What Happens When a Child Walks on a Plank Supported by Pillars?

[mogley76]

Homework Statement

A 5m long uniform plank of mass 8kg is supported by two pillars at 0.5m and 3m from the left hand end. a 20kg child walks along the plank towards the right hand end. calculate

1. the position the child ia at when the plank begins to tip
2. the forces exerted by the supporting pillars at that moment

Homework Equations

none given

The Attempt at a Solution

(8/5) = mass of 1.6kg per metre length of the plank.
The right pillar is positioned at 3m. from the left end, and 2m. from the right.
Torque left = ((3 x 1.6)/2) x 3m. = 7.2kg/m.
Torque right = ((2 x 1.6)/2) x 2m. = 3.2kg/m.
Difference in torques = (7.2 - 3.2) = 4kg/m.
1) (4kg-m/20kg) = 0.2m. the child is right of the right pillar, when tipping begins.
2) At that moment, the left pillar is exerting no force. The right exerts all the force.
(8kg + 20kg) x 9.8 = force of 274.4N. exerted by right pillar.

is this correct?

 

[Quinzio]

yes, correct