A trapdoor on a stage has a mass of 19.2 kg and a width of 1.50 m (hinge side to handle si...

SKETCH:

The mass of the trap door is, and the tension in the rope is. The gravitational force acting on the trapdoor is pointed to the down direction. We can take the hinge is a pivot point. It is shown in below figure.

RESEARCH:

From triangle in figure (a), we have

. . . . . . (1)

From triangle in figure (b), we have

Substitute the equation (1) in above equation, we get

. . . . . . (2)

The torque acting on the door due to force of gravity is given by

. . . . . . (3)

The torque acting on the door due to tension in the rope is given by

. . . . . . (4)

When the system is in static equilibrium, then the net torque acting on the system about the pivot point must be zero.

Substitute the equations (3) and (4) in above equation, we get

Substitute the equation (2) in above equation, we get

. . . . . . (5)

CALCULATE:

Given data

The mass of the trapdoor,

The width of the trapdoor,

The distance from the hinge side of the door to handle on the door,

The height from the floor to handle on the door,

Using the equation (5), the tension in the rope can be calculated as