Answers are given. I need to understand the mathmatical process of how to get th

Question

Answers are given. I need to understand the mathmatical process of how to get them.

(a) Without the wheels, a bicycle frame has a mass of7.15kg. 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 at4.15m/s.

ANSWER: 82.8 J

(b) 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 mass715kg moves forward at0.415m/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.

ANSWER: 66.9 J

Explanation / Answer

velocity = 4.15 m/s mass of whole bicycle (including wheels ) = 7.15 + 2*0.82 = 8.79 Kg so , translational K.E = 0.5 * (8.79) * 4.15^2 = 75.69 J for wheels . Inertia = M * ( R^2 ) / 2 = 0.82 * (0.343^2) /2 = 0.04824 kg m2 w = angular velocity = velocity / radius = 4.15/0.343 = 12.1 rad/sec so , rotational K.E = 2*(0.5)* 0.04824*(12.1^2) = 7.0628 J so total K.E = 75.69 + 7.0628 = 82.753

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