Derive the following: a) F = ma b) Law of conservation of momentum c) Universal law of gravitation d) Acceleration due to gravity is independent of the mass of an object e) Acceleration due to gravity on near the surface of earth
Answers
Explanation:
a )accordin to Newton's 2nd Law of motion, the rate of change of linear momentum of a body is directly proportional to the applied external force and in the direction of the force. It means that the continuing momentum will change faster when a bigger force is applied.
b ) Derivation of Conservation of Momentum
Consider two colliding particles A and B whose masses are m1 and m2 with initial and final velocities as u1 and v1 of A and u2 and v2 of B. The time of contact between two particles is given as t. B=m_{2}(v_{2}-u_{2}) (change in momentum of particle B)
c ) The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In equation form, this is F=GmMr2 F = G mM r 2 , where F is the magnitude of the gravitational force. G is the gravitational constant, given by G = 6.673 × 10−11 N·m2/kg2.
d ) Acceleration due to gravity is independent of mass. These two quantities are independent of each other. Light objects accelerate more slowly than heavy objects when force other then gravity are also at work. In this case the object is fallling but it is not considered as a free fall.
e ) The above acceleration is due to the gravitational pull of earth so we call it acceleration due to gravity, it does not depend upon the test mass. Its value near the surface of the earth is 9.8 ms-2. Therefore, the acceleration due to gravity (g) is given by = GM/r2.
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