1动力学系统

PASCO 实验Experiment 1 Dynamics Cart Accessory Track Set实验一 动力学系统Experiment 1 Acceleration and Harmonic Motion实验1 加速度和简谐振动Equipment Needed:-Dynamics Carts with Mass (ME-9430)-Spring -Base and Supported rod (ME-9355) -Mass balance -Acceleration sensor -50 Newton force sensor -Motion sensor -Dynamic Cart Track with End stop and Pivot clampPurpose目的The Purpose is to measure the period ofoscillation of a spring and mass system on an incline at different angles and compare it to the theoretical value and verify Newton’s Second Law, F=ma. (See Figure 1)目的是测量不同倾角的斜面上的弹簧和物体系统的振动周期，并验证牛顿第二定律，F=ma 。

(看图1) Theory理论For a mass attached to a spring, the theoretical period of oscillation is given bykmT π2= 对于弹簧上的物体，振动的理论周期为km T π2= where T is the time for one complete back-and-forth motion, m is the mass that is oscillating, and k is the spring constant.这里T 是一个来回运动的时间，m 是振动质量，k 是弹簧常数。

Figure 1According to Hooke’s Law, the force exerted by the spring is proportional to the distance the spring is compressed or stretched, F=kx, where k is the proportionality constant. The spring constant can be experimentally determined by applying different forces to stretch the spring different distance. When the force is plotted versus distance, the slope of the res ulting straight line is equal to k. According to Newton’s Second Law,F=ma. F is the net force acting on the object of mass m and a is the resulting acceleration of the object.根据虎克定律，弹簧产生的力与弹簧被压缩或伸长的距离成正比，F=kx,这里k是比例常数。

这样在实验上，可以通过施加不同的力让弹簧压缩或伸长不同的距离来确定。

作力—距离的图，直线的斜率就等于k。

根据牛顿第二定律F=ma, F是作用在物体m上的外力,a是物体的加速度。

Procedure步骤Measurement to find the Theoretical period 找到理论周期的测量①Use the balance to find the mass of the cart and the Acceleration sensor, Record this value M.用天平称出小车和加速度传感器的质量，记下这个值M。

②Set the cart on the track and attach a spring to one end of the cart by inserting the end of the spring in the hole provided in the cart. Then attach the other end of the spring to the end of the track.把小车放在导轨上，把弹簧的一端插入小车的孔中，把弹簧和小车连在一起。

然后把弹簧的另一端与导轨的末端连在一起。

③Incline the track by raising the end of the end of the track that has the spring attached. As the end of the track is raised the spring will stretched. Keep the angle of inclination of the track small enough so the spring is not stretched more than half the length of the track. Record the equilibrium position L0.抬高与弹簧相连的导轨的末端，让导轨倾斜。

导轨的末端升高后，弹簧会伸长。

让导轨的倾角足够小，这样，被拉长的弹簧的长度不超过导轨长度的一半。

记下平衡位置L0。

④Computer Setup: 计算机设置1. Connect the Science Workshop interface to the computer, turn on the interface, and turn on the computer.把科学工作站接口连到计算机上，打开接口，打开计算机。

2. Connect the force sensor’s DIN plug into Analog Channel A of the interface, the motion sensor’s digital plug into Channel 1 and 2.把力传感器的模拟插头接到接口的A通道，把运动传感器的数字插头接到通道1和2。

3. Open the Science Workshop document, let it be required working conditions.打开科学工作站文件，让它处于所需的工作状态。

lick the “REC” button, the computer starts to record data. Drag the cart to stretch the spring, in the graph of Force(N) versus position(m),the slope of the line is equal to the effective spring constant, k.点击“REC”按扭，计算机开始记录数据。

拖动小拉长弹簧，在力-位移的图中，斜率就是弹簧常数k。

Measuring the Experimental Period测量实验周期⑥Computer Setup: 1.Connect the Science Workshop interface to the computer, turn on the interface, and turn on the computer.2.Connect the force sensor’s DIN plug into Analog Channel A of the interface, the计算机设置：1. 把科学工作站接口连到计算机上去，打开接口，打开计算机。

2．把力传感器的模拟插头接到接口的通道A，把加速度传感器的插头接到通道B。

3. 打开科学工作站文件，让它处于所需的工作状态。

acceleration sensor’s DIN plug into Analog Channel B. 3. Open the Science Workshop document, let it be required working conditions.⑦Displace the cart from equilibrium a specific distance and let it go. Click the “REC” button, the computer starts to record data. In the graph of Force(N) versus Time(s), you can get the oscillating experimental period.让小车离开平衡位置一段距离后松手，点击“REC”按扭，计算机开始记录数据。

在力-时间的图中，你可以得到振动的时间周期。

⑧Compare the graph of Force(N) versusTime(s) to the graph of Acceleration(m/s/s)versus Time(s).比较力-时间的图和加速度-时间的图。

Change the angle of the incline and repeatSteps 7 and 8.改变斜面的倾角，重复步骤7和8 Calculations 计算Theoretical Period理论周期①Plot force versus displacement. Draw the best-fit straight line through the data points and determine the slope of the line. The slope is equal to the effective spring constant, k. k=______作出力—位移的图，通过数据点作出最合适的直线，确定直线的斜率。

斜率就是弹簧的弹性系数，k。

k=_____Using the mass of the cart and the spring constant, calculate the period using the theoretical formula. T=______用小车的质量和弹簧常数，用公式计算理论周期。