Q. 445.0( 1 Vote )

The door of an Amirah is 6 ft. high, 1.5 ft. wide and weighs 8 kg. The door is supported by two hinges situated at a distance of 1 ft. from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude.

Answer :

The magnitude of the force exerted is 43N


Given


The dimensions of an Amirah door are given as 6ft high, 1.5ft wide, and weighs a total of 8 kg, the hinges are situated at a distance of 1ft from the end on both sides.


Formula Used


Using Newton’s second law of motion, we know that force is equivalent to the product of mass and acceleration and the resulting force when multiplied by the radius at which it is turned it becomes torque.




where


F is the force applied on the object, m is the mass of the object, r is the length of rotation of the object and is the torque applied.


Explanation


The force exerted by the two hinges are




Hence, if the value of reactionary forces is equal





Let, the reactionary forces of the first hinge be




With the force and reactionary forces value derived let us find the value of resultant force which is





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