1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Gears Problem -- tray for holding the disk in a tabletop Blu-ray player

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    The mechanism that operates the load/unload tray for holding the disk in a tabletop Blu-ray player uses nylon spur gears, a rack, and a belt drive. The gear that meshes with the rack has a module of 2.5 mm. The gears have the numbers of teeth indicated, and the two sheaves have diameters of 7 mm and 17 mm. The rack is connected to the tray that holds the disk. For the tray to move at 0.1 m/s, how fast must the motor turn?

    2. Relevant equations

    3. The attempt at a solution
    d_{1} \omega_{1} = d_{2} \omega_{2} \\
    \omega_{2} = \frac{\omega_{1}d_{1}}{d_{2}} \\
    N_{4} \omega_{4} = N_{3} \omega_{3} \\
    N_{4} \omega_{5} = N_{3} \omega_{2} \\
    N_{4} \omega_{5} = N_{3} \frac{\omega_{1}d_{1}}{d_{2}} \\
    \omega_{1}=\frac{N_{4}\omega_{5}d_{2}}{N_{3}d_{1}} \\

    I know that the module of the gear that meshes with the rack is 2.5[mm] so the module of the rack must also be 2.5[mm].
    v=0.1[m/s]=0.1[\frac{m}{s}] \times 60[\frac{s}{min}]= 6[\frac{m}{min}] \\
    v=6 [\frac{m}{rev}][\frac{rev}{min}] = 6[\frac{m}{rev}][rpm] \\

    I need help from here.

    Also, why is the units of the module [mm] and not [mm/teeth]? The formula for it is 2r/N
    Last edited: Oct 20, 2014
  2. jcsd
  3. Oct 20, 2014 #2
    v=0.1[m/s]=0.1[\frac{m}{s}] \times 60[\frac{s}{min}]= 6[\frac{m}{min}]\\
    v=6 [\frac{m}{rev}][\frac{rev}{min}] = x\omega_{5} \\
    x=14[\frac{tth}{rev} \times 2.5 \frac{mm}{tth}=0.035 \frac{m}{rev} \\
    v=6 [\frac{m}{rev}][\frac{rev}{min}] = 0.035 \frac{m}{rev} \times \omega_{5} \\
    \omega_{5}=171.4285714 [rpm]= 171.4285714 [rpm] \times 2\pi \frac{rad}{rev} \times \frac{1}{60} \frac{min}{s}= 17.95195802 [rad/s]

    Did I get the angular velocity correctly for the gear meshed with the rack/tray?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted