Observing the Force | 观察力

📚 Observing the Force | 观察力

In A-level physics, force is a central idea, yet it cannot be seen directly. We observe a force through its effects: changing shape, changing motion, or balancing another force. This article explains the practical ways in which forces are detected, displayed and measured, with a focus on CIE experimental skills.

在 A-level 物理中，力是核心概念，但力本身无法被直接看到。我们通过力的效应来观察它：改变形状、改变运动状态或平衡另一个力。本文介绍检测、显示和测量力的实用方法，重点关注 CIE 实验技能。

1. What Does It Mean to Observe a Force? | 观察力意味着什么？

A force is a push or a pull arising from an interaction. We cannot see force itself; we infer its presence from observable effects. These effects include extension of a spring, acceleration of a mass, distortion of an object, or a change in direction.

力是相互作用产生的推或拉。我们无法看到力本身；我们通过可观察的效应推断它的存在。这些效应包括弹簧的伸长、质量的加速、物体的形变或运动方向的改变。

An observation is scientifically useful only if it can be repeated and measured. Therefore, observing a force usually means measuring its magnitude, direction and point of application.

只有可重复、可测量的观察才具有科学意义。因此，观察力通常意味着测量它的大小、方向和作用点。

2. Using a Spring Balance: Extension as a Force Indicator | 使用弹簧秤：以伸长量作为力的指示

A spring balance, or newton meter, is the simplest instrument for observing a force. The force stretches a spring inside the meter. The extension is proportional to the applied force, so a scale can be marked in newtons.

弹簧秤（牛顿计）是观察力最简单的仪器。力会拉伸内部的弹簧。伸长量与所施加的力成正比，因此刻度可以直接以牛顿标定。

To read the instrument correctly, the eye must be level with the pointer to avoid parallax error. The spring balance should be held so that the force acts along its axis.

正确读数时，视线必须与指针对齐，以避免视差误差。弹簧秤应保持使力沿其轴线作用。

3. Calibrating a Newton Meter with Known Masses | 用已知质量校准牛顿计

A newton meter can be calibrated by hanging known masses vertically. The weight of a mass m is given by W = mg, where g is the gravitational field strength, approximately 9.81 N kg⁻¹ on Earth.

牛顿计可以通过悬挂已知质量来校准。质量 m 的重量由 W = mg 给出，其中 g 为引力场强度，在地球上约为 9.81 N kg⁻¹。

W = mg

For example, a 100 g mass has a weight of about 0.981 N. By plotting scale reading against known weight, you can check linearity and zero error.

例如，100 g 的质量重量约为 0.981 N。绘制刻度读数与已知重量的关系图，可以检查线性度和零点误差。

4. Hooke’s Law and Linear Force–Extension Graphs | 胡克定律与线性力-伸长图

When observing a force using an elastic material, Hooke’s law states that extension x is proportional to the applied force F, provided the elastic limit is not exceeded: F = kx, where k is the spring constant.

利用弹性材料观察力时，胡克定律指出，在不超过弹性极限的情况下，伸长量 x 与所施加的力 F 成正比：F = kx，其中 k 为弹簧常数。

F = kx

A force–extension graph is a straight line through the origin for an ideal spring. The gradient gives the spring constant k, usually in N m⁻¹. Beyond the limit of proportionality, the graph curves, which indicates permanent deformation.

理想弹簧的力-伸长图是一条过原点的直线。斜率给出弹簧常数 k，单位通常为 N m⁻¹。超过比例极限后，曲线弯曲，表明发生永久形变。

In an experiment, you can observe the force by measuring extension with a ruler and adding slotted masses. The main errors are zero error and reading the ruler at an angle.

在实验中，你可以通过添加槽码并用尺子测量伸长量来观察力。主要误差是零点误差和斜视读数。

5. The Force Board: Observing Vector Addition | 力板：观察力的矢量合成

Forces are vectors, so they have both magnitude and direction. A force board uses three or more spring balances pulling at a knot or ring. When the ring is in equilibrium, the vector sum of the forces is zero.

力是矢量，因此既有大小又有方向。力板使用三个或更多弹簧秤拉同一个结点或圆环。当圆环处于平衡时，各力的矢量和为零。

You can record the magnitude and direction of each force on a sheet of paper and draw a scale vector diagram. The three force vectors should form a closed triangle if equilibrium is achieved.

你可以在纸上记录每个力的大小和方向，并绘制比例矢量图。如果达到平衡，三个力的矢量应形成闭合三角形。

This method directly shows that forces cannot be added as ordinary scalars; direction matters.

这种方法直接表明力不能像普通标量那样相加；方向很重要。

6. Observing Contact and Non-contact Forces | 观察接触力与非接触力

Contact forces, such as friction, tension and normal reaction, are observed at surfaces. Non-contact forces, such as gravitational, magnetic and electrostatic forces, act at a distance through fields.

接触力（如摩擦力、张力和法向反作用力）在表面处被观察到。非接触力（如引力、磁力和静电力）通过场在远处起作用。

For example, a bar magnet can lift a paper clip without touching it. The force is made visible by the alignment of iron filings in a magnetic field, revealing field lines.

例如，条形磁铁无需接触就能吸起回形针。铁屑在磁场中排列，使力变得可见，揭示出磁感线。

Similarly, a charged polythene rod attracts small pieces of paper. These demonstrations remind us that force is an interaction that can cross empty space.

同样，带电的聚乙烯棒吸引小纸片。这些演示提醒我们力是一种可以跨越空间的相互作用。

7. Force Sensors and Data Loggers | 力传感器与数据记录仪

Modern experiments often use electronic force sensors connected to a data logger. A force sensor produces a voltage proportional to the applied force, allowing a graph of force against time to be recorded.

现代实验通常使用连接数据记录仪的电子力传感器。力传感器产生与所施加力成正比的电压，从而记录力-时间图。

Typical sensors have ranges from ±0.5 N to ±50 N and sampling rates up to several thousand hertz. This makes rapid changes observable, such as the force during a collision or a bounce.

常见传感器的量程从 ±0.5 N 到 ±50 N，采样率可达数千赫兹。这使快速变化（如碰撞或反弹过程中的力）可以被观察到。

Before use, the sensor must be calibrated by applying known forces and checking the zero reading when no force is applied.

使用前必须通过施加已知的力来校准传感器，并在未施力时检查零点读数。

8. Observing Force through Acceleration: Newton’s Second Law | 通过加速度观察力：牛顿第二定律

Newton’s second law states that the resultant force F on an object is equal to the rate of change of momentum. For constant mass, this simplifies to F = ma.

牛顿第二定律指出，作用在物体上的合力 F 等于动量的变化率。对于恒定质量，简化为 F = ma。

F = ma

In a dynamics trolley experiment, a force is applied by a falling mass over a pulley. Motion sensors or light gates measure the acceleration a. The gradient of an acceleration–force graph gives 1/m, allowing the mass to be observed indirectly.

在动力学小车实验中，通过滑轮由下落的质量施加力。运动传感器或光门测量加速度 a。加速度-力图线的斜率给出 1/m，从而间接观察质量。

This is one of the clearest ways to ‘observe’ an unbalanced force: the acceleration it produces is directly visible in velocity–time data.

这是“观察”非平衡力最清晰的方法之一：它产生的加速度在速度-时间数据中直接可见。

9. Observing Impulse and Force–Time Graphs | 观察冲量与力-时间图

When a force acts for a short time, the impulse is defined as the change in momentum. Impulse is equal to the area under a force–time graph.

当力作用时间很短时，冲量定义为动量的变化。冲量等于力-时间图下方的面积。

Impulse = FΔt = Δ(mv)

Using a force sensor, you can observe the force during a ball bounce. The graph shows a sharp peak; the area under the peak is the impulse delivered to the ball.

使用力传感器，你可以观察球反弹时的力。图线显示一个尖峰；峰下方的面积即为传递给球的冲量。

Comparing the areas for different drop heights can verify the impulse–momentum relationship experimentally. This is a powerful way of observing a force that lasts only milliseconds.

比较不同下落高度的面积可以实验验证冲量-动量关系。这是观察仅持续几毫秒的力的一种有效方法。

10. Observing Centripetal Force | 观察向心力

An object moving in a circle experiences a resultant force towards the centre. This centripetal force is given by F = mv²/r, where m is mass, v is speed and r is radius.

做圆周运动的物体受到指向圆心的合力。向心力由 F = mv²/r 给出，其中 m 为质量，v 为速率，r 为半径。

F = mv²/r

A simple observation uses a rubber bung whirled on a string. The tension in the string provides the centripetal force. By changing the radius or speed and measuring the tension with a spring balance, you can observe how the force depends on v and r.

一个简单的观察实验是用绳子旋转橡胶塞。绳子的张力提供向心力。通过改变半径或速率并用弹簧秤测量张力，可以观察力如何依赖于 v 和 r。

A force sensor can be mounted in place of the hand to record the tension continuously, giving clearer evidence of the requirement for a centripetal force.

可以用力传感器代替手来连续记录张力，更清晰地证明向心力的必要性。

11. Observing Friction and Limiting Equilibrium | 观察摩擦与极限平衡

Friction opposes motion between surfaces in contact. When a block is pulled horizontally by a spring balance, the force reading increases until the block just begins to move. This maximum static friction is the limiting friction.

摩擦阻碍接触表面之间的运动。用弹簧秤水平拉物块时，力读数会增加，直到物块刚好开始运动。这个最大静摩擦力就是极限摩擦力。

Once the block is moving, the force needed to keep it moving at constant speed is usually smaller; this is the kinetic friction force. Observing both forces on a force–displacement graph reveals the difference.

一旦物块运动起来，保持其匀速运动所需的力通常更小；这是动摩擦力。在力-位移图上观察这两种力可以揭示差异。

For a block on a slope, the angle at which it begins to slide can be used to observe the coefficient of static friction μ = tan θ.

对于斜面上的物块，其开始滑动时的角度可用于观察静摩擦系数 μ = tan θ。

μ = tan θ

12. Turning Effects: Observing Moments | 观察转动效应：力矩

A force can also cause rotation. The moment of a force about a pivot is defined as force × perpendicular distance from the pivot. When an object is in rotational equilibrium, the sum of clockwise moments equals the sum of anticlockwise moments.

力也可以引起转动。力对支点的力矩定义为力 × 力臂（支点到力作用线的垂直距离）。当物体处于转动平衡时，顺时针力矩之和等于逆时针力矩之和。

Moment = Fd

Using a metre rule pivoted at its centre, you can hang known weights at different distances and observe balance. This is a direct way of observing that the turning effect depends on both the size of the force and its distance from the pivot.

使用在中心支起的米尺，你可以在不同距离悬挂已知重物并观察平衡。这是直接观察转动效应取决于力的大小和到支点距离的方法。

The principle of moments confirms that a small force can balance a large force if it acts at a greater distance from the pivot.

力矩原理证实，如果小力作用在距支点更远的位置，可以平衡较大的力。

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Observing the Force | 观察力