Presentation on the topic of motion of thrown bodies. The movement of a body thrown vertically upward. Movement of bodies thrown vertically upward at different speeds

Subject: Free fall. Weightlessness

• Lesson type: combined.
• The purpose of the lesson: give students an idea of ​​the free fall of bodies, as a special case of uniform motion, in which the magnitude of the acceleration vector is a constant value for all bodies; develop the ability to calculate the coordinate and speed of a body at any time of a free falling body; give the concept of weightlessness.
• Equipment for the lesson: ball, sheet of paper, paper ball, metal coin, paper coin, balls of various masses, Newton tube, PC and ID.

• 1. Preparation for the perception of the main material.
• 2. Studying new material.
• 3. Fixing the material.
• 4. Lesson summary.
• 5. Homework.

• 1. Independent work:
• Option 1. 1) What is the mass of a body to which a force of 10 N imparts an acceleration of 2 m/s2?
• 2) What can be the modulus of the resultant forces of 25 N and 10 N?
• Option 2.1) What acceleration does a force of 20 N impart to a body weighing 2 kg?
• 2) One of the forces acting on the body is equal to 15 N. What is the value of the second force if the modulus of the resultant of these forces is equal to 5 N?

• 1) Read and write Newton’s third law mathematically.
• 2) How does uniformly accelerated motion differ from uniform motion?
• 3) Write down the formula for determining speed during uniformly accelerated motion.
• 4) Write down the formula for determining displacement during uniformly accelerated motion.
• 5) What patterns are inherent in uniformly accelerated motion?
• 6) Name the features of Newton’s third law

• Since the force of gravity acting on all bodies near the Earth’s surface is constant, a freely falling body must move with constant acceleration, that is, uniformly accelerated.

1.Historical information.

• Aristotle's theory: The heavier the body, the faster it falls.
• contradiction: if a light body falls slower than a heavy one, will the light body and the heavy one fall more slowly(?), or faster since one is heavier?
• 1) Falling sheet of paper
• and a paper ball. 2)
• 2) Drop various
• by mass of balls.
• 3) Paper drop and
• metal coin 3)
• separately and together.

• Experiments with balls of different masses dropped from the Leaning Tower of Pisa.
• The balls landed almost simultaneously.
• Consequently, if air resistance can be neglected, all falling bodies move uniformly with the same acceleration.

• We come to the same conclusion when studying stroboscopic photographs.
• - photographing a falling ball at regular intervals (page 53 of the textbook), the photos prove that the movement of the ball is uniformly accelerated and the acceleration of gravity g = 9.8 m/s 2
• denoted by the letter g from the Latin word gravitas (“gravitas”), which means “heaviness.”
• Experiments carried out using a Newton tube

confirm that the acceleration of gravity at a given point on the Earth does not depend on the mass, density and shape of falling bodies.

5. Explanation of the fall of bodies of different masses at different speeds .

• F 1 =F t + F c F 2 =F t + F c
• F c F c
• F 1 F t
• F t F t =mg=m . 9.8m/s 2

Formulas characterizing uniformly accelerated motion

Uniformly accelerated motion

Free fall

V x =V ox +a x t

Movement of a body thrown upward

S x =V ox t+(a x t 2)/2

S y =V oy t+(gt 2)/2

V y =V o y -gt

X = X 0 +V x0 t+(a x t 2)/2

S=V oy t-(gt 2)/2

У=У 0 +V 0y t+(g y t 2)/2

У= V 0y t-(g y t 2)/2

3. Dependence of the speed and coordinates of a falling body on time.

3. Dependence of the speed and coordinates of a body thrown vertically upward on time.

• Let the initial position of the body be the origin of coordinates, let the OU axis be directed downward, then the graphs V y (t) and Y (t) :

Weightlessness is a state in which the weight of a body is zero.

• This state occurs if only the force of gravity acts on the body; the body moves translationally with the acceleration of free fall.
• That is, a body suspended on a spring does not cause any deformation of the spring, and a body lying motionless on a support does not exert any force on it.
• x P= m (g - a) g=a P=0

• 1.Ex. 13 (2) A pencil falls from a table 80 cm high to the floor. Determine the time of its fall.
• 2. Will the time of free fall of different bodies from the same height be the same?
• 3. The stone fell from one cliff in 2s, and from the other in 6s. How many times is the second rock higher than the first?
• Homework:
• § 13, 14, ex.13 (1.3); No. 192, 204, 207.
• Answer the questions after the paragraph, know the abstracts written in the notebook.

Questions.

1. Does gravity act on a body thrown up during its ascent?

The force of gravity acts on all bodies, regardless of whether it is thrown up or at rest.

2. With what acceleration does a body thrown up move in the absence of friction? How does the speed of the body change in this case?

3. What determines the maximum height of lift of a body thrown upward in the case when air resistance can be neglected?

The lift height depends on the initial speed. (For calculations, see previous question).

4. What can be said about the signs of the projections of the vectors of the instantaneous velocity of the body and the acceleration of gravity during the free upward movement of this body?

When a body moves freely upward, the signs of the projections of the velocity and acceleration vectors are opposite.

5. How were the experiments depicted in Figure 30 carried out, and what conclusion follows from them?

For a description of the experiments, see pages 58-59. Conclusion: If only gravity acts on a body, then its weight is zero, i.e. it is in a state of weightlessness.

Exercises.

1. A tennis ball was thrown vertically upward with an initial speed of 9.8 m/s. After what period of time will the speed of the rising ball decrease to zero? How much movement will the ball make from the point of throw?

Slide 2

Repetition

2 In the presence of atmosphere, the movement of falling bodies tends to be uniform.

Slide 3

3 Laws characterizing free fall if V0 = 0; V = gt if V0 = 0;

Slide 4

Repetition

4 1. In the tube from which the air has been pumped out, there is a pellet, a cork and a bird feather at the same height. Which body will reach the bottom of the tube later than others? A) Drobinka. B) Cork. B) Bird feather. D) All three bodies will reach the bottom of the tube at the same time. 2. What is the speed of a free falling body after 3 seconds? V0=0m/s, g=10m/s². A) 15 m/s B) 30 m/s C) 45 m/s D) 90 m/s 3. How far will a freely falling body travel in 4 seconds? V0=0m/s,g=10m/s². A) 20m B) 40m C) 80m D) 160m 4. What distance will a freely falling body travel in the 6th second? V0 = 0 m/s, g = 10 m/s². A) 55m B) 60m C) 180m D) 360m

Slide 5

5 11/17/2011 The movement of a body thrown vertically upward. Lesson objectives: 1. Make sure that the movement of a body thrown vertically upward is uniformly accelerated. 2. Obtain basic formulas for movement. 3. Give examples of such movement.

Slide 6

Formulas

6 The movement of a body thrown vertically upward. v = vо - gt y = ho+vot - gt2/2 The OY axis is directed vertically upward

Slide 7

Graphic representation of movement

7 Graph of speed versus time. Graphs of acceleration, path and coordinates versus time.

Slide 8

Movement of bodies thrown vertically upward at different speeds

8 Coordinate versus time V02>V01

Slide 9

9 The island of Iceland has its own valley of geysers - Haukaldur. It is here that the famous Big Geyser is located. When the geyser gathers its strength, it throws a powerful jet 40-60 meters high into the sky three times in a row. This “fireworks” lasts ten minutes, and then the water and steam seem to be drawn back into the vent. Recently, the Great Geyser has been erupting less and less. But its neighbor, the Stockr geyser, is still full of energy and delights tourists with its jets, soaring 30-40 meters up. Problem: At what speed does water erupt from the crater of the Great Geyser and the Shtokkr geyser? How long does the “flight” last? (Water from the mouth of the Great Geyser erupts at a speed of 35 m/s, the “flight” time of the water is 7 s. For the Stockr geyser, these values ​​will be, respectively, 28 m/s and 5.6 s.)

Slide 10

"Squirting cucumber"

10 The most warlike plant is the “mad cucumber.” He goes “rabid” when he is fully mature. The cucumber breaks away from its stem with a crash, and shoots 6-8 meters from the hole where the fruit's stem was just before. It turns out that while the fruit is ripening, gases accumulate inside it. By the time they ripen, their pressure in its cavity reaches three atmospheres! Problem: At what speed must a stream of juice containing seeds erupt in order to reach the height indicated above? How does the energy of the seeds change? (The speed of the jet is 12.6 m/s, while the kinetic energy of the jet is converted into potential energy.)

The force of gravity acts on all bodies on Earth: resting and moving, located on the surface of the Earth and near it.

A body freely falling to the ground moves uniformly accelerated with increasing speed, since its speed is co-directed with the force of gravity and the acceleration of gravity.

A body thrown up, in the absence of air resistance, also moves with constant acceleration caused by the action of gravity. But in this case, the initial speed v0, which was given to the body during the throw, is directed upward, i.e., opposite to the force of gravity and the acceleration of free fall. Therefore, the speed of the body decreases (for each second - by an amount numerically equal to the module of acceleration of free fall, i.e. by 9.8 m/s).

After a certain time, the body reaches its greatest height and stops at some point, i.e. its speed becomes zero. It is clear that the greater the initial speed of the body when thrown, the longer the rise time will be and the greater the height it will rise by the time it stops.

Then, under the influence of gravity, the body begins to fall down uniformly.

When solving problems on the upward movement of a body under the influence of only gravity, the same formulas are used as for rectilinear uniformly accelerated motion with an initial speed v0, only ax is replaced by gx:

It is taken into account that when moving upward, the velocity vector of the body and the acceleration vector of free fall are directed in opposite directions, therefore their projections always have different signs.

If, for example, the X axis is directed vertically upward, i.e., co-directed with the velocity vector, then v x > 0, which means v x = v, a g x< 0, значит, g x = -g = -9,8 м/с 2 (где v - модуль вектора мгновенной скорости, a g - модуль вектора ускорения).

If the X axis is directed vertically downward, then v x< 0, т. е. v х = -v, a g x >0, i.e. g x = g = 9.8 m/s 2 .

The weight of a body moving under the influence of gravity alone is zero. This can be verified using the experiments shown in Figure 31.

Rice. 31. Demonstration of weightlessness of bodies in free fall

A metal ball is suspended from a homemade dynamometer. According to the readings of the dynamometer at rest, the weight of the ball (Fig. 31, a) is 0.5 N. If the thread holding the dynamometer is cut, then it will fall freely (air resistance in this case can be neglected). At the same time, its pointer will move to the zero mark, indicating that the weight of the ball is zero (Fig. 31, b). The weight of a freely falling dynamometer is also zero. In this case, both the ball and the dynamometer move with the same acceleration, without exerting any influence on each other. In other words, both the dynamometer and the ball are in a state of weightlessness.

In the experiment considered, the dynamometer and the ball fell freely from a state of rest.

Now let’s make sure that the body will be weightless even if its initial speed is not zero. To do this, take a plastic bag and fill it about 1/3 with water; then remove the air from the bag by twisting its upper part into a rope and tying it in a knot (Fig. 31, c). If you take the bag by the lower part filled with water and turn it over, then the part of the bag twisted into a rope under the influence of the weight of the water will unwind and fill with water (Fig. 31, d). If, when turning the bag over, you hold the tourniquet, not allowing it to unwind (Fig. 31, e), and then throw the bag up, then both during the rise and during the fall the tourniquet will not unwind (Fig. 31, f). This indicates that during the flight the water does not exert its weight on the bag, as it becomes weightless.

You can throw this package to each other, then it will fly along a parabolic trajectory. But even in this case, the package will retain its shape in flight, which it was given when thrown.

Questions

1. Does the force of gravity act on a body thrown upward during its ascent?
2. With what acceleration does a body thrown upward move in the absence of friction? How does the speed of the body change in this case?
3. What determines the maximum height of lift of a body thrown upward in the case when air resistance can be neglected?
4. What can be said about the signs of the projections of the vectors of the instantaneous velocity of a body and the acceleration of gravity during the free upward movement of this body?
5. Tell us about the course of the experiments shown in Figure 31. What conclusion follows from them?

Exercise 14

A tennis ball is thrown vertically upward with an initial speed of 9.8 m/s. After what period of time will the speed of the rising ball decrease to zero? How much movement will the ball make from the point of throw?