im having trouble with a couple questions.. please help if u can?

Question

... a solid sphere and a hollow sphere of the same mass and radius roll without slipping at the same linear speed. Which has more kinetic energy (solid or hollow) or are they the same?

Answer 1

The hollow sphere has more kinetic energy because its rotational energy is much higher. Since the mass of the two is the same, all of the mass of the hollow one is out at almost the end of the radius while the solid one is closer to the center.
As an example, if both were 10 cm radius and both weighed 10 kg and the hollow one was 1 cm thick, then the radius of rotation of the mass of the hollow one would be 9.5 cm and its density would have to be
10 cm sphere=4.1888e+3 cm3, 9 cm hollow = 3.0536e+3
volume of shell 1.1352e+3 cm3
density of solid = 10/4.1888e+3 = 2.38731856 gm/cm3
density of shell = 10/1.1352e+3 = 8.80902044 gm/cm3
http://www.pha.jhu.edu/~broholm/l19/node8.html#SECTION00012020000000000000
The extra energy is provided by the extra force that it takes to get the hollow shell moving to the same velocity as the solid. The information in the first answer would be correct if the spheres were just moving, not rolling

Answer 2

This is a simple question! If two objects have the same mass and they are moved the same vertical distance under the influence of the same force it is a no brainer that they must have the same kinetic energy.

After all, the GPE of an object at the top of a cliff still equals KE of the same object at the bottom. Since GPE is the mgh and you said the m, g, and h of both objects is the same the KE at the bottom must be equal.

Now, if you had asked, which sphere would win the race down the incline then the answer would have to be that the solid sphere would win. This is because the solid sphere has less rotational inertia than the hollow sphere.

You can get a sense of this yourself by trying to lift a chair with you arm straight out in front of you verses your arm with your elbow bent. Since your arm held straight out has a larger ‘radius’ it is MUCH harder to hold the chair, just as it is ‘harder’ for the hollow sphere to get rolling down the incline.

With you elbow bent the chair is much easier to hold because the ‘radius’ is shorter and thus, with the solid sphere, with its mass closer to its center, it has an ‘easier’ time rolling down the incline.

Answer 3

The First answer is OK only the formula is wrong. It should be
K = 1/2*M*V*V . As you can see, the kinetic energy is a function of the mass and the velocity. Thus, if both spheres have the same mass and the same linear speed, then they have the same kinetic energy.

Thanks,

Miki.

Answer 4

The same.Force[energy]=mass x velocity,which you stated are equal

Answer 5

c. cluster suicides a. social-cognitive d. irrational Thats my vote. Good luck I am really sure of the first one though.