Conservation of Energy with Rotation

In summary, the conversation is about a problem involving a small circular object rolling without slipping on a track and then being launched vertically from a ramp. The question is asking for the maximum height the object will reach after leaving the ramp. After some calculations and mistakes, the correct solution is determined to be 4.7 m.
  • #1
NATURE.M
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Homework Statement



A small circular object with mass m and radius r has a moment of inertia given by I = cmr^2. The
object rolls without slipping along the track shown in the figure. The track ends with a ramp of height R = 2.5 m that launches the object vertically. The object starts from a height H = 6.0 m. To what maximum height will it rise after leaving the ramp if c = 0.40?


The Attempt at a Solution



My solution to this problem is 4.7 m.
So I'm pretty sure my answer is right but the textbook indicates the answer is 5.0 m which confuses me.

I applied conservation of energy from the starting point, mgH to the launch point (when it leave the ramp), mgR + 1/mv^2 + 1/2I[itex]\omega[/itex]^2 , and then solved for v obtaining 6.55m/s.
Then, I used the equation v^2 = 2g(h-R), where h is the maximum height reached (note I'm
pretty sure once the object leaves the ramp, it loses its rotational motion and maintains only
linear motion after-though correct me if I'm wrong). Rearranging and substituting I obtain
h=4.7m.
 
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  • #2
The textbook is correct here. The magnitude of velocity at the end of ramp is not 6.55 m/s.

That said, I suggest that you do not plug in the numbers until you solve everything symbolically. You will see that many things cancel each other out.
 
  • #3
voko said:
The textbook is correct here. The magnitude of velocity at the end of ramp is not 6.55 m/s.

That said, I suggest that you do not plug in the numbers until you solve everything symbolically. You will see that many things cancel each other out.

Rather silly mistake on my part. I rearranged my equations and everything, but for some reason wrote c= 0.60 at the top of my page and kept referencing that value ...
 
  • #4
Which, I assume, means you got the correct result?
 
  • #5
voko said:
Which, I assume, means you got the correct result?

oh yeah I did. Thanks.
 

FAQ: Conservation of Energy with Rotation

What is the definition of conservation of energy with rotation?

Conservation of energy with rotation is a physical law that states that the total energy of a rotating object remains constant as long as there is no external torque acting on it.

How does conservation of energy with rotation apply to real-world situations?

This law applies to real-world situations such as the motion of planets around the sun, the spinning of a top, or the rotation of a bicycle wheel.

What is the relationship between torque and conservation of energy with rotation?

Torque is the measure of the force that causes an object to rotate. In the context of conservation of energy with rotation, torque is responsible for changing the rotational energy of an object.

Can rotational kinetic energy be converted into other forms of energy?

Yes, rotational kinetic energy can be converted into other forms of energy, such as heat or potential energy, through friction or other external forces acting on the rotating object.

How does conservation of energy with rotation relate to the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. Conservation of energy with rotation is a specific application of this law, focusing on the conservation of energy in rotational motion.

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