32
3 Mechanical Aspects of Biosystems
range interactions such as gravity play a significant role for life systems that have
developed near a big mass, like a planet, or which regularly experience significant
accelerations. 7
Our best present theory of how matter behaves uses quantum mechanics rather
than Newtonian mechanics, with forces being replaced by changes in fieldinteraction energies across space. Even so, Newtonian mechanics has proven to
work well from solar-system sizes down to mesoscopic scales.
Newton’s Laws
Newton’s 1st Law: There exists frames of reference, called inertial frames, 8 in
which isolated bodies move uniformly or remain at rest.
Newton’s 2nd Law 9 : When a body is acted on by a net unbalanced force determined by interactions with other nearby objects, the body no longer moves
uniformly, but rather accelerates in proportional to that net force and inversely
proportional to the inertia of the body measured by its mass:
F = m a.
Newton’s 3rd Law 10 : If body A acts on body B with a force F AB , then body B
must act back on body A with an equal and opposite force F BA : F BA = −F AB .
Newton’s Law of Linear Superposition 11 : The Newtonian proposition that forces
add is the following: If one finds that body 2 acts on body 1 with a force F 12
when the two are isolated, and body 3 acts on body 1 with a force F 13 when
the two are isolated, then when all three are present but isolated from others, the
force on 1 due to both bodies 2 and 3 will be F 12 + F 13 .
Newton’s Law of Gravity 12 : An attractive gravitational force exists on each of a
pair of masses, in proportional to each of their masses and inversely proportional
to the square of their distance of separation: F G = Gm 1 m 2 /r 2 .
7 As we have noted, Einstein showed how to make an equivalence between acceleration and gravity.
8 A frame of reference separated from local bodies and moving at constant velocity relative to the
average motion of the distant stars is a good inertial frame.
9 The alternative form of Newton’s 2nd law,
F = dp/dt, where p is the particle momentum,
actually still works in Einstein’s Special Theory.
10 Note: Newton’s 3rd law should NOT be written as ‘for every action there is an equal and opposite
reaction’. The writer of this textbook found this phrasing of Newton’s 3rd law in a sociology
textbook, whose author, with apparent seriousness, claimed it justified the statement that for every
social action there must be an opposing action. Newton would have rolled his eyes.
11 This ‘Law’ is found to hold, to a very good approximation, for electromagnetic forces, but is
violated for very strong gravitational forces, such as nearby black holes. In such cases, we say that
the gravitational effects are acting non-linearly.
12 The number G is Newton’s universal gravitational constant, first directly measured by Henry
Cavendish in 1797. We note that very strong gravitational fields exist near very massive and dense
bodies, such as neutron stars and black holes. In these cases, Newton’s Laws no longer work
well, but Einstein’s General Theory of Relativity successfully (so far) predicts the gravitational
interaction between two or more massive bodies. Near neutron stars and massive black holes, no
simple force law can be used, nor do strong gravitational effects simply add when several bodies
are considered, as they do for Newtonian gravity.
3 Mechanical Aspects of Biosystems
range interactions such as gravity play a significant role for life systems that have
developed near a big mass, like a planet, or which regularly experience significant
accelerations. 7
Our best present theory of how matter behaves uses quantum mechanics rather
than Newtonian mechanics, with forces being replaced by changes in fieldinteraction energies across space. Even so, Newtonian mechanics has proven to
work well from solar-system sizes down to mesoscopic scales.
Newton’s Laws
Newton’s 1st Law: There exists frames of reference, called inertial frames, 8 in
which isolated bodies move uniformly or remain at rest.
Newton’s 2nd Law 9 : When a body is acted on by a net unbalanced force determined by interactions with other nearby objects, the body no longer moves
uniformly, but rather accelerates in proportional to that net force and inversely
proportional to the inertia of the body measured by its mass:
F = m a.
Newton’s 3rd Law 10 : If body A acts on body B with a force F AB , then body B
must act back on body A with an equal and opposite force F BA : F BA = −F AB .
Newton’s Law of Linear Superposition 11 : The Newtonian proposition that forces
add is the following: If one finds that body 2 acts on body 1 with a force F 12
when the two are isolated, and body 3 acts on body 1 with a force F 13 when
the two are isolated, then when all three are present but isolated from others, the
force on 1 due to both bodies 2 and 3 will be F 12 + F 13 .
Newton’s Law of Gravity 12 : An attractive gravitational force exists on each of a
pair of masses, in proportional to each of their masses and inversely proportional
to the square of their distance of separation: F G = Gm 1 m 2 /r 2 .
7 As we have noted, Einstein showed how to make an equivalence between acceleration and gravity.
8 A frame of reference separated from local bodies and moving at constant velocity relative to the
average motion of the distant stars is a good inertial frame.
9 The alternative form of Newton’s 2nd law,
F = dp/dt, where p is the particle momentum,
actually still works in Einstein’s Special Theory.
10 Note: Newton’s 3rd law should NOT be written as ‘for every action there is an equal and opposite
reaction’. The writer of this textbook found this phrasing of Newton’s 3rd law in a sociology
textbook, whose author, with apparent seriousness, claimed it justified the statement that for every
social action there must be an opposing action. Newton would have rolled his eyes.
11 This ‘Law’ is found to hold, to a very good approximation, for electromagnetic forces, but is
violated for very strong gravitational forces, such as nearby black holes. In such cases, we say that
the gravitational effects are acting non-linearly.
12 The number G is Newton’s universal gravitational constant, first directly measured by Henry
Cavendish in 1797. We note that very strong gravitational fields exist near very massive and dense
bodies, such as neutron stars and black holes. In these cases, Newton’s Laws no longer work
well, but Einstein’s General Theory of Relativity successfully (so far) predicts the gravitational
interaction between two or more massive bodies. Near neutron stars and massive black holes, no
simple force law can be used, nor do strong gravitational effects simply add when several bodies
are considered, as they do for Newtonian gravity.