Horizontal projectile motion
An object is thrown at a certain initial velocity level. If an object is only subjected to gravity, such a motion is called flat throwing motion. Flat throwing motion can be regarded as a combination of uniform linear motion in horizontal direction and free falling motion in vertical direction. The object in the flat throwing motion is a constant force, so the flat throwing motion is a curve motion with uniform change, and the trajectory of the flat throwing object is a parabola.
The time of flat throwing action is only related to the vertical height of throwing point; The horizontal displacement of an object landing is related to time (vertical height) and initial horizontal velocity.
Flat throwing motion can be solved in two ways: one is displacement; The other is the speed path.
The displacement path is:
L (horizontal) =vt L (vertical) = 1/2gt 2
There are also ways to speed up:
T=v/t v (vertical) =gt
It can be solved immediately.
Flat throwing motion analysis
The flat throwing action is actually a combination of the following two actions:
(1) is free from external force in the horizontal direction, so it moves in a straight line at a uniform speed, and its speed is the initial speed of flat throwing motion;
(2) In the vertical direction, the object is only subjected to gravity, so it is in a state of free fall.
These two sub-actions are independent and simultaneous, with the independence and synchronization of the sub-actions.
(3) The trajectory of flat throwing: ∵ x = v0t, h = 1/2gt 2.
∴ x2 = h (2v0 ∧ 2)/g is a quadratic equation.
Its trajectory is a parabola.
Law of flat throwing motion
Formula: horizontal direction: s=v0*t
Vertical direction: h = 1/2gt 2
The time t in the two formulas is the same.
And the speed formula √ {v0 2+(gt) 2}
1. Exercise time is only determined by altitude.
Imagine an object being thrown to a height h at a horizontal speed vo. If the air resistance is not considered, the motion of the object in the vertical direction is a free fall, which can be obtained by the formula: h = 1 \ 2gt 2. It can be seen from this formula that the motion time of an object is only related to the height at the beginning of the flat throwing motion. t=√(2h/g)
2. Horizontal displacement is determined by height and initial velocity.
The horizontal motion of the flat projectile is uniform linear motion, and its horizontal displacement will be replaced by: s (horizontal) =v0t=v0√(2h/g).
It can be seen that the horizontal displacement is determined by the initial velocity and the height at the beginning of flat throwing.
3. In any equal time, the change of speed is equal.
Because the motion of a flat projectile is a combination of horizontal uniform linear motion and vertical free fall motion. During the movement, the speed of its horizontal movement remains unchanged. In time, the variation of the horizontal component velocity is zero, the variation of the vertical component velocity is 9.8m/s 2, and the variation of the time convergence velocity is the vector sum of the velocity variations in two directions, the magnitude is:, and the direction is vertical downward. So in equal time, the change of speed is equal, and we can also know that in any equal time, the change of momentum is equal.
4. At any moment, the tangent of the velocity deflection angle is equal to twice the tangent of the displacement deflection angle.
5. At any moment, the reverse extension line of the velocity vector must pass through the midpoint of the horizontal displacement.
6. The object is thrown horizontally from the inclined plane. If the object falls on the inclined plane, the tangent of the included angle between the speed direction and the horizontal direction when the object contacts the inclined plane is twice the tangent of the inclined plane.
7. If an object thrown horizontally from an inclined plane falls on the inclined plane, the included angle between the velocity direction and the inclined plane when the object contacts the inclined plane has nothing to do with the initial velocity when the object is thrown. When an object falls on an inclined plane, the included angle between the velocity direction and the inclined plane has nothing to do with the initial velocity, but only depends on the inclined plane.
Pendulum motion
Simply put, when it is not disturbed by external forces, the pendulum is at rest. Once affected by external forces, it will start to swing from side to side. The greater the external force, the greater the force of its swing back, and the slower the swing back speed under the influence of gravity. Finally, it will return to the original point and present the original static state.
abstract
Acceleration is the ratio of the amount of speed change to the time required for this change to occur. It is a physical quantity that describes the speed change of an object. Usually represented by a, the unit is m/s 2 (meter/square second). Acceleration is a vector, and its direction is the direction in which the speed of an object changes. Its direction is the same as the direction of external force, its direction indicates the direction of speed change, and its size indicates the size of speed change. The acceleration is different in different parts of the earth. Newton's second law of kinematics holds that a=F/m, where f is the external force on the object and m is the mass of the object. Force is the condition to change the motion state of an object, and acceleration is the physical quantity to describe the motion state of an object. There is no necessary relationship between acceleration and speed. When the acceleration is large, the speed can be small, and when the speed is large, the acceleration can also be small. From the differential point of view, acceleration is the derivative of velocity with respect to time and the slope in V-T image. When the acceleration and speed are in the same straight line, the object moves in a variable-speed linear motion, such as the car starts with constant acceleration [1] (uniformly accelerated linear motion) and makes simple vibration (linearly accelerated variable-speed motion); When the acceleration and velocity directions are not in the same straight line, the object moves in a variable speed curve, such as flat throwing motion (uniform acceleration curve motion) and uniform circular motion (variable acceleration curve motion); When the acceleration is zero, the object is stationary or moving in a straight line at a uniform speed. Any complex motion can be regarded as the synthesis of numerous uniform linear motions and uniform acceleration motions. We also think about acceleration with the idea of limit.
formula
S = v0t+ 1/2a (t 2) (v0 is the initial velocity and t is the time).
a=(V-V0)/(t-t0)=△ V/△ t
V=Vo+aX△t
2a△x=v2-v02 acceleration 1 example, uniformly accelerated motion.
curvilinear motion
Calculation formula of acceleration in curvilinear motion;
a=rω^2=v^2/r
Like circular motion, this acceleration is called centripetal acceleration, which is the resultant force of objects and also points to the center of the circle.
But when the acceleration remains constant, it is also possible for an object to move in a curve.
For example, when you push an object forward along a horizontal desktop (that is, when it leaves the desktop, it makes a flat throwing motion), you will find that after it leaves the desktop, it crosses a curve in the air and falls to the ground.
After you let go of your hand and leave the desktop, the object only accepts gravity. Gravity is always vertical downward, so the direction of acceleration is also vertical downward, and the magnitude remains the same. But when the object leaves the table, it still has inertia, so it wants to keep parallel motion. At this time, the speed direction and acceleration direction of the object are not in a straight line. The object will deflect in the direction of the force and draw a curve that deflects to the ground.
But at this time, because gravity remains the same, so add
variable accelerated motion
We must first be clear. The acceleration is a vector. It has size and direction. For example, if a person pushes you from behind with 1N and a person stands in front of you and pushes you with the same amount, you will fall in different directions.
Therefore, if in a movement, the magnitude of acceleration is constant, but the direction is changing, it is no longer a uniform acceleration movement, but a variable acceleration movement. Such as uniform circular motion.
Constant speed motion (speed, direction)
You can also say that the acceleration is zero.
Uniform motion must be uniform linear motion.
Speed is a vector, including magnitude and direction. Uniform motion is uniform motion, and the direction of motion is unchanged, so uniform motion must be uniform linear motion!
Definition: Motion that passes through the same distance in unit time is called uniform motion.
2. Uniform linear motion, velocity, velocity and displacement formula S=υt, S ~ t diagram, υ ~ t diagram.
3. Variable speed linear motion, average speed and instantaneous speed
Basic laws and important inferences of uniform linear motion
(1) The basic laws of linear motion with uniform speed change usually refer to the so-called displacement formula and velocity formula.
S=υ0t+ at2
υ=υ0+at
(2) In the basic law of uniform linear motion, the direction of initial velocity υ0 is usually taken as the reference positive direction, that is, υ 0 > 0. At this point, the direction of acceleration will reflect different types of uniform linear motion:
① A > 0 means uniformly accelerated linear motion;
(2) If a=0, it refers to uniform linear motion;
(3) If a=0, it refers to straight-line motion with uniform deceleration.
(3) The basic law of uniform linear motion can often be transformed into the following deduction form in specific applications.
Inference 1: υ2- =2as-= 2as
Inference 2: = (υ 0+υ)
Inference 3: △ S = A△ T2
Inference 4: = (υ 0+υ)
Inference 5: =
Inference 6: When υ0=υ, there is
s 1:S2:S3:……= 12:22:32:………
Sⅰ:Sⅱ:Sⅲ:……= 1:3:5:………
υ 1 :υ2 :υ3:……= 1 :2 :3 :……
t 1:T2:T3:……= 1:(- 1):(-):……
3. υ-T diagram of uniform linear motion
Using images to express physical laws is intuitive. about
For the linear motion with uniform change, the diagram of υ ~ t with its speed changing with time is shown in the figure.
As shown in 1, there are three main points to grasp about this line.
(1) The intercept on the vertical axis has the physical meaning that the initial velocity of the moving object is υ 0;
(2) The physical meaning of the graph slope is the acceleration a of the moving object;
(3) The physical meaning of "area" under the graph line is that moving objects are corresponding.
The displacement occurred in. Figure 1
4. Laws and characteristics of vertical throwing.
(1) The condition of vertical upward throwing movement: there is an initial velocity of vertical upward υ 0; In the process of motion, it is only acted by gravity, and the acceleration is vertical downward gravity acceleration G.
(2) Law of vertical throwing motion: Vertical throwing motion is a linear motion with constant acceleration and uniform speed change. If the coordinate system is established with the throwing point as the coordinate origin and the vertical direction as the positive direction of the coordinate axis, the displacement and velocity formulas are respectively
S=υ0t- gt2
υ=υ0-gt
(3) Characteristics of vertical throwing action: Vertical throwing action can be divided into "ascending stage" and "descending stage". The former stage is uniform deceleration linear motion, and the latter stage is uniform acceleration linear motion (free fall motion) with zero initial velocity. Its main features are:
(1) time symmetry-"rising stage" and "falling stage" have the same time through the same displacement with equal magnitude and opposite directions, that is
T up =t down.
(2) rate symmetry-when the "rising stage" and "falling stage" pass through the same position, the rates are equal, that is,
Up = down
I'm sorry, that's about it. Please summarize it again.
The picture cannot be uploaded.
Typing is not easy. If you are satisfied, please adopt it.