Hunan Shan Wenzhong

It is difficult to measure the speed of a bullet just out of the gun chamber because of its fast flight speed, but this problem can be solved if you can skillfully use what you have learned.

Firstly, the velocity is measured by the flat throwing motion model.

Example 1. As shown in figure 1, A and B are two vertical sheets of tissue paper. The bullet m passes through a at a horizontal initial velocity, and then passes through B. The difference between the vertical heights of two pieces of paper is H, the distance between A and B is L, and what is the initial velocity of the bullet?

Analysis: According to the knowledge of flat throwing motion, the time for a bullet to fly in the horizontal direction L is the time for the bullet to fall freely in the vertical direction, so there are

Comments: This method skillfully solves the problem of measuring bullet speed in short distance, thus making it possible to measure bullet speed. Because the influence of thin paper on the flying speed of bullets is almost zero, the measurement error of this method is very small.

Secondly, the velocity is measured by the uniform circular motion model.

Example 2. As shown in fig. 2, the paper cylinder with diameter d rotates around the axis at a uniform angular velocity ω, and the gun aims at point A on the cylinder to fire a bullet in the diameter direction. In the range of less than half a revolution of the cylinder, the bullet just passes through point B ... Given that the angle between aO and bO is θ radian, what is the speed of the bullet?

Analysis: according to the meaning of the question, if the cylinder does not rotate, the bullet will land directly; When the cylinder rotates and the bullet hits point B, the time for the bullet to move in the cylinder is equal to the time for the cylinder to rotate, so

Comments: This method is to measure the moving distance d of the bullet by using the time required for the cylinder to rotate at a certain angle at a constant speed. However, due to the action of gravity, it is impossible for the bullet to move at a uniform speed in the cylinder, so the error of this method is greater than that of the first method.

Thirdly, the velocity is measured by combining two models: flat throwing and uniform cylindrical motion.

Example 3. In order to measure the velocity of the bullet when it leaves the gun chamber, two thin disks A and B are fixed on a horizontal axis, and the distance between them is 2m. The rotation speed of the shaft is 3600r/min, and the bullet passes through two disks, leaving two bullet holes A and B, and the included angle of the two holes is 30, as shown in Figure 3. What's the speed at which the bullet goes out of the gun chamber?

Analysis: As shown in Figure 3, the bullet, disc A and disc B are all on the same vertical plane at the moment when the bullet passes through the thin disc A. When the bullet flies between disc A and disc B, both discs A and B rotate at a constant speed. When the bullet passes through disc B, it has already turned to the position shown in Figure 4, that is to say, the flight time of the bullet between disc A and disc B is equal to the time of rotation of 30 degrees. Therefore,

Comments: The bullet actually moves horizontally between plate A and plate B, so measuring the speed of the bullet when it comes out of the gun bore is the initial speed of the flat throwing motion. The measurement of time is based on the rotation of the disk, which makes up for the defect that it is difficult to measure the height h because of the excessive speed of the bullet in the first method, and the error caused by the variable speed movement of the bullet in the cylinder in the second method, so this method has the smallest error among the three methods.

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