Motion of ring/body down an incline

In summary, the velocity of the ring rolling down the incline would be equal to the velocity of the mass sliding down divided by the square root of 2. This is because the kinetic energy of the ring involves both translational and rotational energy, resulting in a different equation for velocity.
  • #1
konichiwa2x
81
0
A body of mass 'm' slides down an incline and reaches the bottom with a velocity 'v'. If the same mass were in the form of a ring which rolls down the incline, what would have been the velcity of the ring?

(A)[tex]v[/tex]

(B)[tex]\sqrt{2}v[/tex]

(C)[tex]\frac{1}{\sqrt{2}}v[/tex]

(D)[tex]\frac{\sqrt{2}}{\sqrt{5}}v[/tex]

How do I do this? please help.
 
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  • #2
Rolling implies rotational energy as well as translational energy. The knietic energy of the ring involves two terms, one for translation and one for rotation.
 
  • #3
ok

[tex] mgh = \frac{mv^2}{2} + \frac{I\omega^2}{2}[/tex]

solving, [tex] velocity = \frac{v}{\sqrt{2}}[/tex]

correct? thanks for your help.
 
  • #4
konichiwa2x said:
[tex] velocity = \frac{v}{\sqrt{2}}[/tex]
Looks good.
 

Related to Motion of ring/body down an incline

1. What is the difference between rolling and sliding motion down an incline?

Rolling motion involves both translation and rotation of the body, while sliding motion only involves translation along the incline. This means that rolling motion is both faster and more stable compared to sliding motion.

2. How does the angle of the incline affect the motion of the ring/body?

The steeper the incline, the faster the ring/body will accelerate due to the force of gravity. A flatter incline will result in a slower acceleration.

3. What is the role of friction in the motion of the ring/body down an incline?

Friction acts in the opposite direction of the motion, slowing down the ring/body. The amount of friction depends on the materials of the ring/body and the incline surface, as well as any external forces.

4. How does the mass of the ring/body affect its motion down an incline?

The greater the mass of the ring/body, the more force is needed to accelerate it down the incline. This means that a heavier ring/body will have a slower acceleration compared to a lighter one.

5. Can the motion of the ring/body down an incline be described by a mathematical equation?

Yes, the motion can be described using Newton's second law of motion, which relates the force, mass, and acceleration of an object. The equation is F = ma, where F is the net force, m is the mass, and a is the acceleration.

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