Question

State newton's 2nd law of motion and prove F = ma

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Answer 1

Explanation:

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

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Answer 2

AnSwer :-

Newton's 2nd law states that,

❝ The rate of change of linear Momentum of a body with time is proportional to the net external force acting on it.❞

➝ F$\sf _{net}$ = dp/dt

➝ F$\sf _{net}$ =d(mv)/dt

➝ F$\sf _{net}$ = m(dv/dt) + v(dm/dt)

➝ F$\sf _{net}$ = ma + v(dm/dt) [ if mass is variable]

➝ F$\sf _{net}$ = ma [ if mass is constant]

Explaination :-

Consirder a body of mass "m" moving with a velocity "v" Let an external force "F" is acting on it in the direction of the velocity, it's velocity changes from v to v + ∆v during an internal "∆t".

The liner Momentum "mv" changes to "m(v + ∆v)"

The change in Momentum ∆p = m∆v

The rate of change in Momentum =∆p/∆t= m∆v/∆t

According to the second law,

• F ∝ rate of change of Momentum

F = K ∆p/∆t,

where, K is proportionality constant.

As the time interval ∆t → 0 , the term ∆p/∆t becomes the derivative dp/dt

thus,

➝ F = K dp/dt

➝ F = dp/dt

➝ F = d(mv)/dt

➝ F = m(dv/dt)

➝ F = ma ⠀⠀⠀⠀⠀⠀⠀[ ∵ a = dv/dt]

hence proved...

|| the second law can also be written as F = K ma to make K = 1 ||

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