Study of the movement of a body thrown horizontally. Topic: Study of the motion of a body thrown horizontally

FEDERAL EDUCATION AGENCY

GOU VPO "UFA STATE AVIATION TECHNICAL UNIVERSITY"

Department of Natural Sciences and General Professional Disciplines

Lab Report No. 6

STUDYING THE MOTION OF A BODY THROWN HORIZONTALLY

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Checked:.

Laboratory work № 6

Study of the motion of a body thrown horizontally

Goal of the work:

Determine the dependence of the flight range of a body thrown horizontally on the height of the throw.

To experimentally confirm the validity of the law of conservation of momentum for two balls during their central collision.

Exercise 1. Study of the motion of a body thrown horizontally

A steel ball is used as the body under study, which is launched from the upper end of the chute. Then the ball is released. The ball launch is repeated 5-7 times and S avg is found. Then increases the height from the floor to the end of the gutter, repeat launching the ball.

We enter the measurement data into the table:

For height H = 81 cm.

№ experience	S, mm	S Wed, mm	N, mm	S Wed / , mm

For height H = 106 cm.

№ experience	S, mm	S Wed, mm	N, mm	, mm	S Wed / , mm

Task 2. Study of the law of conservation of momentum

We measure the mass of the steel ball m 1 and m 2 on the scales. We attach a device to the surface of the work table to study the motion of a body thrown horizontally. Place it where the ball fell Blank sheet white paper, glue it with tape and cover it with carbon paper. A plumb line determines the point on the floor above which the edges of the horizontal section of the gutter are located. They launch the ball and measure its flight range in the horizontal direction l 1. According to the formula
We calculate the speed of the ball and its momentum P 1.

Next, we install another ball opposite the lower end of the gutter, using a knot with a support. The steel ball is launched again, the flight range l 1 ’ and the second ball 2 ’ are measured. Then the velocities of the balls after the collision V 1 ’ and V 2 ’, as well as their impulses p 1 ’ and p 2 ’, are calculated.

We will enter the data into a table.

P 1, kg m/s

P 1 ', kg m/s

P 2 ', kg m/s

1.15 m/s

0.5 m/s

0.74 m/s

P 1 = m 1 · V 1 = 0.0076 · 1.15 = 0.009 m/s

P 1 ' = m 1 · V 1 ' = 0.0076 · 0.5 = 0.004 m/s

P 2 ' = m 2 · V 2 ' = 0.0076 · 0.74 = 0.005 m/s

Conclusion: In this laboratory work, I studied the motion of a body thrown horizontally, established the dependence of the flight range on the height of the throw, and experimentally confirmed the validity of the law of conservation of momentum.

In physics for grade 9 (I.K.Kikoin, A.K.Kikoin, 1999),
task №4
to the chapter " LABORATORY WORKS».

Purpose of the work: to measure the initial speed imparted to a body in the horizontal direction as it moves under the influence of gravity.

If a ball is thrown horizontally, it moves along a parabola. Let us take as the origin of coordinates starting position ball. Let's direct the X axis horizontally and the Y axis vertically downwards. Then at any time t

Flight range l is

the value of the x coordinate that it will have if instead of t we substitute the time of the body falling from a height h. Therefore we can write:

It's easy to find from here

fall time t and initial speed V 0:

If you launch a ball several times under constant experimental conditions (Fig. 177), then the flight range values will have some scatter due to the influence various reasons, which cannot be taken into account.

In such cases, the arithmetic mean of the results obtained in several experiments is taken as the value of the measured quantity.

Measuring tools: ruler with millimeter divisions.

Materials: 1) tripod with coupling and foot; 2) tray for launching the ball; 3) plywood board; 4) ball; 5) paper; 6) buttons; 7) carbon paper.

Work order

1. Using a tripod, support the plywood board vertically. At the same time, use the same foot to pinch the protrusion of the tray. The curved end of the tray must be horizontal (see Fig. 177).

2. Attach a sheet of paper at least 20 cm wide to the plywood with thumbtacks and place carbon paper on a strip of white paper at the base of the installation.

3. Repeat the experiment five times, launching the ball from the same place in the tray, remove the carbon paper.

4. Measure the altitude h and flight range l. Enter the measurement results in the table:

7. Launch the ball along the chute and make sure that its trajectory is close to the constructed parabola.

The first goal of the work is to measure initial speed, communicated to the body in the horizontal direction when it moves under the influence of gravity. The measurement is carried out using the installation described and depicted in the textbook. If air resistance is not taken into account, then a body thrown horizontally moves along a parabolic trajectory. If you choose the point where the ball begins its flight as the origin of coordinates, then its coordinates change over time in the following way: x=V 0 t, a

The distance that the ball flies before the moment of falling (l) is the value of the x coordinate at the moment when y = -h, where h is the height of the fall, from here we can obtain at the moment of falling

Completing of the work:

1. Determination of initial speed:

Calculations:

2. Construction of the trajectory of the body.

The solution of the problem:

purpose of the work: to measure the initial speed imparted to a body in the horizontal direction as it moves under the influence of gravity.
If a ball is thrown horizontally, then it moves along a parabola. We take the initial position of the ball as the origin of coordinates. let's direct the x axis horizontally and the y axis vertically downwards. then at any time t

A
y =

flight range l is
the value of the x coordinate that it will have if instead of t we substitute the time of the body falling from a height h. so we can write:

easy to find from here
fall time t and initial speed v 0:

if you launch a ball several times under constant experimental conditions (Fig. 177), then the flight range values will have some scatter due to the influence of various reasons that cannot be taken into account.

in such cases, the arithmetic mean of the results obtained in several experiments is taken as the value of the measured quantity.
measuring instruments: ruler with millimeter divisions.
materials: 1) tripod with coupling and foot; 2) tray for launching the ball; 3) plywood board; 4) ball; 5) paper; 6) buttons; 7) carbon paper.
order of work
1.Use a tripod to support the plywood board vertically. At the same time, use the same foot to pinch the protrusion of the tray. the bent end of the tray must be horizontal (see Fig. 177).
2. Attach a sheet of paper at least 20 cm wide to the plywood with pins and place carbon paper on a strip of white paper at the base of the installation.
3. Repeat the experiment five times, launching the ball from the same place in the tray, remove the carbon paper.
4. Measure the altitude h and flight range l. Enter the measurement results in the table:

number experience	h, m	l, m	l wed, m	v 0av, m/s

5. calculate the average value of the initial speed using the formula

6. using the formulas x =

find the coordinate
x of the body (y coordinate has already been calculated) every 0.05 s and plot the trajectory of movement on a piece of paper attached to a plywood board:

t, s	0,05	0,10	0,15	0,2
x, m
y, m	0,012	0,049	0,110	0,190

7. Launch the ball along the chute and make sure that its trajectory is close to the constructed parabola.
The first goal of the work is to measure the initial speed imparted to the body in the horizontal direction as it moves under the influence of gravity. The measurement is carried out using the installation described and depicted in the textbook. If air resistance is not taken into account, then a body thrown horizontally moves along a parabolic trajectory. if you choose the point where the ball begins its flight as the origin of coordinates, then its coordinates change over time as follows: x=v 0 t, a

the distance that the ball flies before the moment of falling (l), this is the value of the x coordinate at the moment when y = -h, where h is the height of the fall, from here it can be obtained at the moment of falling

completing of the work:
1. determination of initial speed:

Experience no.	h, m	l, m	l wed, m	v 0 m/s	v 0cp m/s
1	0,2	0,16	0,15	0,79	0,74
2	0,2	0,14		0,69
3	0,2	0,15		0,74
4	0,2	0,135		0,67
5	0,2	0,165		0,82
6	0,2	0,145		0,71

calculations:

2. constructing the trajectory of body movement:

t, s	0,5	1	1,5	2
x, m	0,037	0,074

Goal of the work: measure the initial speed of a body thrown horizontally into the Earth's gravity field.

Equipment, measuring instruments: steel ball, arc-shaped tray, laboratory stand, plywood board, two sheets of white paper, carbon paper, measuring ruler

Theoretical background:

The diagram of the experimental setup is shown in the figure. The ball, starting to move at the top of the arc-shaped tray, flies out horizontally at point O with an initial speed v 0, flying along a vertical plywood board. The chute is fixed in a tripod so that point O is at a height h above the horizontal plywood board on which the ball falls.

To fix the point at which the ball falls, place a sheet of white paper on the board, and attach a sheet of copy paper on top. The ball falling onto the board leaves a mark on the white paper.

The movement of a ball thrown horizontally from a height h occurs in the vertical XY plane (X is the horizontal axis directed to the right, Y is vertical axis, pointing down). The point of departure of the ball is chosen as the starting point. (Figure 2).

O V 0 X 0 v 0 l X

l avg Y fig.1 fig. 2

Using the measured data, height h and flight range l, you can find the flight time and initial speed of the ball and write down the equation for the trajectory of motion y(x).

To find these quantities, we write the law of motion of the ball in coordinate form. Acceleration free fall g is directed vertically downwards. Along the X axis the movement will be uniform, and along the Y axis it will be uniformly accelerated.

Consequently, the coordinates (x,y) of the ball at an arbitrary moment in time are determined by the equations

at the point of impact y = h, therefore from equation (2) one can find its flight time:

The coordinate x of the ball at the point of impact is equal to the flight distance of the ball l, which is measured in the work with a ruler. From equation (1) it is easy to find the initial speed of the ball taking into account expression (3).

Work order:

1. Collect experimental setup, set the height of the ball to about 20 cm. Measure the height h with a ruler with millimeter divisions. Determine the absolute measurement error Δh =

2. Write down the resulting height h meas = h ± Δh

3. Calculate the flight time of the ball using formula (3). In this case, g = 9.81 m/s 2.

4. To measure the flight range, launch the ball five times from the same point on the arc-shaped tray. Enter the measurement results l k (k = 1, ..., 5) into Table 1.

Table 1

7. Calculate the random error Δl av =

8. Calculate the maximum absolute error Δl = Δl av + Δl pr =

9. Write down the result of measuring the flight range l =

5. Calculate the initial speed of the ball using formula (4) v 0 =

11.Calculate relative error indirect measurement initial speed (see Table 2 of the reference material).

12. Find the absolute error of indirect measurement of the initial speed Δv 0 =

13. Write down the final result of measuring the initial speed of the ball.

Additional task. Compare the actual ballistic trajectory of the ball with the calculated one.

1. To obtain the estimated trajectory y(x) of a ball thrown horizontally, express the time t from equation (1):

Substituting it into equation (2), you get the parabola equation (5)

2. Using equations (1), (2) and knowing v 0av, find the x and y coordinates of the ball every 0.05 s. Construct the calculated trajectory of movement on a piece of paper attached to a vertical plywood board. For convenience, use the table. 3.

t, s	0,05	0,10	0,15	0,20
y, m
x, m

3. Launch the ball along the chute, compare its actual ballistic trajectory with the calculated trajectory.

4. Draw a conclusion: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________-

Laboratory work No. 4

Laboratory work No. 6

Goal of the work:

1) Establish the dependence of the flight range of a body thrown horizontally on the height of the throw.

2) Experimentally confirm the validity of the law of conservation of momentum for two balls during their central collision.

Description of work:

The ball rolls down a curved chute, Bottom part which is horizontal. After separation from the chute, the ball moves along a parabola, the apex of which is at the point of separation of the ball from the chute. Let's choose a coordinate system as shown in Figure 1.

Initial height of the ball h and flight range / are related by the ratio . According to this formula, when the initial altitude decreases by 4 times, the flight range decreases by 2 times. Having measured h and /, you can find the speed of the ball at the moment of separation from the chute using the formula

Equipment: tripod with coupling and clamp, curved groove, metal ball, sheet of paper, sheet of carbon paper, plumb line, measuring tape.

Progress:

1. Assemble the installation shown in the figure. Lower section
gutters should be horizontal and distance h from the bottom
the edge of the gutter to the table should be 40 cm. Clamping feet
should be located near the top end of the gutter.

2. Place a sheet of paper under the chute, weighing it down with a book so that
it did not move during the experiments. Mark on this sheet with
using a plumb point A, located on the same vertical with
the lower end of the gutter.

3. Place the ball in the groove so that it touches the clamp, and release the ball without pushing. Notice (roughly) the spot on the table where the ball lands 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 copy paper with the “working” side down. Press down these sheets with a book so that they do not move during experiments.

4. Place the ball back into the groove so that it touches the clamp and release without pushing. Repeat this experiment 5 times, making sure
so that the sheet of copy paper and the sheet underneath it
didn't move. Carefully remove the sheet of carbon paper without
moving the sheet underneath, and mark any point lying between the prints. Please note that visible
there may be less than 5 prints because some
fingerprints may merge.

5. Measure the distance l from the marked point to point A.

6. Repeat steps 1-5, lowering the gutter so that the distance from
bottom edge The gutter to the table was 10 cm (initial height). Measure the corresponding value of the flight range and calculate the ratios and .

Write down the results of measurements and calculations in the table:

Exercise 1. Study of the motion of a body thrown horizontally

As the body under study, we use a steel ball, which is launched from the upper end of the chute. Then we release the ball. We repeat the launch of the ball 5-7 times and find S avg. Then we increase the height from the floor to the end of the gutter and repeat the ball launch.

We enter the measurement data into the table:

For height H = 81 cm.

Experience no.	S, mm	S avg., mm	N, mm	, mm	S avg / , mm
		40,6		28,5	1,42

For height H = 106 cm.

Experience no.	S, mm	S avg., mm	N, mm	, mm	S avg / , mm
				32,6	1,41

	47,5

	48,5

Task 2. Study of the law of conservation of momentum

We measure the mass of the steel ball m 1 and m 2 on the scales. We attach a device to the surface of the work table to study the motion of a body thrown horizontally. Place a clean sheet of white paper where the ball falls, glue it with tape and cover it with carbon paper. A plumb line determines the point on the floor above which the edges of the horizontal section of the gutter are located. The ball is launched and its flight range in the horizontal direction l 1 is measured. According to the formula

We calculate the speed of the ball and its momentum P 1 .

Next, we install another ball opposite the lower end of the gutter, using a knot with a support. The steel ball is launched again, the flight range l 1 ’ and the second ball l 2 ’ are measured. Then the velocities of the balls after the collision V 1 ’ and V 2 ’, as well as their impulses p 1 ’ and p 2 ’, are calculated.

Let's find the average value and absolute measurement error using the formulas

, .

Let's calculate the relative measurement error

We will enter the data into a table.

Experience no.	m 1, kg	m 2, kg	l 1, m	V 1, m/s	P 1, kg m/s	l 1 ', m	l 2 ', m	V 1 ', m/s	V 2 ', m/s	H, m	P 1 ', kg m/s	P 2 ', kg m/s
1.	0,0076	0,0076	0,47	1,15	0,0076	0,235	0,3	0,5	0,74	0,81	0,004	0,005

1.15 m/s

0.5 m/s

0.74 m/s

P 1 = m 1 V 1 = 0.0076 1.15 = 0.009 m/s

P 1 ’ = m 1 V 1 ’ = 0.0076 0.5 = 0.004 m/s

P 2 ' = m 2 V 2 ' = 0.0076 0.74 = 0.005 m/s