Lab work is the study of the movement of the body in a circle. Determination of body weight by weighing on a scale. Indicate whether the purpose of the work has been achieved

Elasticity and gravity

Objective

Determination of the centripetal acceleration of the ball when it uniform motion around the circumference

Theoretical part of the work

Experiments are carried out with a conical pendulum: a small ball suspended from a thread moves in a circle. In this case, the thread describes a cone (Fig. 1). Two forces act on the ball: the force of gravity and the force of elasticity of the thread. They create centripetal acceleration directed along the radius towards the center of the circle. The acceleration modulus can be determined kinematically. It is equal to:

To determine the acceleration (a), you need to measure the radius of the circle (R) and the period of revolution of the ball around the circle (T).

Centripetal acceleration can be determined in the same way using the laws of dynamics.

According to Newton's second law, Let's write down given equation in projections on the selected axes (Fig. 2):

Oh: ;

Oy: ;

From the equation in the projection onto the Ox axis, we express the resultant:

From the equation in projection onto the Oy axis, we express the elastic force:

Then the resultant can be expressed:

and here is the acceleration: , where g \u003d 9.8 m / s 2

Therefore, to determine the acceleration, it is necessary to measure the radius of the circle and the length of the thread.

Equipment

Tripod with clutch and claw, measuring tape, ball on a thread, a sheet of paper with a drawn circle, a clock with a second hand

Working process

1. Hang the pendulum from the tripod leg.

2. Measure the radius of the circle with an accuracy of 1mm. (R)

3. Position the tripod with the pendulum so that the extension of the cord passes through the center of the circle.

4. Take the thread with your fingers at the suspension point, rotate the pendulum so that the ball describes a circle equal to that drawn on paper.

6. Determine the height of the conical pendulum (h). To do this, measure the vertical distance from the suspension point to the center of the ball.

7. Find the acceleration module using the formulas:

8. Calculate the errors.

Table Results of measurements and calculations

Computing

1. Period of circulation: ; T=

2. Centripetal acceleration:

; a 1 =

; a 2 =

Average value of centripetal acceleration:

; a cp =

3. Absolute error:

∆a 1 =

∆a 2 =

4. Average value of absolute error: ; Δа ср =

5. Relative error: ;

Output

Record responses questions in full sentences

1. Formulate the definition of centripetal acceleration. Write it down and the formula for calculating the acceleration when moving in a circle.

2. Formulate Newton's second law. Write down its formula and wording.

3. Write down the definition and formula for calculating

gravity.

4. Write down the definition and formula for calculating the elastic force.

LAB 5

Body movement at an angle to the horizon

Target

Learn to determine the height and range of flight when the body moves with an initial speed directed at an angle to the horizon.

Equipment

Model "Movement of a body thrown at an angle to the horizon" in spreadsheets

Theoretical part

The movement of bodies at an angle to the horizon is a complex movement.

Movement at an angle to the horizon can be divided into two components: uniform movement along the horizontal (along the x axis) and simultaneously uniformly accelerated, with free fall acceleration, along the vertical (along the y axis). This is how a skier moves when jumping from a springboard, a jet of water from a hose, artillery shells, projectiles

Equations of motion s w:space="720"/>"> And

we write in projections on the x and y axes:

For X-axis: S=

To determine the flight altitude, it must be remembered that at the top point of the ascent, the speed of the body is 0. Then the ascent time will be determined:

When falling, the same time passes. Therefore, the travel time is defined as

Then the lift height is determined by the formula:

And the flight range:

The greatest flight range is observed when moving at an angle of 45 0 to the horizon.

Working process

1. Write in a workbook theoretical part work and draw a graph.

2. Open the file "Movement at an angle to the horizon.xls".

3. In cell B2, enter the value of the initial speed, 15 m/s, and in cell B4, enter the angle of 15 degrees(only numbers are entered in the cells, without units of measurement).

4. Consider the result on the graph. Change the speed value to 25 m/s. Compare Graphs. What changed?

5. Change the speed to 25 m/s and the angle to -35 degrees; 18 m/s, 55 degrees. Consider charts.

6. Perform formula calculations for speeds and angles(by options):

8. Check your results, look at the graphs. Draw graphs to scale on a separate A4 sheet

Table Values of sines and cosines of some angles

	30 0	45 0	60 0
Sinus	0,5	0,71	0,87
Cosine (Cos)	0,87	0,71	0,5

Output

Write down the answers to the questions complete sentences

1. On what quantities does the flight range of a body thrown at an angle to the horizon depend?

2. Give examples of the movement of bodies at an angle to the horizon.

3. At what angle to the horizon is the greatest range of flight of the body at an angle to the horizon?

LAB 6

4.2.1. Prepare the scales and, with the permission of the laboratory assistant, weigh the body. Determine the instrumental error of the scales.

4.2.2. Record the measurement result in standard form: m=(m±Δm) [dimension].
5. CONCLUSION

Indicate whether the goal of the work has been achieved.

Record body weight measurements in two ways.

5.3. Compare results. Draw a conclusion
6. CONTROL QUESTIONS

6.1. What is inertial mass, gravitational mass, how are they defined? Formulate the principle of equivalence of inertial and gravitational mass.
6.2. What are direct measurements and indirect measurements? Give examples of lines and indirect measurements.
6.3. What is the absolute error of the measured value?
6.4. What is the relative error of the measured value?
6.5. What is the confidence interval of the measured quantity?
6.6. List the types of errors and give them brief description.
6.7. What is the accuracy class of the device? What is the price division of the device?
How is the instrumental error of the measurement result determined?
6.8. How the relative error and absolute error of indirect measurement are calculated.
6.9. How is the standard recording of the final measurement result made? What requirements must be met?

6.10. Measure the linear size of the body with a caliper. Record the measurement result in standard form.

6.11. Measure the linear size of the body with a micrometer. Record the result.

Laboratory work №2.

The study of the movement of the body in a circle

1. PURPOSE OF THE WORK. Determination of the centripetal acceleration of a ball during its uniform motion in a circle.

2. INSTRUMENTS AND ACCESSORIES. A tripod with a clutch and a foot, a ruler, a tape measure, a ball on a thread, a sheet of paper, a stopwatch.

BRIEF THEORY

The experiment is carried out with a conical pendulum (Fig. 1). Let a ball suspended on a thread describe a circle with a radius R. There are two forces acting on the ball: gravity and tension in the string. Their resultant creates a centripetal acceleration directed towards the center of the circle. The acceleration modulus can be determined using kinematics:

(1)

To determine the acceleration, it is necessary to measure the radius of the circle R and the period T circulation of the ball around the circle.
Centripetal acceleration can also be determined using Newton's 2nd law:

We choose the direction of the coordinate axes as shown in Fig.1. We project equation (2) onto the selected axes:

From equations (3) and (4) and from the similarity of triangles we get:

Fig.1. . (5)

Thus, using equations (1), (3) and (5), centripetal acceleration can be determined in three ways:

. (6)

Component module F x can be directly measured with a dynamometer. To do this, we pull the ball with a horizontally located dynamometer to a distance equal to the radius R circle (Fig. 1), and determine the dynamometer reading. In this case, the elastic force of the spring balances the horizontal component F x and equal in size.

In this work, the task is to verify experimentally that numerical values centripetal acceleration, obtained in three ways, will be the same (the same within the absolute errors).

WORK TASK

1. Determine the mass m balls on the scales. Weighing result and instrumental error ∆ m write in table 1.

2. We draw a circle with a radius of about 20 cm on a piece of paper. We measure this radius, determine the instrumental error, and write the results in table 1.

3. Position the tripod with the pendulum so that the continuation of the thread passes through the center of the circle.

4. Take the thread with your fingers at the point of suspension and rotate the pendulum so that the ball describes the same circle as the circle drawn on paper.

5. Counting the time t, for which the ball makes a given number of revolutions (for example, N= 30) and estimate the error ∆ t measurements. The results are recorded in table 1.

6. Determine the height h conical pendulum and instrumental error ∆ h. Distance h measured vertically from the center of the ball to the point of suspension. The results are recorded in table 1.

7. We pull the ball with a horizontally located dynamometer to a distance equal to the radius R of the circle, and determine the dynamometer reading F= F x and instrumental error ∆ F. The results are recorded in table 1.

Table 1.

∆m

∆R

∆t

∆h

∆F

∆g

∆ π

from

m/s 2

8. Calculate the period T circulation of the ball around the circle and the error ∆ T:

9. Using formulas (6), we calculate the values of centripetal acceleration in three ways and the absolute errors of indirect measurements of centripetal acceleration.

OUTPUT

In the output, write in standard form the values of centripetal acceleration obtained in three ways. Compare the obtained values (see section "Introduction. Measurement errors"). Make a conclusion.

TEST QUESTIONS

6.1. What is a period T

6.2. How can you experimentally determine the period T the circle of the ball?

6.3. What is centripetal acceleration, how can it be expressed in terms of the period of revolution and in terms of the radius of the circle?

6.4. What is a conical pendulum. What forces act on the ball of a conical pendulum?

6.5. Write down Newton's 2nd law for a conical pendulum.

6.6. What are the three methods for determining centripetal acceleration offered in this lab?

6.7. What measuring devices are used to determine the values physical quantities given in table 1?

6.8. Which of the three methods for determining centripetal acceleration gives the most accurate value of the measured quantity?

Lab #3

Similar information.

IPreparatory stage

The figure schematically shows the swing, known as "giant steps". Find the centripetal force, radius, acceleration and speed of a person swinging around a pole. The length of the rope is 5 m, the mass of a person is 70 kg. The pole and the rope form an angle of 300 during circulation. Determine the period if the rotation frequency of the swing is 15 min-1.

Hint: A body rotating in a circle is affected by gravity and the elastic force of the rope. Their resultant imparts centripetal acceleration to the body.

Enter the results of the calculations in the table:

Turnaround time, s

Speed

Period of circulation, s

Radius of circulation, m

Body weight, kg

centripetal force, N

circulation speed, m/s

centripetal acceleration, m/s2

II. main stage

Objective:

Devices and materials:

1. Before the experiment, a load, previously weighed on a balance, is suspended on a thread to the leg of the tripod.

2. Under the hanging load, place a sheet of paper with a circle drawn on it with a radius of 15-20 cm. Place the center of the circle on plumb line passing through the point of suspension of the pendulum.

3. At the point of suspension, the thread is taken with two fingers and the pendulum is carefully brought into rotational motion, so that the radius of rotation of the pendulum coincides with the radius of the drawn circle.

4. Bring the pendulum into rotation and counting the number of revolutions, measure the time during which these revolutions occurred.

5. Record the results of measurements and calculations in the table.

6. The resultant force of gravity and the force of elasticity, found during the experiment, is calculated from the parameters of the circular movement of the load.

On the other hand, the centripetal force can be determined from the proportion

Here, the mass and radius are already known from previous measurements, and in order to determine the centrifugal force in the second way, it is necessary to measure the height of the suspension point above the rotating ball. To do this, pull the ball a distance equal to the radius of rotation and measure the vertical distance from the ball to the suspension point.

7. Compare the results obtained in two different ways and draw a conclusion.

IIIcontrol stage

In the absence of scales at home, the purpose of work and equipment can be changed.

Objective: measurement of linear velocity and centripetal acceleration in uniform circular motion

Devices and materials:

1. Take a needle with a double thread 20-30 cm long. Insert the tip of the needle into an eraser, a small onion or a plasticine ball. You will receive a pendulum.

2. Raise your pendulum by the free end of the thread above a sheet of paper lying on the table, and bring it into uniform rotation around the circle shown on the sheet of paper. Measure the radius of the circle along which the pendulum moves.

3. Achieve a stable rotation of the ball along a given trajectory and use the clock with a second hand to fix the time for 30 revolutions of the pendulum. Using known formulas, calculate the modules of linear velocity and centripetal acceleration.

4. Make a table to record the results and fill it out.

References:

1. Frontal laboratory classes in physics in high school. Manual for teachers edited. Ed. 2nd. - M., "Enlightenment", 1974

2. Shilov work at school and at home: mechanics.-M .: "Enlightenment", 2007

We know from the textbook (pp. 15-16) that when moving uniformly in a circle, the speed of a particle does not change in magnitude. In fact, from a physical point of view, this movement is accelerated, since the direction of the velocity is continuously changing in time. In this case, the speed at each point is practically directed along the tangent (Fig. 9 in the textbook on page 16). In this case, acceleration characterizes the rate of change in the direction of velocity. It is always directed towards the center of the circle along which the particle moves. For this reason, it is commonly called centripetal acceleration.

This acceleration can be calculated using the formula:

The speed of movement of a body in a circle is characterized by the number of complete revolutions per unit of time. This number is called the rotational speed. If the body makes v revolutions per second, then the time it takes to complete one revolution is

seconds. This time is called the rotation period.

To calculate the speed of a body in a circle, you need the path traveled by the body in one revolution (it is equal to the length

circles) divided by the period:

in this work we

we will observe the movement of a ball suspended on a thread and moving in a circle.

An example of a job.

No. 1. Studying the movement of the body in a circle

Objective

Determine the centripetal acceleration of the ball as it moves uniformly in a circle.

Theoretical part

Experiments are carried out with a conical pendulum. A small ball moves along a circle with radius R. In this case, the thread AB, to which the ball is attached, describes the surface of a right circular cone. It follows from the kinematic relations that an = ω 2 R = 4π 2 R/T 2 .

Two forces act on the ball: the force of gravity m and the force of the thread tension (Fig. L.2, a). According to Newton's second law m = m + . Having decomposed the force into components 1 and 2 , directed along the radius to the center of the circle and vertically upwards, we write Newton's second law as follows: m = m + 1 + 2 . Then we can write: ma n = F 1 . Hence а n = F 1 /m.

The modulus of the component F 1 can be determined using the similarity of triangles OAB and F 1 FB: F 1 /R = mg/h (|m| = | 2 |). Hence F 1 = mgR/h and a n = gR/h.

Let's compare all three expressions for a n:

and n \u003d 4 π 2 R / T 2, and n \u003d gR / h, and n \u003d F 1 / m

and make sure that the numerical values of the centripetal acceleration obtained in three ways are approximately the same.

Equipment

A tripod with a clutch and a foot, a measuring tape, a compass, a laboratory dynamometer, balances with weights, a ball on a thread, a piece of cork with a hole, a sheet of paper, a ruler.

Work order

1. Determine the mass of the ball on the balance with an accuracy of 1 g.

2. Thread the thread through the hole in the cork and clamp the cork in the leg of the tripod (Fig. L.2, b).

3. Draw a circle on a sheet of paper with a radius of about 20 cm. Measure the radius to the nearest 1 cm.

4. Position the tripod with the pendulum so that the continuation of the thread passes through the center of the circle.

5. Taking the thread with your fingers at the suspension point, rotate the pendulum so that the ball describes the same circle as the one drawn on paper.

6. Count the time during which the pendulum makes a given number (for example, in the range from 30 to 60) revolutions.

7. Determine the height of the conical pendulum. To do this, measure the vertical distance from the center of the ball to the suspension point (we consider h ≈ l).