Without the wheels, a bicycle frame has a mass of 7.49 kg. Each of the wheels ca

Question

Without the wheels, a bicycle frame has a mass of 7.49 kg. Each of the wheels can be roughly modeled as a uniform solid disk with a mass of 0.820 kg and a radius of 0.343 m. Find the kinetic energy of the whole bicycle when it is moving forward at 3.60 m/s. Before the invention of a wheel turning on an axle, ancient people moved heavy loads by placing rollers under them. (Modern people use rollers, too. Any hardware store will sell you a roller bearing for a lazy susan.) A stone block of mass 749 kg moves forward at 0.360 m/s, supported by two uniform cylindrical tree trunks, each of mass 82.0 kg and radius 0.343 m. No slipping occurs between the block and the rollers or between the rollers and the ground. Find the total kinetic energy of the moving objects.

Explanation / Answer

part A: Total KE of the system = KE trnas + KE rota

KEtotal = 0.5 mf V^2 + 0.5 Mw^2 + 0.5 Mw v^2 + ( 0.5 IwW^2 + 0.5 Iw W^2)

Upon Solving

KE = 0.5 mf V^2 + 3/2 Mw V^2

KE = (0.5 * 7.49 * 3.6^2) + (1.5 * 0.82 * 3.6^2)

KE = 64.47 Joules

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Trans KE = 0.5 ms V^2 + 0.5 mtee v^2 + 0.5 mtree v'^2

KE trans = 0.5 Ms v^2 + 0.5 mtrs V^2

KE rotational = 0.5 Is W^2 + 0.5 Itree W^2

I tree = 0.5 M tree

W = v'/ R = V/2R

KErot = 1/8 M tree v^2

KEtotal = 0.5 mt v^2 + 0.5 mtrv^2 + 1/8 m tre v^2

KE = 0.5 me v^2 + 3/8 mtrr v^2

KE = (0.5 * 749 * 0.36^2) + (3/8 * 82 * 0.36^2)

KE = 52.52 Joules

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