Question

If you try opening a door by pushing too close to the side where the hinges are, you may find it difficult to push open. Suppose you are trying to open a door that is 75 cm wide. a. If you push on the door at a point 15 cm away from the hinges, what is the mechanical advantage? b. What is the best mechanical advantage that you can obtain for any door that you simply push open?

Answer 1

The best mechanical advantage that can be obtained for a door that is opened by simply pushing is 2

Step-by-step explanation:

The parameters given are;

Width of the door = 75 cm

Point of pushing the door = 15 cm from the hinges

The mechanical advantage, MA is given by the relation

`MA = (Door \, force)/(Applied \, force) = (Point \ of \ pushing \ the \ door)/(Center \ of \ mass \ of \ door)`

The center of mass of an even door should be located at the middle, therefore;

The center of mass of the door = 75/2 = 37.5 cm

Hence;

`MA = (15)/(37.5) = (2)/(5) = 0.4`

Which means more force than the door resistance will need to be applied to open the door

b. The best mechanical advantage is gotten by pushing farthest away from the hinges which for an even door is two times the location of the center of mass of the door

In the above question, we have;

`Best \ MA = (Point \ of \ pushing \ the \ door)/(Center \ of \ mass \ of \ door) = (75)/(37.5) = 2`

Hence the best mechanical advantage that can be obtained for a door that is opened by simply pushing = 2.