Rot KE is equal to 1/2mv^2 with:

m=mass

v=speed of center of gravity

The latter is the geometrical center of gravity of the crosssection of the cylinder. If full the the center of gravity is r/2 from the middle and if it spins with W then we get half of the trans KE. If hollow them the center of gravity is at r from the middl and we get KEtrans=KErot.
 
  • #7
Lok said:
Not really. I've only read the article. If full or hollow the difference is KErotational equals half or exactly the KEtranslational. Seems logical.

This is incorrect. If the cylinder rolls without slipping, then

w=v/r.

If it is full, then moment of inertia

I=(1/2)mr^2

and we have rotational energy = (1/2)*translational kinetic energy:

R=(1/2)Iw^2 = (1/2)*((1/2)mr^2)*(v/r)^2 = (1/4)mv^2 = K/2

If, however, the cylinder is hollow, then moment of inertia

I=mr^2

and we have rotational energy = translational kinetic energy:

R=(1/2)Iw^2 = (1/2)*(mr^2)*(v/r)^2 = (1/2)mv^2 = K
 
  • #8
Lok said:
The latter is the geometrical center of gravity of the crosssection of the cylinder. If full the the center of gravity is r/2 from the middle and if it spins with W then we get half of the trans KE. If hollow them the center of gravity is at r from the middl and we get KEtrans=KErot.

The center of mass is at the center of the cylinder regardless of whether it is full or hollow. This is obvious by the rotational symmetry of the cylinder.
 
  • #9
I don't see the wrong in my assumptions ... :P

Considering the final answer 100J, is the Cylinder full or hollow?
 
  • #10
2Tesla said:
The center of mass is at the center of the cylinder regardless of whether it is full or hollow. This is obvious by the rotational symmetry of the cylinder.

I'm talking about the center of gravity of the crossection. That is as if the whole mass of the cylinder would be in a point that rotates at a distance around the middle of the cylinder.
 
  • #11
If it is hard to understand them imagine a donut or torus. The crossection would be a full circle and the center of gravity of it would be in it's center.

Most round object Volume and Inertia formulas can be found like this.
 
  • #12
Thanks Telsa! that's just it!
Why couldn't I think of that lol lol!
exactly you are right.!
 

Related to Kinetic Energy in Rolling Motion

What is kinetic energy in rolling motion?

Kinetic energy in rolling motion is the energy an object possesses due to its motion while rolling. It is a form of mechanical energy and depends on the mass and velocity of the object.

How is kinetic energy in rolling motion different from kinetic energy in linear motion?

Kinetic energy in rolling motion is different from kinetic energy in linear motion because it involves both rotational and translational motion. In linear motion, the energy is solely dependent on the object's velocity, while in rolling motion, it also depends on the object's rotational speed.

What is the formula for calculating kinetic energy in rolling motion?

The formula for calculating kinetic energy in rolling motion is KE = 1/2 * I * ω^2, where KE is kinetic energy, I is the moment of inertia, and ω is the angular velocity of the object.

How does the mass and velocity affect the kinetic energy in rolling motion?

The kinetic energy in rolling motion is directly proportional to both the mass and velocity of the object. This means that an increase in either of these factors will result in an increase in kinetic energy.

What are some real-world applications of kinetic energy in rolling motion?

Kinetic energy in rolling motion is commonly used in various forms of transportation, such as cars, trains, and bicycles. It is also utilized in sports equipment, such as wheels on skateboards and rollerblades. Additionally, it is essential in the design of industrial machinery, such as conveyor belts and gears.

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