Hollow sphere rolling up a ramp

• mjolnir80
In summary, the problem involves a hollow sphere rolling at 5 m/s on a horizontal floor before coming to a 30 degree incline. The method to solve this problem involves using the conservation of energy equation, 1/2mv^2 + 1/2I\omega^2 = mgh, and finding the rotational inertia of a hollow sphere. The condition for rolling without slipping is also important to consider. Even though the radius of the sphere is not given, it may not be necessary to solve the problem.
mjolnir80

Homework Statement

a hollow sphere is rolling long a horizontal floor at 5 m/s when it comes to a 30 degree incline. how far up the incline does it roll before reversing direction?

The Attempt at a Solution

it seems like conservation of energy would work best for this problem
1/2mv^2 + 1/2I$$\omega$$^2 = mgh
im just having some problems finding $$\omega$$
am i doing this right? and if so any clues on how to find $$\omega$$?

Assuming the sphere is rolling without slipping, ω and v are directly related. (What's the condition for rolling without slipping?) What's the rotational inertia of a hollow sphere?

v=$$\omega$$r right? but we don't have the radius of the sphere
or do we....?

mjolnir80 said:
v=$$\omega$$r right?
Right.
but we don't have the radius of the sphere
or do we....?
Maybe you don't need it. (Just call it "r" and see what happens.)

What is a hollow sphere?

A hollow sphere is a three-dimensional shape that is completely round and has an empty space inside. It is similar to a solid sphere, but with a hollow center.

What is a ramp?

A ramp is a sloping surface that is used to move objects from a lower level to a higher level. It is often used to make it easier to move objects that are too heavy to be lifted straight up.

How does a hollow sphere roll up a ramp?

A hollow sphere rolls up a ramp due to the force of gravity. When the sphere is placed at the bottom of the ramp, gravity pulls it downwards. As it rolls, it gains kinetic energy, which allows it to overcome the incline of the ramp and roll upwards.

What factors affect the rolling of a hollow sphere up a ramp?

The factors that affect the rolling of a hollow sphere up a ramp include the angle of the ramp, the weight of the sphere, and the surface of the ramp. A steeper ramp will require more force to overcome, a heavier sphere will roll slower, and a smoother surface will result in a smoother and faster roll.

What is the significance of studying the rolling of a hollow sphere up a ramp?

Studying the rolling of a hollow sphere up a ramp is important for understanding the principles of motion, such as gravity and kinetic energy. It also has practical applications, such as in the design of ramps for transportation and the development of toys and games.

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