Question

DERIVE AN EXPRESSION FOR FORCE FROM NEWTON'S SECOND LAW OF MOTION

Answer 1

Answer:

Newton's second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In equation form, Newton's second law of motion is a=Fnetm a = F net m .

Answer 2

Answer:

• The Expression is F = M a

Explanation:

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Statement:

The rate of change of momentum is directly proportional to the External Force applied to the body.

Units:

• S.I Unit = Newton.
• C.G.S Unit = dynes.

Now, from the statement.

$\displaystyle \dashrightarrow\tt F_{ext} \propto \left(\dfrac{d\;P}{d\;t}\right)\\\\\\\dashrightarrow\tt F_{ext} \propto \left(\dfrac{d\;(M\;v)}{d\;t}\right)\\\\\\\dag\tt \qquad P=Mv\\\\\\\dashrightarrow\tt F_{ext}\propto M\;.\;\left(\dfrac{d\;v}{d\;t}\right)\\\\\\\dashrightarrow\tt F_{ext}\propto M\;.\;a\\\\\\\dag\tt \qquad\left(\dfrac{d\;v}{d\;t}\right)=a\\\\\\\dashrightarrow\tt F_{ext}=K\;(M\;a)\\\\\\\dag\tt \qquad K=Constant$

Now, the units of Force are taken in such a way that the Constant i.e. K has a value of 1.

Therefore,

$\displaystyle \dashrightarrow\tt F_{ext} = 1\times (M\;a)\\\\\\\dashrightarrow \large{\underline{\boxed{\red{\tt F_{ext}=M\;a}}}}$

Hence Derived!

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