Tip 1: The difference between speed and acceleration

The science

Tip 1: The difference between speed and acceleration

According to the first law of mechanics, every bodytends to maintain a state of rest or uniform rectilinear motion, which is essentially the same thing. But such serenity is possible only in space.

What is the difference between speed and acceleration

Speed possible without acceleration, but impossibleacceleration without speed. With uniform rectilinear motion, the physical body has a constant speed, acceleration under these conditions is zero. In the real world, the body acts on a variety of different forces, under the influence of which the uniformity of the movement is violated. The force of inhibition causes the appearance of negative acceleration, leading to a decrease in speed. The nature of the motion is changed to accelerated / decelerated with constant or variable acceleration. The speed in the linear uniform motion shows the dependence of the traversed path on time and is numerically equal to the distance per unit time. Acceleration demonstrates the nature of the change in speed along the path during the accelerated / slow movement of the object in space. The relationship between the parameters "path" - "time" - "speed" is linear, and acceleration is a quadratic function of the "time" argument. When the constantly changing characteristics of the body's motion process, a parameter such as instantaneous speed appears. This quantity is defined as the first derivative of the function S = F (t), i.e. v = F "(t), where: S is the path, t is the time, v is the velocity. The acceleration is the second derivative of the function S = F (t), hence a = F" (t) or a = v "( t), where a is the acceleration. In the case of uniform rectilinear motion, the general form of the formula describing such a motion is the equation of the straight line: S = v * t + v₀, where v₀ is the initial velocity. The speed of such motion has a constant value. The derivative of the constant is zero, and there is no acceleration. In the case of an arbitrary curvilinear motion, the velocity vector at each instant is directed along the tangent to the trajectory, and the position of the acceleration vector coincides with the velocity vector, which is defined as the vector difference of the instantaneous and zero velocities. Zero speed is the value of this parameter at the moment of the beginning of the accelerated motion. In the particular case of motion along the circle, the acceleration is directed toward the center, the velocity coincides with the tangent. Vectors of speed and acceleration are mutually perpendicular.

Tip 2: How to calculate the first space velocity

The first space speed - this speed, at which the object can become an artificial satellite of the Earth. Its size (about 8 km / s) is known to any schoolboy. At the same time, many forget that speed has not only magnitude, but also direction.

Instructions

If some body is dispersed to even veryhigh speed in the vertical direction, then using up the reserves of kinetic energy, it will still come back. The reason is the absence in this direction of any forces other than earthly attraction. So there must be a force opposing the force of gravity. Such a force takes place if the body participates in the rotational motion relative to the Earth (more precisely, its center). With this movement, centripetal acceleration appears, creating a force directed opposite to gravity.

Now you have the right to conclude that the speed It is directed along the tangent to the circle along which the body moves. It is called linear speedrotational motion. If the mass of the body is m, then the corresponding centrifugal force is Fv = m (v ^ 2 / L), where L is the distance from the center of the Earth to the body. If we use the height h of removing the body from the surface, then L = R + h (R is the radius of the Earth).

Gravitational force of attraction of two massesγ (Mm / L ^ 2) = γ (Mm / (R + h) ^ 2), where γ is the gravitational constant. Equate its centrifugal force (see Figure 1). Obtain γ (Mm / (R + h) ^ 2) = m (v ^ 2 / (R + h)). Swipe and find v. v = √ (γM / (R + h).) Now, note that h is negligible compared to R or R + h≈ R. Also note that the gravity acceleration g = γM / R ^ 2. Then v = √ (gR), R = 6357 * (10 ^ 3) m, g = 9.81 m / s ^ 2 and then v≈7.91 km / s.

How to calculate the first space <strong> speed </ strong>

Together, by the completion of the solution of the problem ofthe first cosmic speed can not but arise the question of how to be with the height h? Indeed, in the final calculation this value did not participate. The fact is that even the heights on which spacecraft are flying are too small in comparison with the radius of the earth. And their masses are just as insignificant in comparison with the mass of our planet. Nevertheless, the main requirement remains to h. More thickness of the atmosphere. In its dense layers, bodies with such velocities simply burn out.