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How long would it take Exena to close the door if she doubled the magnitude of the force applied to the door

User Npjohns
by
7.3k points

1 Answer

2 votes

Answer:

y /y₀ = 1 /√2 = 0.70

Step-by-step explanation:

To close the door, a torque must be applied in such a way that there is an angular acceleration and after a period of time the angle of the door moves.

If the force is doubled keeping the other parameters without altering angular acceleration is

F r = I α

α = F r / I

if we double the force

α = 2F r / I

α=2 α₀

let's use the angular kinematics relations

θ = w₀ t + ½ α t²

we assume the door was still before pushing it

θ = ½ a t²

t = √ (2θ / a)

as we saw the angular acceleration is double

t = √ (2θ / 2a₀)

t = 1 / √2 a₀

the relationship between the two times is

y /y₀ = 1 /√2 = 0.70

This time that has been reduced closes the door.

User NuAlphaMan
by
8.2k points
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