Question

You open a door pushing it at 0.40 m from the axis of rotation, perpendicularly to the door. the door is 31 kg and has a width of 0.45 m , your force is 23 n . how long does it take to rotate the door to 60 degrees from zero (closed)? express your answer with the appropriate units.

Answer 1

To calculate the time it takes to rotate the door to 60 degrees, first calculate the torque exerted on the door. Then, calculate the moment of inertia of the door. Next, use these values to calculate the angular acceleration. Finally, use the angular displacement and angular acceleration to find the time.

Step-by-step explanation:

To calculate the time it takes to rotate the door to 60 degrees from the closed position, we need to first calculate the torque exerted on the door. We can use the formula:

Torque = Force x Distance

Torque = 23 N x 0.4 m = 9.2 N·m

Next, we need to calculate the angular acceleration of the door. We can use the formula:

Angular Acceleration = Torque / Moment of Inertia

In this case, the moment of inertia of a rectangular door can be approximated as 1/3 x Mass x Width².

Moment of Inertia = 1/3 x 31 kg x (0.45 m)² = 3.42 kg·m²

Now we can calculate the angular acceleration:

Angular Acceleration = 9.2 N·m / 3.42 kg·m² = 2.69 rad/s²

Finally, to find the time it takes to rotate the door to 60 degrees, we can use the formula:

Angular displacement = 60 degrees = (60 degrees) x (π/180 radians per degree)

Time = (√(2 x Angular Displacement / Angular Acceleration)

Time = (√(2 x (60 degrees x π/180 radians per degree) / 2.69 rad/s²) = 3.53 seconds