A car accelerates uniformly from rest. Initially, its door is slightly ajar (open). Calculate how far (in m ) the car travels before the door slams shut. Assume the door has a frictionless hinge, a un

Question

A car accelerates uniformly from rest. Initially, its door is slightly ajar (open). Calculate how far (in m ) the car travels before the door slams shut. Assume the door has a frictionless hinge, a uniform mass distribution and a length of 1.2 m from front to back.

TestHub · Accepted Answer

​ τ = ma ( 2 ℓ ​ ) sin θ ​ α = ( 3 m ℓ 2 ​ ) ( ma 2 ℓ ​ ) sin θ ​ ; α = 2 ℓ 3 a ​ sin θ ​ for slightly open θ is very small sin θ ≈ θ α = ( 2 ℓ 3 a ​ ) θ ; d t 2 d 2 θ ​ = ( ω 2 ) θ θ = θ 0 ​ cos ( ω t ) time taken to shut = 4 T ​ = 4 2 π / ω ​ = 2 2 ℓ 3 a ​ ​ π ​ = π 6 a ℓ ​ ​ distance travelled by car = 0 + 2 1 ​ at 2 = 2 1 ​ ap 2 6 a ℓ ​ = 12 π 2 ℓ ​ = 12 ( 10 ) ( 1.2 ) ​ = 1 m

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