A rectangular gate is inclined at an angle of 30 degrees from the horizontal. It
ID: 1824448 • Letter: A
Question
A rectangular gate is inclined at an angle of 30 degrees from the horizontal. It is 4 ft wide by 6 feet long. If it is hung from its upper end which is 8 feet below the waters top edge, what minimum applied force (bottom) is needed to open the gate?(in kips)A rectangular gate is inclined at an angle of 30 degrees from the horizontal. It is 4 ft wide by 6 feet long. If it is hung from its upper end which is 8 feet below the waters top edge, what minimum applied force (bottom) is needed to open the gate?(in kips)
A rectangular gate is inclined at an angle of 30 degrees from the horizontal. It is 4 ft wide by 6 feet long. If it is hung from its upper end which is 8 feet below the waters top edge, what minimum applied force (bottom) is needed to open the gate?(in kips)
Explanation / Answer
It will depend greatly on the door. The equation for torque is r(displacement vector from axis) X F(force). The torque required to open the door will be the same as the torque required to overcome the static friction in the door hinges. Apply enough torque, the static friction will be overcome, and the door will start to move. Apply even more torque, and the door will open faster. The friction in the hinges will be very different for different doors and different hinges. Heavier doors will probably, on average, be harder to open because gravity will likely be causing a torque on the hinges, increasing normal forces within the hinge. Old or rusty hinges will obviously also require more torque than new or well designed hinges. If you are feeling ambitious, you could devise an experiment to find the torque required to open your door. Tie a rope to the knob, set up a pulley on a tripod or stand, and run the rope over the pulley. Attach weights, starting small and adding more, until the door opens / moves. Then, the torque required to open your door is T=Rwg, where r is the distance in meters from hinge to knob, w is the mass in kilograms of the weights, and g is 9.8. Or you could make a rough estimate. Most doors, i would imagine, are fairly easy to open and would be under 50N.