How Fast Does a Falling Window Hit?

[farshadian]

Hi I'm having trouble with my injury mechanics problem where a rigid window with frame falls from a vertical position on a person sitting below.

Homework Statement

The decorative wood-framed window below has been inadvertently left
unrestrained in a nominally stable vertical position. The window pivots around its base until it strikes a person on the top of the head. Model the falling window to determine the velocity at head contact. then estimate the force applied to the head if the impulse is over 5 ms (assumed triangular contact).

Density of wood is 0.673 g/cc and glass is 2.6g/cc

DIMENSIONS are
2.0m wide frame
1.2 m high
15 cm thickness

Frame width is 20 cm everywhere and glass is in center.

a person is sitting 1.1m away from the center of the base (path of contact is

Homework Equations

I know your supposed to use impulse and moment
and the parallel axis theorem. I can't figure out how to find the CoG for the block which is one of the first steps

The Attempt at a Solution

cirumfrance of the falling obj. about the person is = pi * r /4 = 0.864 m
Area of whole thing is 2m*1.2m = 2.4 m2
Glass area is 0.8*1.6= 1.28 m2
area of the frame is 1.12m2 and its volume is 0.0064m3
volume of frame is .168 m3
mass of frame is .113 g and the window is .0166g




can anyone point me in the right direction?

 

[tiny-tim]

welcome to pf!

hi farshadian! welcome to pf!

you need the moment of inertia of the whole window about the base (you can add the m.i. of the glass to that of the wood) …

what formulas do you know for https://www.physicsforums.com/library.php?do=view_item&itemid=31" of a rectangle?

(the area and volume don't matter)

show us what you get ​

 

[farshadian]

Ya i figured it out,

I think you can do it without parallel axis theorem But i used it.
Ixx = Ix + mr^2 = (xy^3/3 - xy^3/3) + m*y^2 = 41.5 m^4
^^^ for wood, repeate for glass)
angular accel. (alpha) which is torque over the above inertia
torque was mgh sin (90) , so
w (omega) = root (2 alpha) = v/r .: v = 8.78 m/s

impact wise, the triangle means peak accel is at half impusle time. so you find the force at that time. but that is a different part of the question.happy pi day!

 

[tiny-tim]

happy pi day!

many circular returns to you too!