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ohaa [14]
3 years ago
7

The objects listed are placed at the top of a ramp and roll down to the bottom without slipping. Assuming that there is no air r

esistance, rank them in order from fastest average rolling speed to slowest. a. large marble b. basteball c. manhole cover d. wedding ring
Physics
1 answer:
Thepotemich [5.8K]3 years ago
7 0

Explanation:

For each object, the initial potential energy is converted to rotational energy and translational energy:

PE = RE + KE

mgh = ½ Iω² + ½ mv²

For the marble (a solid sphere), I = ⅖ mr².

For the basketball (a hollow sphere), I = ⅔ mr².

For the manhole cover (a solid cylinder), I = ½ mr².

For the wedding ring (a hollow cylinder), I = mr².

If we say k is the coefficient in each case:

mgh = ½ (kmr²) ω² + ½ mv²

For rolling without slipping, ωr = v:

mgh = ½ kmv² + ½ mv²

gh = ½ kv² + ½ v²

2gh = (k + 1) v²

v² = 2gh / (k + 1)

The smaller the value of k, the higher the velocity.  Therefore:

marble > manhole cover > basketball > wedding ring

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