1. Not finding help here? Sign up for a free 30min 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!

Direction of force exerted by ground for the ladder problem

  1. Jan 3, 2017 #1
    This question pertains to the classic ladder-leaning-against frictionless wall scenario. The system is in static equilibrium. The ladder is thin and can be assumed to be made of a homogeneous material so that the center-of-mass lies at the geometric center.

    The forces in this scenario is well-known, and diagrammed as follows. This type of problem can be solved by equating the sum of forces and torques to zero at any and all points, as is commonly done in static equilibrium problems.
    Pic14.jpg

    My question is: Is the direction of the force exerted by the ground on the ladder aligned with the ladder itself? That is, is the force exerted by the ground on the ladder in the direction \theta, as shown in the diagram?

    This hypothesis seems plausible to me, because as theta becomes large (ladder is almost vertical), the force in question is also almost at 90 degrees. As theta approaches zero (ladder is almost horizontal), there is a large horizontal component, so the force is almost horizontal (to the right).

    Could anyone confirm or disprove my hypothesis?
     
  2. jcsd
  3. Jan 3, 2017 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Suppose it were. Consider moments about the mid point of the ladder.
     
  4. Jan 3, 2017 #3

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Why not solve the equations and see for yourself?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted