Mechanics is the study of the motions of objects and the forces that change it.
Long ago Isaac Newton found out that the change of momentum is equal to force .
This is expressed in mathematics like this :
In other words, Newton found out that force is equal to mass times acceleration .
With this equation, F=ma , a lot about the motion of objects can be found out.
For example, John was pushing Mary (50 kg) with a force of 5 Newtons for 10 seconds. What
would be the velocity of Mary (who was ice skating) after 10 seconds?
This type of questions can be solved with Newton's equation F=ma . Here are
the steps involved to solve the question.
To find the velocity v, both sides must be integrated :
Since F=5 Newtons, m=50 kg
To find the constant C, the initial condition must be given. The initial condition
in this problem is that Mary has a velocity of 0 at time 0, or t=0, v=0.
The equation for Mary's velocity turns out to be :
After 10 seconds her velocity would be :
Even the position of Mary after 10 seconds can be found :
Since ,
After 10 seconds of 5 Newtons of push, Mary would have a velocity of 1 m/s and a
position of 5 (m) away from her original position.
In conclusion, F=ma enables us to find the velocity, mass, force, acceleration,
and the position of moving objects .