The cart consists of a uniform purple platform, m_plat = 125 kg, that sits on th

Question

The cart consists of a uniform purple platform, m_plat = 125 kg, that sits on the two blue wheels. We will model each blue wheel as a uniform disk. Each blue wheel has radius r = 200 mm and mass m_Disk = 30 kg. We will model each wheel as a uniform disk. The coefficient of friction at all contact points is sufficiently high to prevent the wheels from slipping either relative to the fixed surface below or the purple platform above. The system is sitting at rest when an inquisitive investigator applies a horizontal force P = 200 N. Note that the wheels' mass centers move at half the velocity of the purple platform. Determine the speed of the platform after it has moved 2 m, starting from rest.

Explanation / Answer

use Work-energy theorem

Workdone = gain in kinetic energy(linear and rotational) of disks and platform

P*d = (1/2)*m_plot*v^2 + 2*(1/2)*m_disk*(v/2)^2 + 2*(1/2)*I*w^2

= (1/2)*m_plot*v^2 + 2*(1/2)*m_disk*(v/2)^2 + 2*(1/2)*(1/2)*m_disk*r^2*w^2

= (1/2)*m_plot*v^2 + 2*(1/2)*m_disk*(v/2)^2 + (1/2)*m_disk*(r*w)^2

= (1/2)*m_plot*v^2 + 2*(1/2)*m_disk*(v/2)^2 + (1/2)*m_disk*(v/2)^2

200*2 = (1/2)*125*v^2 + 30*v^2/4 + 30*v^2/8

==> v = 2.32 m/s

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