Is F=ma Newton's 2nd Laws of Motion?

That is a good question. F=ma is a special case of Newton's 2nd Law of Motion . Newton's second law states that: The rate of change of linear momentum is proportional to the applied force and acts in the same direction as the force. Newton's 2nd Law implies F=ma only if the mass of the change of momentum stays constant. Here I will write how you can get F=ma from the second law if the mass stays the same.

Final momentum: P_f=m_f x v_f , m_f is final mass, v_f is final velocity

Initial momentum: P_i=m_i x v_i , m_i is the initial mass, v_i is the initial velocity

now F is proportional to the rate of change of momentum.

F=k x (P_f - P_i)/t

F= k x ( m_f x v_f - m_i x v_i)/t

We know the mass stays the same so m_f=m_i

F= k x ( m_i x v_f - m_i x v_i)/t

Factorise m_i out

F= k x m_i x(v_f - v_i)/t

write m_i =m to make it look nicer

F= k x m x(v_f - v_i)/t

we know v_f = v_i + at from our SUVAT equations so

a = (v_f - v_i)/t by rearranging the equations

Plug this in the equation then we get

F=ma

MZ
Answered by Mohsin Z. Physics tutor

12841 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Explain quantitatively how an object can follow circular motion whilst on a ramp with no friction in the radial direction.


Why is an object that moves in a circular path accelerating when it has constant speed?


State similarity and difference between the electric field lines and the gravitational field lines around an isolated positively charged metal sphere.


If a star with a radius of 600000km has a surface temperature of 6000K, calculate its luminosity


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences