A 75 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much? Assume the earth is a perfect sphere. Explain why the readings differ.
Solution Step 1 of 6 Gravitational force is the force exerted by an massive object like earth on the other objects having mass. It is due to the weight of the object, as given below, when an object of mass m placed on table, Normal force is the force,which acts when an object comes in contact with other or the surface, there will be an resultant force which is perpendicular to the contact surface and it is know as normal force.As in figure below, for a book on the table, N is the normal force, Centripetal force is the force that is acted on the object in circular motion, which is directed towards the center. As in figure below 2 The centripetal force is given by Fc= mr Where m and v are the mass and velocity of the object under circular motion and r is the radius. Step 2 of 6 The pictorial representation of the given problem, Step 3 of 6 The free body diagram for the man on the north pole, At north pole, Due to gravitational force of the earth; weight will be acting downward as in figure above. Also due to the contact of man with the surface of earth, their will be a normal force that will be acts perpendicular to the surface of the earth and in magnitude, it is equal to the gravitational force. That is, n p F = mg……...1 G Where n is the normal force on man at north pole, F force due to gravity, m is the mass p G of man and g is acceleration due to gravity.