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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Subjects
Science State Board
Class 10
Laws of motion
Textbook questions

27. Answer in detail V

Exercise condition:

5 m.

Deduce the equation of a force using Newton’s second law of motion.

Consider,

‘\(m\)’ be the mass of a moving object, moving along a straight line with an initial speed of ‘\(u\)’ after the time ‘\(t\)’, the velocity of the object changes to ‘\(v\)’ due to the influence of an unbalanced external force '\(F\)'. Then,

Initial momentum of the body (\(P_i\)):

\(m \times t\)
\(m \times v \times t\)
\(m \times v\)
\(m \times u\)

Final momentum of the body (\(P_f\)):

\(m \times v\)
\(m \times u\)
\(m \times t\)
\(m \times v \times t\)

Change in momentum,

\(\Delta p\ =\ P_{f}-P_{i}\)
\(\Delta p\ =\ (m\times P_{f})-(m \times P_{i})\)
\(\Delta p\ =\ (m\times P_{i})-(m \times P_{f})\)
\(\Delta p\ =\ P_{i}-P_{f}\)

According to Newton's Second law,

\(Force\ \propto \frac{Change\ in\ momentum}{Mass}\)
\(Force\ \propto \frac{Change\ in\ momentum}{Time}\)
\(Force\ \propto \frac{Momentum}{Time}\)
\(Force\ \propto \frac{Momentum}{Mass}\)

Substituting the Values,

\(F \propto \frac{m \times t}{(v-u)}\)
\(F \propto \frac{m}{(v-u)\times t}\)
\(F \propto \frac{m \times(v-u)}{t}\)
\(F \propto \frac{(v-u)\times t}{m}\)

\(Force (F) = Mass (m) \times Velocity (v) \times Time (t)\)
\(Force (F) = Mass (m) \times Velocity (v)\)
\(Force (F) = Mass (m) \times Acceleration (a)\)

is needed to retain the motion of an object moving with uniform velocity.
Whenever the net force acting on an object is to zero, the velocity of the object will definitely change.
Thus, a change in momentum occurs in force. The change may happen either in magnitude or in direction, or in both.

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