Solving problem dealing with PE + KE WITHOUT mass values?

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In the discussion, students are trying to determine the release height for a solid cylinder so that it matches the speed of a solid sphere at the bottom of a ramp, given that the sphere was released from 13.7 cm. The initial potential energy converts into kinetic energy, which includes both translational and rotational components. The moment of inertia plays a crucial role, as it differs between the cylinder and sphere, affecting their speeds. Participants are encouraged to reference educational materials on rolling dynamics for further clarification. Understanding these concepts is essential for solving the problem accurately.
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A group of students perform the same "Conservation of Mechanical Energy" experiment that you performed in lab by allowing a solid sphere and then a solid cylinder to roll down the ramp. The solid sphere was released from a height of 13.7 cm. From what height hcylinder should the solid cylinder be released so that it has the same speed as the solid sphere when it reaches the bottom of the ramp?


I just said "13.7 cm" but I got marked as "INCORRECT"
Does anyone know the answer?
 
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Hint: how is the moment of inertia of a cylinder different than that of a sphere?
 
The initial potential energy at the top of the ramp transforms into kinetic energy at the bottom. The kinetic energy is the sum of the translational KE and the rotational one. The rotational energy depends of the moment of inertia, which depends on the shape.

ehild
 
Wait what?
Can you put that in an equation?
I have no idea what you just said :(
 
Have you studied rotational dynamics? Do you know what rolling means?

Try to read http://www.physics.ohio-state.edu/~gan/teaching/spring99/C12.pdf. Scroll down, there is an example about rolling down an incline.

ehild
 

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