Question

What is newtons second law of motion and derive the expression for newtons second law of motion?​

Answer 1

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 .

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Answer 2

☆ Answer :-

• We have to prove the netwons second law of motion.

☆ Word Statement :-

★ Force acting on an object is directly proportional to the rate of change of its momentum with respect to time. It takes place in the direction in which the force applied.

Lets do Derivation:-

★ Derivation by Calculus Method:-

• Consider a body of mass m moving with a velocity of u

f force act on the body for time T velocity after t is v

Then ,

• Initial momentum of body is mu
• Final momentum of body is mv
• Change in momentum is ( mv - mu )

↠ m{ v - u }

Time taken = t - 0 ↠ t

Rate of change of p ↠ Change in momentum / Time taken

↠ m( v - u ) / t. ......... 1

According to statement the force is directly proportional to the rate of change of momentum. So,

↠F proportional to m( v - u ) / t

From 1st equation of motion

↠ v = u + at

OR

↠ v - u / t = a .......... 2

From 1 & 2

F proportional ma

OR

↠ F = kma. { where k is constant }

F = kdp/dt (p= momentum)

F = dp/dt (k= constant=1)

F = dmv/dt (p=mv)

F = mdv/dt

☆ Unit:-

↠Newton or kgm/sec²

↠ Dyne(CGS unit)

↠ 1 N = 10^5 dyne

☆ Newton’s second law of motion states :-

➹ The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.

➹ The first one is done using differential process.

☆ Newtons law uses :-

➹ Using Newton's Second Law we can know how much force is acting on the car.

➹ If the forces are unbalanced, the object will accelerate.

➹ F = ma is very important because it shows the relationship between forces and motion.

➹ It allows you to calculate the acceleration.

☆ Examples:-

↠ Cricket player increases time to reduce force or momentum$.$

↠ Karate player reduce time to increase force.

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