1
$\begingroup$

Does this form of reasoning have a name. I often see it but am a little confused on how to read/understand it and wanted to look more into it but don't know what to call it

Ex. Let's call the force law between the objects $F(m_1,m_2,r)$. We know that if we put the body $m_1$ in free fall, the acceleration doesn't depend on the mass, so

$$F(m_1,m_2,r)=m_1G(m_2,r)$$ So that the mass will cancel in Newton's law to give a universal acceleration. This gives you the relation

$$F(\lambda m_1,m_2,r)=\lambda F(m_1,m_2,r).$$

Source: Combining Proportions to get Newton's Law of Universal Gravitation

Improve this question
$\endgroup$
6
  • $\begingroup$ Are you asking whether there is a name for mathematical reasoning in general (based on the title of the question), or specifically a name for the type of scaling argument you give in your example? $\endgroup$
    – Andrew
    Sep 28, 2021 at 12:41
  • 2
    $\begingroup$ A function with this property is called homogeneous. In this case homogeneous of degree 1. If that's what your asking $\endgroup$
    – tomtom1-4
    Sep 28, 2021 at 12:50
  • 1
    $\begingroup$ This is not exactly the case, but dimensional analysis helps you to check the soundness of mathematical relations between physical quantities. $\endgroup$
    – Davide Dal Bosco
    Sep 28, 2021 at 12:57
  • $\begingroup$ What you've learned in mathematics classes applies to physics classes as well. I am not familiar with any new version of math named for use in physics or engineering $\endgroup$
    – Steeven
    Sep 28, 2021 at 12:58
  • 1
    $\begingroup$ There's no use in the inference$$F(m_1,\,m_2,\,r)=m_1G(m_2,\,r)\implies F(\lambda m_1,\,m_2,\,r)=\lambda F(m_1,\,m_2,\,r)$$alone. The linked source uses the second mass in a similar way to show$$F(m_1,\,m_2,\,r)=m_1m_2F(1,\,1,\,r).$$It's probably worth asking about the whole argument. $\endgroup$
    – J.G.
    Sep 28, 2021 at 13:32

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.