Sphere on Incline: Kinetic Energy of a Rolling Sphere

In summary, a solid sphere of uniform density with a mass of 4.6 kg and a radius of 0.28 m rolls without slipping down a 35° incline for a distance of 3.9 m. If there is no friction between the sphere and the incline, the translational kinetic energy at the bottom will depend on whether the sphere rolls or just slips down the incline. In the case of slipping, the final kinetic energy will equal the initial potential energy. However, if the sphere rolls, some energy will go into its rolling motion, affecting the final kinetic energy. To determine this, the equation for rotational energy of a sphere and its moment of inertia must be considered.
  • #1
conniechiwa
50
0
A solid sphere of uniform density starts from rest and rolls without slipping a distance of d = 3.9 m down a q = 35° incline. The sphere has a mass M = 4.6 kg and a radius R = 0.28 m.
https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys101/fall07/homework/08/03/3.gif

Suppose now that there is no frictional force between the sphere and the incline. Now, what is the translational kinetic energy of the sphere at the bottom of the incline?
 
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  • #2
I figured out that the velocity is 5.6 m/s, but I don't know what the KE tran would be at the bottom without friction.
 
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  • #3
The problem statement is incomplete, but I infer that you are being asked for the translational KE at the bottom for the two cases: the ball rolls down the incline, or it just slips down the incline (frictionless case).

If it just slips, then the KE final equals the PE initial, right? Why?

If it rolls, then some energy goes into the rolling motion (look up moment of inertia). What is the equation for the rotational energy of a sphere? What does that do to the final KE of the sphere at the bottom?
 
  • #4
nvm i figured it out.
 
  • #5
Doh!
 

FAQ: Sphere on Incline: Kinetic Energy of a Rolling Sphere

How does the angle of the incline affect the kinetic energy of a rolling sphere?

The angle of the incline affects the kinetic energy of a rolling sphere because it determines the amount of potential energy the sphere has at the start of its motion. As the angle of the incline increases, the potential energy also increases, resulting in a higher kinetic energy for the rolling sphere.

Can the shape of the sphere affect its kinetic energy on an incline?

Yes, the shape of the sphere can affect its kinetic energy on an incline. A sphere with a larger radius will have more rotational inertia, meaning it will require more energy to roll down the incline compared to a smaller sphere. This results in a lower kinetic energy for the larger sphere.

How does the mass of the sphere impact its kinetic energy on an incline?

The mass of the sphere has a direct impact on its kinetic energy on an incline. A heavier sphere will have more inertia, meaning it will require more energy to start rolling and maintain its motion. This results in a higher kinetic energy for a heavier sphere compared to a lighter one.

What is the relationship between the speed of the rolling sphere and its kinetic energy?

The speed of the rolling sphere is directly proportional to its kinetic energy. As the speed of the sphere increases, its kinetic energy also increases. This relationship is described by the equation KE = 1/2 * mv^2, where KE is kinetic energy, m is the mass of the sphere, and v is the speed of the sphere.

How does friction affect the kinetic energy of a rolling sphere on an incline?

Friction can decrease the kinetic energy of a rolling sphere on an incline. As the sphere rolls down the incline, it experiences frictional forces that act in the opposite direction of its motion. These forces convert some of the kinetic energy into heat, resulting in a decrease in the sphere's overall kinetic energy.

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