“Study of the motion of a body in a circle under the action of two forces”

Goal of the work: determination of the centripetal acceleration of a ball during its uniform motion in a circle.

Equipment: 1. tripod with coupling and foot;

2. measuring tape;

3. compass;

4. laboratory dynamometer;

5. scales with weights;

6. ball on a thread;

7. a piece of cork with a hole;

8. sheet of paper;

9. ruler.

Work order:

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

2. We pass the thread through the hole and clamp the plug in the tripod foot (Fig. 1)

3. Draw a circle on a piece of paper, the radius of which is about 20 cm. We measure the radius with an accuracy of 1 cm.

4. We position the tripod with the pendulum so that the extension of the cord 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 a circle equal to that drawn on the paper.

6. We count the time during which the pendulum makes, for example, N=50 revolutions. Calculating the circulation period T=

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.

8. Find the modulus of normal acceleration using the formulas:

a n 1 = a n 2 =

a n 1 = a n 2 =

9. Using a horizontal dynamometer, we pull the ball to a distance equal to the radius of the circle and measure the modulus of the component F

Then we calculate the acceleration using the formula a n 3 = a n 3 =

10. We enter the measurement results into a table.

Experience no.	R m	N	∆t c	T c	h m	m kg	F N	a n1 m/s 2	a n 2 m/s 2	a n 3 m/s 2

Calculate the relative calculation error a n 1 and write the answer in the form: a n 1 = a n 1av ± ∆ a n 1av a n 1 =

Draw a conclusion:

Control questions:

1. What type of motion is the movement of a ball on a string in laboratory work? Why?

2. Make a drawing in your notebook and indicate the names of the forces correctly. Name the points of application of these forces.

3. What laws of mechanics are satisfied when the body moves in this work? Draw graphically the forces and write the laws correctly

4. Why is the elastic force F, measured experimentally, equal to the resultant forces applied to the body? Name the law.

Date__________ FI________________________________________ Class 10_____

Laboratory work No. 1 on the topic:

“STUDYING THE CIRCULAR MOTION OF A BODY UNDER THE INFLUENCE OF ELASTICITY AND GRAVITY FORCES.”

Goal of the work: determination of the centripetal acceleration of a ball during its uniform motion in a circle.

Equipment: tripod with coupling and foot, measuring tape, compass, dynamometer

laboratory, scales with weights, weight on a string, sheet of paper, ruler, cork.

Theoretical part of the work.

Experiments are carried out with a conical pendulum. A small ball moves along a circle of radius R. In this case, the thread AB, to which the ball is attached, describes the surface of a right circular cone. There are two forces acting on the ball: gravity
and thread tension (Fig. a). They create centripetal acceleration , directed radially towards the center of the circle. The acceleration modulus can be determined kinematically. It is equal to:

.

To determine the acceleration, it is necessary to measure the radius of the circle and the period of revolution of the ball along the circle.

Centripetal (normal) acceleration can also be determined using the laws of dynamics.

According to Newton's second law
. Let's break down the force into components And , directed radially to the center of the circle and vertically upward.

Then Newton's second law will be written as follows:

.

We choose the direction of the coordinate axes as shown in Figure b. In projections onto the O 1 y axis, the equation of motion of the ball will take the form: 0 = F 2 - mg. Hence F 2 = mg: component balances gravity
, acting on the ball.

Let's write down Newton's second law in projections onto the O 1 x axis: man = F 1 . From here
.

The modulus of the component F 1 can be determined in various ways. Firstly, this can be done from the similarity of triangles OAB and FBF 1:

.

From here
And
.

Secondly, the modulus of the component F 1 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 of the circle (Fig. c), and determine the reading of the dynamometer. In this case, the elastic force of the spring balances the component .

Let's compare all three expressions for a n:

,
,
and make sure that they are close to each other.

Progress.

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

2. Secure the ball suspended on a thread in the tripod leg using a piece of cork.

3 . Draw a circle with a radius of 20 cm on a piece of paper (R= 20 cm = ________ m).

4. We position the tripod with the pendulum so that the extension of the cord passes through the center of the circle.

5 . Taking the thread with your fingers at the suspension point, set the pendulum into rotational motion

above a sheet of paper so that the ball describes the same circle as the one drawn on the paper.

6. We count the time during which the pendulum makes 50 full revolutions (N = 50).

7. Calculate the period of revolution of the pendulum using the formula: T = t / N.

8 . Calculate the value of centripetal acceleration using formula (1):

=

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

10 . Calculate the value of centripetal acceleration using formula (2):

=

11. Pull the ball with a horizontal dynamometer to a distance equal to the radius of the circle and measure the modulus of the component .

Then we calculate the acceleration using formula (3): =

12. The results of measurements and calculations are entered into the table.

Circle radius R , m	Speed N	t , With	Circulation period T = t / N	Pendulum height h , m	Ball mass m , kg	Center acceleration m/s 2	Center acceleration m/s 2	Center acceleration m/s 2

13 . Compare the obtained three values ​​of the centripetal acceleration module.

__________________________________________________________________________ CONCLUSION:

______________________________________________________________________________________________________________________________________________________________________________________________________________________________

Additionally:

Find the relative and absolute error of indirect measurement a c (1) and (3):

Formula 1). ________ ; Δa c = · a c = ________;

Formula (3). _________; Δa c = · a c = _______.

No. 1. Study of body movement in a circle

Goal of the work

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

Theoretical part

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

Two forces act on the ball: the force of gravity m and the tension force of the thread (Fig. L.2, a). According to Newton's second law, m = m +. Having decomposed the force into components 1 and 2, directed radially to the center of the circle and vertically upward, we write Newton’s second law as follows: m = m + 1 + 2. Then we can write: ma n = F 1. Hence a 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 = 4 π 2 R/T 2, and n =gR/h, and n = F 1 /m

and make sure that the numerical values ​​of the centripetal acceleration obtained by the three methods are approximately the same.

Equipment

A tripod with a coupling and a foot, a measuring tape, a compass, a laboratory dynamometer, a scale with weights, a ball on a string, a piece of cork with a hole, a sheet of paper, a ruler.

Work order

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

2. Pass the thread through the hole in the plug and clamp the plug in the tripod foot (Fig. L.2, b).

3. Draw a circle on a piece 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 the 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 assume h ≈ l).

9. Pull the ball with a horizontal dynamometer to a distance equal to the radius of the circle and measure the modulus of component 1.

Then calculate the acceleration using the formula

Comparing the obtained three values ​​of the centripetal acceleration module, we are convinced that they are approximately the same.

.

IPreparatory stage

The figure shows a schematic diagram of a swing known as a giant step. Find the centripetal force, radius, acceleration and speed of rotation of the person on the swing around the pole. The length of the rope is 5 m, the mass of the person is 70 kg. When the pole and the rope rotate, they form an angle of 300. Determine the period if the rotation frequency of the swing is 15 min-1.

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

Enter the calculation results into the table:

Circulation time, s

Speed

Circulation period, s

Circulation radius, m

Body weight, kg

centripetal force, N

circulation speed, m/s

centripetal acceleration, m/s2

II. Main stage

Goal of the work:

Equipment and materials:

1. Before the experiment, hang a load, previously weighed on a scale, on a thread from the tripod leg.

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

3. At the suspension point, take the thread with two fingers and carefully bring the pendulum into rotation, so that the radius of rotation of the pendulum coincides with the radius of the drawn circle.

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

5. Write the results of measurements and calculations in a table.

6. The resultant force of gravity and elastic force, found during the experiment, is calculated from the parameters of the circular motion 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 to 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 by two different methods and draw a conclusion.

IIIControl stage

If there are no scales at home, the purpose of the work and equipment can be changed.

Goal of the work: measurement of linear velocity and centripetal acceleration during uniform circular motion

Equipment and materials:

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

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

3. Achieve stable rotation of the ball along a given trajectory and, using a clock with a second hand, record 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. A manual for teachers, edited. Ed. 2nd. - M., “Enlightenment”, 1974

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