物理学专业英语翻译3.2

3.2 专业英语阅读翻译

3.2.1 Linear Motion with Constant Acceleration （匀加速直线运动）

A very common and simple type of one -dimensional motion occurs when the acceleration is constant, or uniform.（一种非常常见并且简单的一维运动发生时加速度是恒定的，或者说是匀速的。） Consequently, the velocity increases or decreases at the same rate throughout the motion.（因此，速度的增加或减少在整个运动过程中保持相同的速率。）

For motion along a straight line, we choose a rectangular coordinate system that is oriented so that one of the axes (for example, the x -axis) is along the line.（对于沿直线运动，我们选择一个直角坐标系，该坐标系是使其中一个轴（例如x 轴）的方向沿直线运动。） Then, components of position vector, velocity, and acceleration lie along this direction, and the y and z components are zero.（然后，位置矢量、速度和加速度的分量沿这个方向，y 轴和z 轴的分量为零。） The vector equations then become scalar equations.（向量方程就变成了标量方程。） If thevelocity is v 0 at time t=0, and v at some later time t, the corresponding acceleration is （如果速度在t=0的时刻为v 0，在稍后的t 时刻变为v ,则对应的加速度为）

t

v v t v v t v a 000-=--=∆∆=

（3-1) A Case in Point -Freely Falling Bodies （一个自由落体运动的例子） It is well -known that all objects, when dropped, will fall toward the earth with nearly

constant acceleration.（众所周知，当物体在掉落的时候，都会以几乎恒定的加速度落向地球。） In the idealized case, where air resistance is neglected, such motion is referred to as free fall .（在不考虑空气阻力的理想情况下，这种运动被称为自由落体运动。）

We shall denote the acceleration due to gravity by the symbol g . （我们将用符号g 表示重力加速度。）The magnitude of g decreases with increasing altitude （g 的大小随高度的增加而减小。）. Furthermore, there are slight variations in g with altitude.（此外，g 的值随海拔高度的改变而略有变化。） The vecor g is directed downward toward the center of the earth.（矢量g 的方向是竖直向下指向地心的。） At the earth's surface, the magnitude of g is approximately 9. 80 m/s 2.（在地球表面，g 的大小约等于9.80m/s 2。）

If we neglect air resistance and assume that the gravitational acceleration does not vary with altitude, then the motion of a freely falling body is equivalent to motion in one dimension under constant acceleration.（如果我们忽略空气阻力，假设重力加速度不随高度变化，那么自由落体运动等效于恒定加速度下的一维运动。） Therefore our kinematic equations for constant acceleration can be applied. （因此，我们可以应用恒定加速度的运动学方程。）We shall take the vertical direction to be the y axis and call y positive upward. （我们取竖直方向为y 轴，称y 轴正方向为向上。）With this choice of coordinates, we have a=-g. （根据坐标的选择，我们有a=-g .）The negative sign simply indicates that the acceleration is downward. （负号表示加速度的方向向下。）We get the following expressions:（我们得到以下表达式：）

gt v v -=0 (3-2)

20021gt t v y y -

=- (3-3) )(20202y y g v v --=- (3-4)

You should note that the negative sign for the acceleration is already included in these expressions. （你应该注意到加速度的负号已经包含在这些表达式中了。）Therefore, when using these equations in any free -fall problem, you should simply substitute g=9. 80 m/s 2.（因此，当在任何自由落体问题中使用这些方程时，你应该简单地代入g=9.80m/s 2。）

3.2.2 Projectile Motion （抛体运动）

Anyone who has observed a football in motion (or , for that matter , any object thrown in the air) has observed projectile motion. （任何观察过足球比赛的人（或任何抛在空中的物体）都观察过抛体运动。）This very common form of motion is surprisingly simple to analyze if the following three assumptions are made: （这个常见的运动的非常简单的分析如下面三个假设：）

(1) the acceleration due to gravity, g , is constant over the range of motion and is directed downward,（（1）重力加速度g 在运动范围内是恒定的并且向下的，） (2)the effect of air resistance is negligible,（（2）空气阻力的影响可以忽略不计，） and (3) the rotation of the earth does not affect the motion.（（3）地球的自转不影响运动。） With these assumptions, we shall find that the path of a projectile, which we call it trajectory, is always a parabola.（有了这些假设，我们就会发现抛体运动的轨迹总是一条抛物线。）

If we choose our reference frame such that the y direction is vertical and positive upward,（如果我们选择的参考系使y 轴的方向竖直向上，）then a y =-g(as in one -dimensional free fall) and a x =0 (since air friction is neglected). （那么a y =-g （如一维自由落体）和 a x =0（因为忽略了空气阻力）。）Furthermore, let us assume that at t=0 , the projectile leaves the origin(x 0=y 0=0) with a velocity v 0 , as in Fig. 3-1.（我们假设在t=0的时候，弹丸以速度v 0离开原点(x 0=y 0=0)，如图3-1所示。）

Fig. 3-1 The parabolic trajectory of a projectile that leaves the origin with a velocity v 0

（图3-1以速度v 0离开原点的抛体运动的抛物线轨迹）

If the vector makes an angle with the horizontal, then the initial velocity and acceleration have components （如果矢量与水平方向成夹角，则初速度和加速度有分量）

θcos 00v v x = （3-5a ）

θsin 00v v y = （3-5b ）

g a a y x -==,0 （3-6）

Notice that v x does not depend on v y and vice versa: The horizontal and vertical components of projectile motion are independent . （注意v x 不依赖于v y 反之亦然：抛体运动的垂直分量和水平分量是独立。）The velocity components and coordinates for the projectile at any time t are