Objective: study of the dependence of the flight range of a body thrown horizontally on the height from which it began to move.
Equipment: tripod with clutch and claw, arcuate chute, steel ball, film marker, guide of the device for studying rectilinear motion, scotch.
Theoretical basis work
If a body is thrown horizontally from a certain height, then its motion can be considered as a horizontal motion by inertia and a uniformly accelerated vertical motion.
The body moves horizontally in accordance with Newton's first law, since, apart from the resistance force from the side of the air, which is not taken into account, no forces act on it in this direction. The force of air resistance can be neglected because a short time the flight of a body thrown from a small height, the action of this force will not have a noticeable effect on the movement.
The force of gravity acts on the body vertically, which imparts acceleration to it. g(acceleration free fall).
Considering the movement of the body under such conditions as the result of two independent movements horizontally and vertically, it is possible to establish the dependence of the flight range of the body on the height from which it is thrown. Considering that the speed of the body V at the time of the throw is directed horizontally, and there is no vertical component of the initial velocity, then the fall time can be found using the basic equation uniformly accelerated motion:
Where .
During this time, the body manages to fly horizontally, moving uniformly, the distance . Substituting the already found flight time into this formula, we obtain the desired dependence of the flight range on altitude and speed:
From the resulting formula, it can be seen that the throw distance is in quadratic dependence on the height from which the throw is. For example, if the altitude is quadrupled, the flight range will double; with a ninefold increase in height, the range will increase by a factor of three, and so on.
This conclusion can be confirmed more strictly. Let when thrown from a height H 1 range will be S 1 , when thrown at the same speed from a height H 2 = 4H 1 range will be S 2 .
According to formula (1):
Then dividing the second equation by the first one, we get:
or 2)
This dependence, obtained theoretically from the equations of uniform and uniformly accelerated motion, is verified experimentally in the work.
The paper investigates the motion of a ball that rolls down a chute. The chute is fixed at a certain height above the table. This ensures the horizontal direction of the speed of the ball at the moment of the beginning of its free flight.
Two series of experiments are carried out, in which the heights of the horizontal section of the gutter differ by a factor of four, and the distances are measured S 1 and S 2, but which the ball is removed from the chute horizontally. To reduce the influence on the result of side factors, the average value of the distances is determined S 1sr and S 2Wed. Comparing the average distances obtained in each series of experiments, they conclude how true equality (2) is.
Work order
1. Attach the chute to the tripod shaft so that the curved part of the chute is placed horizontally at a height of about 10 cm from the table surface. Place a marker film at the place where the ball is supposed to fall on the table.
2. Prepare a table to record the results of measurements and calculations.
| experience number | H 1m | S 1m | S 1sr, m | H 2, m | S 2, m | S 2av, m |
3. Test run the ball from the top edge of the chute. Determine where the ball falls on the table. The ball must fall into middle part films. Adjust the position of the film if necessary.
4. Measure the height of the horizontal part of the gutter above the table H 1 .
5. Launch the ball from the top edge of the chute and measure on the table surface the distance from the bottom edge of the chute to the place where the ball fell S 1 .
6. Repeat the experiment 5-6 times.
7. Calculate the average value of the distance S 1Wed.
8. Increase the height of the chute by 4 times. Repeat a series of ball launches, measure and calculate H 2 ,S 2 ,S 2sr
9. Check the validity of equality (2)
10. Calculate the speed reported to the body in the horizontal direction?
5. How will the flight range of a body thrown horizontally from a certain height change if the throwing speed is doubled?
6. How and how many times should the speed of a body thrown horizontally be changed in order to obtain the same flight range at a height that is half that?
7. Under what conditions does curvilinear motion?
8. How should a force act so that a body moving in a straight line changes the direction of its movement?
9. What is the trajectory of a body thrown horizontally?
10. Why does a body thrown horizontally move along curvilinear trajectory?
12. What determines the range of a body thrown horizontally?
If the speed \(~\vec \upsilon_0\) is not directed vertically, then the motion of the body will be curvilinear.
Consider the motion of a body thrown horizontally from a height h with the speed \(~\vec \upsilon_0\) (Fig. 1). Air resistance will be neglected. To describe the movement, it is necessary to choose two coordinate axes - Ox and Oy. Origin of coordinates is compatible with initial position body. Figure 1 shows that υ 0x= υ 0 , υ 0y=0, g x=0 g y= g.
Then the motion of the body will be described by the equations:
\(~\upsilon_x = \upsilon_0,\ x = \upsilon_0 t; \qquad (1)\) \(~\upsilon_y = gt,\ y = \frac(gt^2)(2). \qquad (2) \)
An analysis of these formulas shows that in the horizontal direction the speed of the body remains unchanged, i.e. the body moves uniformly. In the vertical direction, the body moves uniformly with acceleration \(~\vec g\), i.e., in the same way as a freely falling body without initial velocity. Let's find the trajectory equation. To do this, from equation (1) we find the time \(~t = \frac(x)(\upsilon_0)\) and, substituting its value into formula (2), we obtain\[~y = \frac(g)(2 \ upsilon^2_0) x^2\] .
This is the equation of a parabola. Therefore, a body thrown horizontally moves along a parabola. The speed of the body at any moment of time is directed tangentially to the parabola (see Fig. 1). The modulus of speed can be calculated using the Pythagorean theorem:
\(~\upsilon = \sqrt(\upsilon^2_x + \upsilon^2_y) = \sqrt(\upsilon^2_0 + (gt)^2).\)
Knowing the height h with which the body is thrown, you can find the time t 1 , through which the body will fall to the ground. At this point the coordinate y equal to the height: y 1 = h. From equation (2) we find \[~h = \frac(gt^2_1)(2)\]. From here
\(~t_1 = \sqrt(\frac(2h)(g)).\qquad(3)\)
Formula (3) determines the flight time of the body. During this time, the body will cover a distance in the horizontal direction l, which is called the flight range and which can be found on the basis of formula (1), given that l 1 = x. Therefore, \(~l = \upsilon_0 \sqrt(\frac(2h)(g))\) is the flight range of the body. The modulus of the body's velocity at this moment is \(~\upsilon_1 = \sqrt(\upsilon^2_0 + 2gh).\).
Literature
Aksenovich L. A. Physics in high school: Theory. Tasks. Tests: Proc. allowance for institutions providing general. environments, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsy i vykhavanne, 2004. - S. 15-16.
Laboratory work (experimental task)
DETERMINATION OF THE INITIAL SPEED OF THE BODY,
THROWN HORIZONTALLY
Equipment: pencil eraser (eraser), measuring tape, wooden blocks.
Objective: experimentally determine the value of the initial velocity of a body thrown horizontally. Assess the credibility of the result.
Equations of motion material point in projections on the horizontal axis 0 X and vertical axis 0y look like this:
The horizontal component of the velocity during the movement of a body thrown horizontally does not change, therefore, the path of the body during the free flight of the body horizontally is determined as follows: https://pandia.ru/text/79/468/images/image004_28.gif" width="112 " height="44 src="> From this equation, find the time and substitute the resulting expression in the previous formula. Now you can get calculation formula to find the initial velocity of a body thrown horizontally:
Work order
1. Prepare sheets for the report on the work done with preliminary entries.
2. Measure the table height.
3. Place the eraser on the edge of the table. Click to move it in a horizontal direction.
4. Mark the spot where the elastic will reach the floor. Measure the distance from the point on the floor where the edge of the table is projected to the point where the elastic band falls on the floor.
5. Change the flight height of the eraser by placing a wooden block (or box) under it on the edge of the table. Do the same for the new case.
6. Conduct at least 10 experiments, enter the measurement results in the table, calculate the initial speed of the eraser, assuming the free fall acceleration is 9.81 m/s2.
Table of measurement and calculation results
|
experience | Body flight height | body flight range | Initial body speed | Absolute error speed |
h | s | v 0 | D v 0 |
|
The average |
7. Calculate the magnitude of the absolute and relative errors of the initial velocity of the body, draw conclusions about the work done.
test questions
1. A stone is thrown vertically upwards and the first half of the way moves uniformly slow, and the second half - uniformly accelerated. Does this mean that its acceleration is negative on the first half of the path, and positive on the second?
2. How does the velocity modulus of a body thrown horizontally change?
3. In which case the object that fell out of the car window will fall to the ground earlier: when the car is standing still or when it is moving: Neglect air resistance.
4. In what case is the module of the displacement vector of a material point the same as the path?
Literature:
1.Giancoli D. Physics: In 2 vols. T. 1: Per. from English - M.: Mir, 1989, p. 89, task 17.
2. , Experimental tasks in physics. Grades 9-11: a textbook for students of educational institutions. - M .: Verbum-M, 2001, p. 89.
Laboratory work No. 5 in physics Grade 9 (answers) - Studying the movement of a body thrown horizontally
5. Measure in all five experiments the height of the fall and the range of the ball. Enter the data in the table.
| Experience | h | l | v |
| 1 | 0.33 m | 0.195 m | |
| 2 | 0.32 m | 0.198 m | |
| 3 | 0.325 m | 0.205 m | |
| 4 | 0.33 m | 0.21 m | |
| 5 | 0.32 m | 0.22 m | |
| Wed | 0.325 m | 0.206 m | 0,8 |
7. Calculate the absolute and relative error direct measurement distance of the balloon. Record the measurement result in interval form.
Answer security questions
1. Why is the trajectory of a body thrown horizontally half a parabola? Bring evidence.
The speed of a body thrown horizontally does not change along the x axis, but increases along the y axis due to the action of the force g on the body (acceleration of free fall).
2. How is the velocity vector directed in various points trajectory of a body thrown horizontally?
The vector of a body thrown horizontally is directed tangentially.
3. Is the motion of a body thrown horizontally uniformly accelerated? Why?
Is an. The path of a ball thrown horizontally is curvilinear and uniformly accelerated, since this path is characterized by two independent directions: horizontal and the direction of free fall g, which has a constant effect on the body.
Findings: learned to calculate the modulus of the initial velocity of a body thrown in a horizontal direction and located under the action of gravity.
Supertask
Using the results of the work, determine final speed movement of the ball (before resisting it with a sheet of paper). What angle does this velocity make with the surface of the sheet?
Grade 10
Lab #1
Definition of free fall acceleration.
Equipment: a ball on a thread, a tripod with a clutch and a ring, a measuring tape, a clock.
Work order
Model mathematical pendulum is a metal ball of small radius, suspended on a long thread.
pendulum length determined by the distance from the suspension point to the center of the ball (according to formula 1)
where - the length of the thread from the point of suspension to the place where the ball is attached to the thread; is the diameter of the ball. Thread length measured with a ruler, ball diameter - caliper.
Leaving the thread taut, the ball is removed from the equilibrium position by a distance that is very small compared to the length of the thread. Then the ball is released without giving it a push, and at the same time the stopwatch is turned on. Determine the period of timet , during which the pendulum makesn = 50 complete oscillations. The experiment is repeated with two other pendulums. The obtained experimental results ( ) are entered in the table.
Measurement number
t , with
T, s
g, m/s
By formula (2)
calculate the period of oscillation of the pendulum, and from the formula
(3) calculate the acceleration of a freely falling bodyg .
(3)
The measurement results are entered in the table.
Calculate the arithmetic mean from the measurement results and middle absolute error
.The final result of measurements and calculations is expressed as 
.
Grade 10
Lab No. 2
Studying the motion of a body thrown horizontally
Objective: measure initial speed body thrown horizontally to investigate the dependence of the flight range of a body thrown horizontally on the height from which it began to move.
Equipment: tripod with sleeve and clamp, curved chute, metal ball, a sheet of paper, a sheet of carbon paper, a plumb line, a measuring tape.
Work order
The ball rolls down a curved chute Bottom part which is horizontal. Distanceh from the bottom edge of the chute to the table should be 40 cm. The jaws of the clamp should be located near the top end of the chute. Place a sheet of paper under the chute, pressing it down with a book so that it does not move during the experiments. Mark a point on this sheet with a plumb line.BUT located on the same vertical with the lower end of the gutter. Release the ball without pushing. Note (approximately) the spot on the table where the ball will land as it rolls off the chute and floats through the air. Place a sheet of paper on the marked place, and on it - a sheet of carbon paper with the “working” side down. Press down these sheets with a book so that they do not move during the experiments. measure distance from marked point to pointBUT . Lower the chute so that the distance from the bottom edge of the chute to the table is 10 cm, repeat the experiment.
After leaving the chute, the ball moves along a parabola, the top of which is at the point where the ball leaves the chute. Let's choose a coordinate system, as shown in the figure. Initial ball height and flight range related by the ratio According to this formula, with a decrease in the initial height by 4 times, the flight range decreases by 2 times. Having measured and you can find the speed of the ball at the moment of separation from the chute according to the formula 
