Rolling and sliding sphere on flat surface

Therefore, the initial kinetic energy of B is equal to the initial linear kinetic energy, which is 1/2 mv^2. The ratio of Vb/Va is equal to 1. In summary, the ratio of Vb/Va is equal to 1, as ball B slides without rotating and therefore has the same initial kinetic energy as ball A, which rolls without slipping.
  • #1
versatilehong
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Homework Statement



In a laboratory experiment two spherical balls are launched on a °at surface. Both are
uniform spheres of radius R and mass m. They are both given the same amount of
initial kinetic energy K0. However:
-ball A rolls without slipping
-ball B slides without rotating
What is the ratio Vb/Va?

Homework Equations


Moment of inertia of solid sphere= 2/5 (mr^2)


The Attempt at a Solution


for the rotating, I did

KErolling=1/2 mv^2 = 1/2 Iw^2 => KEo = 7/10 mv^2

then for the slipping, I'm having a bit of problem. I am not sure if i have to include the friction force or not. Without friction, it'd be F=ma, then KEo=ma, I'm not sure if i can substitute KEo as F or not..

Thanks
 
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  • #2
Since B slides without rotating, the friction force must be zero.
 

1. What is the difference between rolling and sliding of a sphere on a flat surface?

The main difference between rolling and sliding of a sphere on a flat surface is the type of motion. Rolling involves both translation and rotation, while sliding only involves translation. In rolling, the sphere maintains contact with the surface at all times, while in sliding, there is no contact between the surface and the sphere.

2. What factors affect the speed of a rolling sphere on a flat surface?

The speed of a rolling sphere on a flat surface is affected by several factors, including the mass and size of the sphere, the force applied to the sphere, and the friction between the sphere and the surface. The shape and smoothness of the surface can also impact the speed of the rolling sphere.

3. How does the shape of the surface affect the motion of a rolling sphere?

The shape of the surface can greatly affect the motion of a rolling sphere. A flat surface allows for smooth and consistent rolling, while a curved or uneven surface may cause the sphere to deviate from its path or even stop rolling altogether. The shape of the surface also impacts the amount of friction between the sphere and the surface, which can affect the speed and direction of the rolling motion.

4. Can a rolling sphere change direction on a flat surface?

Yes, a rolling sphere can change direction on a flat surface. This change in direction can be caused by external forces, such as a change in the direction of the applied force, or by changes in the surface, such as a curved or angled incline. The shape and size of the sphere can also impact its ability to change direction while rolling.

5. How does the speed of a rolling sphere change over time?

The speed of a rolling sphere can change over time due to several factors. As the sphere rolls, it may encounter changes in the surface, such as inclines or declines, which can impact its speed. Friction between the surface and the sphere can also cause a decrease in speed over time. Additionally, the force applied to the sphere, as well as the sphere's shape and size, can also affect its speed as it rolls over time.

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