Сформулируйте вопросы на английском языке и дайте ответы на них. Чему равна гравитационная сила? Сформулируйте закон всемирного тяготения. Что такое инертная и гравитационная масса?
What is the gravitational force? Formulate the law of universal gravitation. What is the inertial and gravitational mass?
Newton’s law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
where F – is the force between the masses, G – is the gravitational constant, m1 – is the first mass, m2 – is the second mass, r – isthe distance between the centres of the masses.
Inertial mass is a measure of an object’s resistance to changing its state of motion when a force is applied. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force.
Gravitational mass is the physical property of an object that causes it to interact with other objects through the gravitational force. According to the equivalence principle, gravitational mass is equivalent to inertial mass.
Сформулируйте вопросы на английском языке и дайте ответы на них. Что такое импульс частицы? Сформулируйте законы сохранения энергии и импульса для системы частиц.
What is the momentum of a particle? Formulate the laws of conservation of energy and momentum for a system of particles.
Momentum of a particle is the product of the mass and velocity of a particle.
Where m – mass, v – velocity.
Law of conservation of energy for a system of particles: the total energy of the system of particles is costant? When this system is isolated (no external forces act on the system).
-
mechanical case, T
– kinetic, V
– potential energy.
Law of conservation of momentum for a system of particles: in an isolated system of particles the total momentum is constant.
For example, two particles interact. Because of Newton’s third law, the forces between them are equal and opposite.
;
.
Therefore:
or
-
case of two particles.
-
law of conservation of momentum.
Сформулируйте вопросы на английском языке и дайте ответы на них. Сформулируйте универсальный закон сохранения энергии. Выведите теоретически закон сохранения импульса.
Formulate the universal law of conservation of energy. Derive theoretically the momentum conservation law.
Energy can neither be created (produced) nor destroyed by itself. It can be only transformed from one form to another, but the total energy of an isolated system is always constant.
According to the second Newton’s law for the system of N particles:
where 
momentum
of the system
and 
—
the
resultant of all the forces acting on particles of the system
Here 
—
the
resultant of the forces,
acting
on the n-th
particlefrom
side of m-th,
and 
—
the
resultant of all external forces acting on
k-th
particle.According to the
third Newton's law, power type
and 
will
be equal to the absolute value and opposite in direction, i.e. 
.
Therefore,
the second sum in the right-hand part of the expression (1) is equal
to zero, we obtain that the derivative of momentum in the system over
time is equal to the vector sum of all external forces acting on the
system:
Internal forces are excluded by Newton's third law.
For systems of N particles in which the sum of all external forces is equal to zero
or
for systems, on the particles of which, no external forces act 
(for
all k from 1 to n),
we
have
As you know, if derivative from an expression is zero, the expression has a constant value with respect to the variable differentiation, so:
(constant
vector).
That is, the total momentum of the system of N particles, where N any integer, is a constant value.