Question

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

Answer 1

Answer:

  y /y₀ = 1 /√2 = 0.70

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.