# Car door shutting at a certain acceleration

1. Feb 21, 2010

1. The problem statement, all variables and given/known data
A car has its door open at 90 degrees. The door is considered a uniform square sheet of steel of side .8 m and mass 20kg. The hinges on the door are frictionless. At time t = 0 the car accelerates with constant acceleration a = 3 m/sec^2. How long does it take the door to close?

2. Relevant equations
Torque = Mass * radius * acceleration
Torque = Mass * radius^2 * alpha

3. The attempt at a solution
T = 20 (Mass) * (.8)(Radius) * 3 (Acceleration)
T = 48
alpha = 48(Torque) / (.8^2)(Radius) * (20)(Mass) = 3.75
Now that I have angular acceleration, I need only to integrate twice to find the time.
omega = 3.75t
theta = 3.75t^2 / 2 theta = 90 degrees or pi/2 in radians so,
pi/2 = 3.75t^2 / 2 pi/3.75 = t^2 t = sqr root (pi/3.75)

t = .92 seconds

Hopefully these are the correct formulas, but I could use someone to check if these are right. Thanks in advance.

Last edited: Feb 22, 2010
2. Feb 22, 2010