In dynamics, the basic laws that Newton established prove the existence of a frame of reference, inertial. In relation to it, bodies move in a uniform and rectilinear order or are at rest. Provided there is no influence of other bodies, or in the case when it is compensated. These provisions are the meaning of the first law of Newton.
From the history
The existence of such a pattern suggested even Galileo. He made an experiment with a vessel on which a glass ball could roll faster. If you let him go, he will roll and stop only when he reaches the other edge of the vessel at the same height from which he was lowered. If you take a longer vessel, the result will be identical.
If you imagine an infinitely long container that does not have a second edge, the ball will move at constant speed indicators that are straight and uniform, infinite time, since the other edge is simply absent. If you imagine an infinitely long container that does not have a second edge, the ball will perform movement at a constant speed, in a straightforward and uniform way an infinite number of times, since the other edge is simply absent.
This observation allowed the scientist to realize that this is a natural state of objects. Movement is just as natural as peace. Prior to this, it was believed that any movement is caused by the action of force.
More modern research
Imagine a parachutist who makes a long jump. What forces act on it? First of all, it is gravity, which draws a person to the earth.
Secondly, it is the air resistance force, which counteracts the force of gravity. When these two forces are equal, the paratrooper falls at a constant speed.
Conclusions from the examples
We can say that in such a frame of reference a fundamental property is manifested. If we consider a certain body in it, on which the force does not act, or such an action is compensated, then the body either rests or the movement occurs in a uniform way when the speed is constant on one line. The basic laws of dynamics are manifested precisely in the described process.
Analysis of Newton's second law
Consider a cyclist, on which two forces act horizontally:
- pressing the pedals;
- air resistance and friction.
When these two forces are equal, their total effect is zero. Then, in accordance with Newton’s first law, the bicycle moves in a straightforward and even manner.
What will happen if the cyclist presses the pedals harder? Then F (t) will increase and acceleration will begin to occur. If you remove this force, only the opposing resistance force remains - F (sopr), which causes a slowdown.
Confirmation of the second law of dynamics
Newton argued that the force indices are equal to the mass times acceleration. This means that cases are considered when there is a resultant force and there is no equilibrium. F (equals) is the sum of all applied forces.
Then it follows that a (acceleration) = F (equal) / m
It follows that it is the force that causes acceleration, and not vice versa. If there is power, there is acceleration.
Example
Take a bus with a mass of 2000 kg. Horizontally, two forces act on this vehicle:
- engine traction;
- air resistance and friction.
Let the thrust force of the bus engine be equal to 3000 N and the drag force to 2500 N. In order for the application of Newton’s second law to be rational, it will be necessary to find the resultant force.
F (equals) = 500 N to the right, since the force has directions.
It follows that acceleration is a force divided by mass, as evidenced by the dynamics of its basic laws.
To solve problems using Newton’s second law, it is important to determine precisely this resultant force.
Proof of Newton's Laws
Consider the box example. When she lies on the table, several forces act on this object:
- severity
- support reactions.
If you push the box to the right, friction will arise between it and the table. Let us calculate the resultant force and acceleration.
Vertical forces are balanced here, cancel each other out. The resultant vertical force is zero. Right and left forces act, the difference of which shows an advantage to the right. The acceleration of the box can be calculated by dividing the mass of this item by the difference in the force.
Examination of Newton's first two statements helped formulate the rule of the basic law of motion dynamics.
About Newton's Third Law
The basic law of dynamics in rotational motion is the fact that action is equal to counteraction. When one body attracts or repels another, then it is attracted and repelled from the first with the same force.
Imagine a car that drives into a wall at speed. In this case, the machine presses on the wall with a certain force. The wall responds and performs an equal effect on the vehicle.
Therefore, when the car pushes the wall forward, the latter pushes the car back. The effect of these forces is completely different. The wall remains in the same position, and transport is much less lucky. The reason for this effect is a significant difference in mass:
a = F / m
The wall has a small mass and a large acceleration. And vice versa, in relation to the car. When two bodies interact, two forces arise that must meet the requirements:
- be equal in size;
- opposite in direction;
- to be attached to different bodies;
- have the same nature.
Balloon experience
The basic law of body dynamics can be considered with an example of an inflatable balloon. If you release it, the ball will push air out of the nozzle, which contributes to pushing forward. This will be proof of Newton’s third law. It is simple but often difficult to use for solving problems.
About the dynamics of rotational motion
Knowledge of the basic law of the dynamics of a rigid body allows us to consider the laws of rotational motion. For this, it is necessary to recall the solution of the basic problems of mechanics, when at any moment in time it is possible to indicate the position of the body in space relative to other bodies.
In this case, we are talking about one-dimensional motion. It is known that there is a type of motion in which each point moves along the axis of rotation.
In this case, different points of the body move at different speeds along different paths. In this case, the axis and rotation angles remain common. Considering the rotational motion, it is better to assume that the main task of mechanics is solved if it was possible to indicate the angle of rotation of the body at any time.
This will be the application of the basic law of dynamics with respect to the rotational body.
How to calculate body acceleration?
The basic law of the dynamics of the rotational motion of a body requires the determination of the forces that affect it. Knowing this information, one can apply Newton’s second law and find the acceleration of the body at any time.
Knowing such data and applying the laws of kinematics, you can find the coordinates of the body at the moment. This is the technology for solving the main problem of mechanics. We reformulate it under the rotational motion, moving in the opposite direction from the desired result. To determine the value of the angle of rotation of the body at any time, it is necessary to recall the kinematics of rotational motion, which includes angular acceleration.
There is an equation to answer the question of what angular acceleration will be .
To create such an equation, it is necessary to recall the laws of kinematics about rotational motion. If the translational type of motion is characterized by speed, then when considering the rotational motion, the analogous concept will be the indicators of angular velocity - a physical quantity that determines how the angle that the body is rotated over a certain time period relates to the time this ratio takes place.
The angular velocity must be multiplied by the distance from the axis of rotation to the point of interest to us. The simplest form of rotational rotation is uniform, when in the same time the body rotates at the same angles without acceleration.
On a body that rotates uniformly, each point has its own speed of movement. Moreover, it changes in the direction of centripetal acceleration.
The direction of this action occurs along the tangent radius to the center of the circle.
Uneven rotation - this is a measure of the relationship with which the angular velocity changes over a time period relative to the duration of this period.
From here follows the law on the change in angular velocity:
W (t) = Wo + Et
The component acceleration can be directed not only along the radius, but also along the tangent. This is important to take into account during the measurement process.
To summarize
In accordance with the basic laws of dynamics, the body performs the movement in a uniform and straightforward manner until other forces act on it. If the body is at rest, this will continue until the beginning of the impact on it of force.
It follows that movement is as natural for the body as peace. To change this or that state, a certain force must be applied to the body.
The second paragraph of the fundamental law of dynamics states that the resultant force causes acceleration. If F (equal) = 0, then the acceleration number will also be zero. In this case, the speed indicators will also be constant or zero.
It follows that the rule of the first Newtonian law smoothly flows into the second. For scientists of the 17th century, this evidence was the greatest discovery.
With the help of Newton’s third law, it is possible to successfully solve the problems from the Dynamics section.