# Newton's Second Law of Motion

1. Jun 26, 2013

### andyrk

"The rate of change of linear momentum of a body with time is directly proportional to the net force acting on it."

=>F$\propto$dp/dt​
Then how do we suddenly come to:
F=dp/dt?​
We took the proportionality constant as 1 but why?
How to determine that the constant of proportionality is 1?

2. Jun 26, 2013

Linear momentum is defined as p=mv

Assuming there is no change in mass and differentiating,
you get F=dp/dt

3. Jun 26, 2013

### WannabeNewton

4. Jun 26, 2013

Expanding on WannabeNewton's post the Newton is defined such that the constant of proportionality is one. Imagine proving by experiment that a is proportional to F/M where the unit of F is yet to be defined. We can write:

a=kF/M

If now we define one Newton as being the resultant force that gives a mass of 1kg an acceleration of 1 metre per second squared then k becomes one.
I could come up with an alternative definition and suggest that the unit of force should be the turnip where one turnip is the resultant force that gives 2.7kg an acceleration 4.6 m/second squared. K would now be an awkward number and I dont think people will use my definition.

5. Jun 26, 2013

### PeterO

Defining the unit so that the constant of proportionality is 1 also explains why the Newton is such a whoosey amount, meaning that most forces encountered have a large value - like my weight is approx 1000N. A newton is more like the weight of small chocolate bars.

6. Jun 26, 2013

### andyrk

Not equal, proportional.
What about the proportionality constant then?

7. Jun 26, 2013