a) Without the wheels, a bicycle frame has a mass of 8.16 kg. Each of the wheels
ID: 2189502 • Letter: A
Question
a) Without the wheels, a bicycle frame has a mass of 8.16 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 2.85 m/s. (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 mass 816 kg moves forward at 0.285 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
a).
mass of the bicycle frame = 8.16 kg
mass of the solid disk wheel = 0.82 kg
radius of the solid disk wheel = 0.343 m
velocity of the bicycle = 2.85 m/s
total kinetic energy of the system = linear kinetic energy of the both solid disks wheel and mass of the frame+ rotation energy of the disks
total kinetic energy = (1/2)*m1v2+2*[(1/2)m2v2+(1/2)*I2] = (1/2)*m1v2+m2v2+I2
moment of the inertia of the disk, I =mr2
=v/r
therefore,
total kinetic energy = (1/2)*8.16*2.852+0.82*2.852+(0.82*0.3432)*(2.85/0.343)2= 46.46 J
b).
mass of the stone = 816 kg
velocity = 0.285 m/s
mass of the uniform cylindrical tree trunk = 82 kg
radius = 0.343 m
total kinetic energy of the system = linear kinetic energy of the both solid disks wheel and mass of the frame+ rotation energy of the disks
total kinetic energy = (1/2)*m1v2+2*[(1/2)m2v2+(1/2)*I2] = (1/2)*m1v2+m2v2+I2
moment of the inertia of the solid cylinder, I =(1/2)*mr2
=v/r
therefore,
total kinetic energy = (1/2)*816*0.2852+82*0.2852+(1/2)*(82*0.3432)*(0.285/0.343)2= 43.13 J
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.