Kinetic energy of a rolling hoop

In summary, the problem involves finding the amount of work required to stop a 120 kg hoop rolling at a speed of 0.240 m/s on a horizontal floor. Using the equation for the moment of inertia of a hoop, the kinetic energy formula, and simplifying the units, the work required is calculated to be 6.91 J. This is because the total kinetic energy of the hoop is equal to the work done on it to stop.
  • #1
Jrlinton
134
1

Homework Statement


A 120 kg hoop rolls along a horizontal floor so that its center of mass has a speed of 0.240 m/s. How much work must be done on the hoop to stop it?

Homework Equations


I of hoop=MR^2

The Attempt at a Solution


KE=0.5*m*v^2+0.5*(mR^2)(v/R)^2
=0.5*120kg*.24^2m/s+0.5*(120kg*R^2)(.24m/s^2/R^2)
=6.912 J

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  • #2
Your calculation looks good. You might want to trim the significant digits in your result to match the given data. If this is a "show your work" type question rather than a web based "enter the solution" assignment, you might want to include a note as to why the total KE is the same as the work required.
 

1. What is the formula for calculating the kinetic energy of a rolling hoop?

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

2. How does the mass and radius of the hoop affect its kinetic energy?

The mass and radius of the hoop do not directly affect its kinetic energy. However, they do affect the moment of inertia, which is a factor in the kinetic energy formula. A hoop with a larger moment of inertia will have a higher kinetic energy than a hoop with a smaller moment of inertia, assuming they have the same angular velocity.

3. Does the surface the hoop is rolling on impact its kinetic energy?

Yes, the surface the hoop is rolling on can impact its kinetic energy. Friction and other forces may come into play, which can affect the speed and angular velocity of the hoop, ultimately impacting its kinetic energy. In a frictionless environment, the surface would not affect the hoop's kinetic energy.

4. Can the kinetic energy of a rolling hoop be negative?

No, the kinetic energy of a rolling hoop cannot be negative. Kinetic energy is a measure of an object's energy in motion, and it is always a positive value. If the hoop were to slow down and stop, its kinetic energy would decrease, but it would never be negative.

5. How does the shape of the hoop affect its kinetic energy?

The shape of the hoop does not directly affect its kinetic energy. However, the shape can impact the moment of inertia, which is a factor in the kinetic energy formula. For example, a hollow hoop will have a different moment of inertia than a solid hoop with the same mass and radius, resulting in different kinetic energies.

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