Car door shutting at a certain acceleration

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The discussion revolves around calculating the time it takes for a car door to close when the car accelerates at 3 m/sec². The door is modeled as a uniform square sheet of steel with specific dimensions and mass, and the solution involves calculating torque and angular acceleration. The initial calculations yield a torque of 48 and an angular acceleration of 3.75. However, there are questions raised about the use of moment of inertia and the physical principles applied in the calculations. The thread highlights a need for clarification on the formulas used and suggests reviewing relevant physics concepts.
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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.
 
Last edited:
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Hi Mastablade! :smile:

Sorry, I don't understand any of this. :redface:

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. :smile:​
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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