A stationary truck has its rear door wide open as shown. At t = 0 the truck starts to accelerate with constant acceleration a then the door will begin to close and at any time 't' the door makes angle θ with its original orientation. Assume that the door has mass m uniformly distributed along its length L.
(i) The tangential force F t on door is equal to
Text Solution
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Ans.
(i)
Sol. Σ f t = f t – ma cos θ = – 
mL α ….(1)
Σ f n = f n – ma sin θ = 
mL ω 2 ….(2)
Also Στ = f t . 
= 
mL 2 α ….(3)
From (1) and (3) α = 
∴ f t = 
ma cos θ
(ii)
Sol. α = ω 
= 
∴ 
= 
d θ
ω = 
(iii)
Sol. ω = 
∴ 
= 
∴ t = 
d θ
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