7th grade math total review of the semester answer 5

Updated on educate 2024-07-06
4 answers
  1. Anonymous users2024-02-12

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  4. Anonymous users2024-02-09

    Three methods for measuring bullet velocity.

    Hunan Shan Wenzhong.

    The velocity of a bullet that has just come out of the chamber is difficult to measure due to its high speed, but this problem can be solved if we apply what we have learned skillfully.

    1. Use the flat throwing motion model to measure the velocity.

    Example 1As shown in Figure 1, A and B are two pieces of thin paper placed vertically, the bullet M passes through A and then passes through B with the horizontal initial velocity, and the difference between the two vertical heights of the two pieces of paper is H, and the distance between A and B is L, then what is the initial velocity of the bullet?

    Analysis: From the knowledge of flat throwing motion, it can be seen that the time of the bullet flying l in the horizontal direction is the time when the bullet falls freely in the vertical direction.

    Comments: This method cleverly solves the problem of measuring the extremely short time required for a small distance of bullet motion, making it possible to measure the velocity of the bullet. Since the effect of the thin paper disc on the flight speed of the bullet is almost zero, the measurement error of this method is very small.

    2. Use a uniform circular motion model to measure speed.

    Example 2As shown in Figure 2, the paper cylinder with diameter D rotates at a constant speed around the axis at angular velocity, and the muzzle is aimed at point A on the cylinder to fire a bullet in the direction of diameter, and the bullet passes through point B exactly when the cylinder rotates less than half a turn. Knowing that the angle between ao and bo is radian, what is the velocity of the bullet?

    Analysis: According to the inscription, if the cylinder does not rotate, the bullet will hit directly on it; If the cylinder rotates and the bullet hits point B, then the time for the bullet to move in the cylinder is equal to the time taken for the cylinder to turn, so.

    Comments: This method measures the bullet velocity by using the time taken by the cylinder to rotate at a certain angle at a uniform speed to measure the time taken by the bullet to move the distance d, but because the bullet is affected by gravity during the movement, it is impossible to move at a uniform speed in the cylinder, so the error of this method is larger than the first method.

    3. The speed is measured by combining the two models of flat throwing and constant cylinder motion.

    Example 3In order to determine the velocity of the bullet when it is ejected out of the chamber, two thin discs A, B, A, and B are fixed on a horizontally placed shaft rod and are 2m apart from each other in parallel, the rotation speed of the shaft rod is 3600r min, the bullet passes through the two discs and leaves two bullet holes A and B, and the angle between the radius where the two holes are measured is 30°, as shown in Figure 3, what is the velocity of the bullet out of the chamber?

    Analysis: As shown in Figure 3, at the moment when the bullet penetrates the thin disc A, the bullet, the disc A, and the disc B are all in the same vertical plane, and when the bullet flies between disc A and disc B, disc A and disc B all rotate at a constant speed, and when the bullet penetrates disc B, it has turned to the position of Figure 4, which indicates that the flight time of the bullet between disc A and disc B is equal to the time of rotation at an angle of 30 °, therefore.

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