Respuesta :
Answer:
0.674 s = t
Explanation:
Assuming that the door is completely open, exena need to rotate the door 90°.
Now, using the next equation:
T = I∝
Where T is the torque, I is the moment of inertia and ∝ is the angular aceleration.
Also, the torque could be calculated by:
T = Fd
where F is the force and d is the lever arm.
so:
T = 220N*1.25m
T = 275 N*m
Addittionaly, the moment of inertia of the door is calculated as:
I = [tex]\frac{1}{3}Ma^2[/tex]
where M is the mass of the door and a is the wide.
I =[tex]\frac{1}{3}(750/9.8)(1.25)^2[/tex]
I = 39.85 kg*m^2
Replacing in the first equation and solving for ∝, we get::
T = I∝
275 = 39.85∝
∝ = 6.9 rad/s
Now, the next equation give as a relation between θ (the angle that exena need to rotate) ∝ (the angular aceleration) and t (the time):
θ = [tex]\frac{1}{2}[/tex]∝[tex]t^2[/tex]
Replacing the values of θ and ∝ and solving for t, we get:
[tex]\sqrt{\frac{2(\pi/2)}{6.9 rad/s}}[/tex] = t
0.674 s = t
