Лабораторные работы / Решенная лабораторная по физике 03b

The laboratory work N^o 3,b.

Studying of velocity of a bullet with the help of a rotating platform.

Had done by the student gr: 220473я F.N.S. Pavlov F.E.

Checked by ______________________ date ____________

Purpose: to apply the law of conservation of a projection of the angular momentum to define the velocity of a bullet with a shot.

The order of performing a work:

1. Measure the masses of the disc, trap and bullet.

2. Symmetrically to install the trap on the any distance from the axis of rotation of the disc and fix it.

3. Push disc by hand and to measure the time and angel of a turning of a disc (8 times).

4. Find average meanings: <>, <>.

5. Make a shot after that the bullet would get in a trap. Measure the angel of a turning of a disc (8 times). Then to define an average meaning <>.

6. Define the moment of inertia of the disc with the traps by formula .

7. Define the velocity of the bullet by formula .

8. Write data of measurements and calculations in the table 1-3.

Theoretical description:

Making a shot from a spring pistol in a trap, we shall result the trap in a rotary movement. And on the basis of the law on conservation of a projection of the angular momentum, we can write down:

mVl = (J + ml²)w (1)

Where m - weight of a bullet, l - shoulder of a momentum of a bullet, distance from an axis of rotation up to a line of a impulse of the bullet, V - speed of the bullet, J - moment of inertia of a platform with a trap concerning an axis of rotation, w - angular speed of a platform at once after impact. From here follows, that

V = (J + ml²)w/(ml) (2)

Allowing with that after the impact the platform will rotates with the uniformly deceleration and up to the complete stop on an angle  , we shall express w through the angular acceleration  and the angle : w² = 2. It is possible to find , from the additional supervision of a rotary movement of a disk caused by a push of a hand:

= 2/t² (3)

where  - An angle of a turn of the platform up to a stop, t – the time of turning.

Finally for V we have:

The formula for the definition of a moment of inertia of the disk with traps:

(4)

where т_d – the mass of the disk, r_d – the radius of the disk , т_t – the mass of the trap, l - the distance up to the center of rotation:

Table N^o1.

m, kg	m, kg	md, kg	md, kg	mg, kg	mg, kg	rd, m	rd, m	l, m	l, m
0.0131	0.00005	0.69	0.005	0.1645	0.00005	0.15	0.005	0.14	0.005

J = ½*0.69*0.15² + 0.1645*0.14² = 0.011 kg m².

Table N^o2.

N	l, m	<l>, m	l, m	, rad	t, s	, s-2	<>, s-2	,s-2	, rad	<>, rad	, rad
1	0.14	0.14	0.005	1.74	5.6	0.11	0.10	0.035	1.31	1.35	0.058
2				0.23	2.41	0.07			1.36
3				1.01	4.32	0.10			1.43
4				1.99	6.42	0.07			1.38
5				0.96	4.1	0.09			1.34
6				0.28	2.78	0.08			1.4
7				0.91	3.97	0.07			1.26
8				0.65	2.95	0.15			1.34

We shall compute this by using the formulas:

Table N^o3.

V, m/s	V, m/s	E, %
4.52	0.4384	9.7

From V = <V>  V=4.520.4384

Conclusion:

so we have studied to apply the law of conservation of a projection of the angular momentum to define the velocity of a bullet with a shot.