Results 1 to 2 of 2

Math Help - Extra credit word problem

  1. #1
    Newbie
    Joined
    Oct 2006
    Posts
    4

    Extra credit word problem

    I need some help with this bonus problem. Any help would be appreciated.

    A train rolls down a track at 60mph. It has wheels with radius = 15 in. The wheels contain a flange designed to hold the train on the track that extends 1 in from the radius of the riding surface

    Since Point A (on the flange) is farther from the center of the wheel than Point B (the wheel), it is moving faster than B.

    Due to this phenomenon, there is portion of the rotation that Point A is moving backward with respect to the ground.

    Find the duration of this time period in seconds (Accurate to 10 decimals).

    Hint: The answer is very near one hundredth of a second.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,804
    Thanks
    115
    Quote Originally Posted by anna_sims View Post
    ...
    A train rolls down a track at 60mph. It has wheels with radius = 15 in. The wheels contain a flange designed to hold the train on the track that extends 1 in from the radius of the riding surface
    Since Point A (on the flange) is farther from the center of the wheel than Point B (the wheel), it is moving faster than B....
    Hi,

    I've attached a diagram of the described situation.

    R is the radius pointing to A resp. A'. R = 16"
    r is the radius pointing to B. r = 15"

    When the wheel performs the angle \alpha, the the point A moves back.

    You've got right triangles so you can calculate \alpha:

    \cos(\frac{1}{2} \alpha)=\frac{15}{16}. Thus \alpha = 40.728°

    The perimeter of the (active) wheel = p=2 \pi \cdot r=30\pi ft

    Now calculate the number of revolutions per second. I've got 8.8837885 rps. (Please check my result carefully. I'm the king of mistakes here!).

    That means the wheel performs 8.8837885 * 360° = 3198.16° per second.

    The time which is needed to perform the angle \alpha:

    t=\frac{40.728 ^\circ}{3198.16^\circ} \approx 0.012734807 s

    (By the way: Why do you want a time exact to billionst second?)

    EB
    Attached Thumbnails Attached Thumbnails Extra credit word problem-eisenbahnrad.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. could use some help on an extra credit problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 10th 2011, 03:48 PM
  2. Replies: 7
    Last Post: October 11th 2009, 10:45 AM
  3. Calc 2 extra credit problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 17th 2009, 04:38 AM
  4. Extra-credit problem
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: March 17th 2008, 08:25 PM
  5. extra credit problem i got :(
    Posted in the Algebra Forum
    Replies: 10
    Last Post: June 17th 2006, 07:01 PM

Search Tags


/mathhelpforum @mathhelpforum