Ballistic Pendulum

A collision between two bodies can be elastic or inelastic. In an elastic collision the two bodies rebound with no loss of kinetic energy. In an inelastic collision one or both bodies can be deformed, or they can stick together. Either of these processes absorbs some of the systems kinetic energy. The system can also dissipate kinetic energy in producing sound or heat. Since there are no external forces acting on the system at the time of the collision, linear momentum must be conserved in both cases.

两个物体之间的碰撞可以是弹性碰撞或非弹性碰撞。在弹性碰撞中，两个物体碰撞后反弹，动能没有损失。在非弹性碰撞中，一个或两个物体可能会变形，或者它们可能会粘在一起。这两种过程都会吸收系统的一部分动能。系统也可能通过产生声音或热量来耗散动能。由于碰撞发生时系统内没有外力作用，因此在这两种情况下动量都必须守恒。

In this lab you will study an inelastic collision using a Blackwood ballistic pendulum. The colliding bodies are a small metal ball, which is fired from a spring loaded gun, and a metal receptacle, or catcher. The receptacle is also the bob of a simple pendulum. Initially the pendulum is at rest. When the gun fires, the ball collides with the pendulum and is trapped in the catcher which then starts to swing. A ratchet and pawl system catches the pendulum at the height of its swing.

在本实验中，你将使用一个Blackwood弹力 pendulum 研究非弹性碰撞。碰撞的两个物体是一个小金属球，它由弹簧枪发射，另一个是金属容器，或称为捕获器。该容器同时也是单摆的摆球。最初，单摆处于静止状态。当枪发射时，球与单摆碰撞并被卡入捕获器中，然后单摆开始摆动。一个棘轮和棘爪系统会在单摆摆动的最高点将其卡住。

The best way to understand this experiment is to divide it into three separate events. First, the gun fires and the ball of mass m travels horizontally with initial velocity U In the absence of external forces, the horizontal component of its velocity will not change. The horizontal component of the ball's initial linear momentum is:

理解这个实验的最佳方式是将其分为三个独立的事件。首先，枪发射，质量为m的球水平以初始速度U运动。在没有外力作用的情况下，其水平速度分量不会改变。球的初始线性动量的水平分量为：

In the second event, the ball collides with the "catcher" of mass M and is trapped by the spring. The system loses kinetic energy in the deformation of the spring and the creation of sound. Linear momentum, however, must be conserved. The pendulum, of mass (M + m), moves with a new horizontal velocity, V. The momentum of the system is now:

在第二个事件中，球与质量为M的'捕手'相撞并被弹簧卡住。系统在弹簧形变和产生声音的过程中损失了动能。然而，线性动量必须守恒。质量为(M + m)的单摆以新的水平速度V运动。系统的动量现在为：

由于两个动量相等，我们可以解出U：

Finally, the system acts like a simple pendulum. It moves upward and is caught by the ratchet at the highest part of its swing. The ratchet and pawl are designed to exert negligible force on the pendulum while it is moving upward, so mechanical energy is conserved. This means that the pendulum's kinetic energy at the bottom of its swing must equal its potential energy at the top of its swing. The change in height, h, of the center of mass can be easily measured. We can then solve for V:

最后，系统 behaves 像一个单摆。它向上移动，并在摆动的最高点被棘轮卡住。棘轮和棘爪设计为在摆动向上时对摆锤施加的力可以忽略不计，因此机械能守恒。这意味着摆锤在摆动底部的动能必须等于在摆动顶部的势能。质心的 height 变化 h 可以很容易地测量。我们然后可以求解 V：

将此V的值代入方程3：

There is a different, more direct way to measure the initial velocity of the ball. We can fire the gun horizontally from a known height and measure its range, R. The velocity, U, is given by:

测量球的初速度有另一种更直接的方法。我们可以从已知高度水平发射枪，测量其射程 R。速度 U 由下式给出：

where T is the time of flight. We can solve for the time of flight because the ball's horizontal and vertical motion are independent. As it moves horizontally, the ball also falls because of the influence of gravity. If the ball drops a distance Y:

其中 T 是飞行时间。我们可以求出飞行时间，因为球的水平运动和垂直运动是相互独立的。当球水平运动时，它也由于重力的影响下落。如果球下落的距离为 Y：

使用米制单位。质量测量精度为0.001千克，长度测量精度为0.001米。

永远不要把枪对准任何人！！！

Your instructor will show you how to load and fire the gun. Occasionally the ball will miss the catcher; therefore do not fire it if anyone is within range of the ball.

您的老师会教您如何装填和发射枪。偶尔球会偏离捕手；因此如果有人在球的射程范围内，请不要发射。

Be careful when you remove the ball from the catcher; push the spring inward to release the ball. The spring will break if you pull it backwards.

当你从捕手处取出球时要小心；将弹簧向内推以释放球。如果向后拉弹簧，弹簧会断裂。

1. Unscrew the set screw that holds the pendulum at the top of the apparatus. Measure the mass of the ball (m) and of the ball and pendulum together (M + m). Reassemble the apparatus. Make sure that the pendulum can swing freely with a minimum of side-to-side motion.

松开固定在装置顶部的螺钉，测量球的质量（m）以及球和摆锤的总质量（M + m）。重新组装装置。确保摆锤可以自由摆动，且摆动幅度尽可能小。

2. Fire the gun and record the number of the notch in which the pendulum comes to rest. Repeat twice. If the notch numbers vary greatly, or if you have other problems, consult your instructor.

射击枪支，并记录单摆最终停在的缺口编号。重复两次。如果缺口编号差异很大，或者你遇到其他问题，请咨询你的指导教师。

3. While the pendulum is hanging freely, measure the height of the center of mass marker from the base of the apparatus.

当单摆自由悬挂时，测量质心标记与装置底座之间的高度。

4. Average the notch numbers and raise the pendulum to that notch. Measure the height of the center of mass marker from the base of the apparatus. The difference between the two heights is h.

4. 计算缺口编号的平均值，并将单摆提升到该缺口处。测量质心标记从装置底座到的高度。两者的高度差为h。

5. 用方程6计算球的初速度。

6. Leave the pendulum raised. Position the apparatus near the end of the table so that it is aimed out across the floor with a range of about three meters. Shoot the ball and note where it hits the floor. Make sure that the gun does not move. Use masking tape to secure a piece of cork pad with a carbon set on it to the floor where the ball landed.

6. 保持摆锤抬高。将装置放置在桌子末端，使其朝向地板，覆盖范围约为三米。发射球体，并注意它落在地板上的位置。确保枪不移动。用贴纸将一块带有碳粉的软木垫贴在球体落地的位置。

7. Fire the ball three more times or until you have three marks on the carbon set.

再向碳靶射击三次或直到在碳靶上得到三个标记。

8. Put the gun back on the gun rod but do not cock it. Measure the distance from the bottom of the ball to the floor. This is Y. Also, measure the horizontal distance from the point on the floor directly below the ball to the center of the marks on the carbon set. This distance is R.

将枪重新放回枪杆上，但不要上膛。测量球底到地面的距离。这距离是Y。同时，测量从球正下方地面上的点到碳集上标记中心的水平距离。这个距离是R。

9. Use equation 9 to find U. Find the percent difference between the two values for U.

9. 使用方程9计算U。找出两个U值之间的百分比差异。

1. Only a fraction, F, of the ball's kinetic energy is transferred to the ball and catcher during the collision:

只有碰撞过程中，球的动能的一部分F被传递给球和接球手：

通过一些代数运算，你可以证明：

碰撞中转移的动能分数是多少？

2. Why was the distance Y measured from the bottom of the ball rather than the center of mass?

为什么距离Y是从球底测量而不是质心？

3. In part II, if the velocity of the ball had been doubled due to a stronger gun spring, how would the ball's time of flight have changed?

3. 在第二部分中，如果由于更强的弹簧枪，球的速度加倍，球的飞行时间会如何变化？

4. Which method of finding the velocity of the ball do you think was more accurate? Explain why.

The Ballistic Pendulum