Car door shutting at a certain acceleration

[Mastablade]

Homework Statement

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?

Homework Equations

Torque = Mass * radius * acceleration
acceleration = radius * alpha
Torque = Mass * radius^2 * alpha

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.

 

[tiny-tim]

Hi Mastablade!

Sorry, I don't understand any of this.

What is the torque ?

Why are you not using moment of inertia ?

What physical principle are you using ?

Go back to your book, and read the chapter again. ​