Find a method to determine the number of objects in the box solely by the sound produced while shaking the box. How does the accuracy depend on the properties of the objects, the box, and the packing density?

找到一种方法，仅通过摇晃盒子时产生的声音来确定盒子中的物体数量。精确度如何取决于物体的属性、盒子和包装密度？

By looking through a single water droplet placed on a glass surface, one can observe that the droplet acts as an imaging system. Investigate the magnification and resolution of such a lens.

通过观察放置在玻璃表面上的单个水滴，人们可以观察到水滴充当成像系统。探究这样一个透镜的放大倍数和分辨率。

‍Construct a rigid ramp walker with four legs (e.g. in the form of a ladder). The construction may begin to 'walk' down a rough ramp. Investigate how the geometry of the walker and relevant parameters affect its terminal velocity of walking.

构建一个带有四条腿的刚性斜坡行走器（例如梯形）。该结构可能开始沿粗糙斜坡“行走”。研究行走器的几何形状和相关参数如何影响其行走的终端速度。

A lightweight ball is suspended from a thread in the area between two charged plates. If the ball is also charged it will be deflected to one side at a certain angle. What is the accuracy of such a device for measuring the amount of charge on the ball? Optimize your device to measure the smallest possible charge on the ball.

一个轻质的球悬挂在两个带电板之间的线程区域。如果球也带电，它将以某个角度偏向一侧。这种装置测量球上电荷量的准确性如何？优化你的装置以测量球上的最小可能电荷。

A ping pong ball is placed in a container of water. When the container is dropped, the ping pong ball will get launched to a great height. What maximum height can you reach with up to 2 liters of water?

将乒乓球放入装有水的容器中。当容器掉落时，乒乓球将被发射到很高的高度。使用最多2升水可以达到多高的最大高度？

The responses of an LRC circuit driven by an AC source can be changed by inserting either a non-magnetic metal rod or a ferromagnetic rod into the inductor coil. How can we obtain the magnetic and electric properties of the inserted rod from the circuit’s responses?

由交流电源驱动的LRC电路的响应可以通过将非磁性金属棒或铁磁性棒插入感应线圈来改变。我们如何从电路的响应中获得插入棒的磁性和电性？

When a large, thin and flexible plate (e.g. plastic, metal or plexiglass) is bent, it may produce a loud and unusual howling sound. Explain and investigate this phenomenon.

当一个大型、薄型和灵活的板（例如塑料、金属或有机玻璃）弯曲时，它可能会产生响亮和不寻常的嚎叫声。解释并调查这一现象。

By looking through a single water droplet placed on a glass surface, one can observe that the droplet acts as an imaging system. Investigate the magnification and resolution of such a lens.Place a large disk-shaped magnet on a non-magnetic conductive plate. When a smaller magnet is moved under the plate, the magnet on top may levitate under certain conditions. Investigate the levitation and the possible motion of the magnet on top.

将一个大的圆盘形磁铁放在一个非磁性导电板上。当一个较小的磁铁在板下移动时，上面的磁铁在某些条件下可能会悬浮。探究悬浮和上面磁铁的可能运动。

A functional solar cell can be created using conducting glass slides, iodine, juice (e.g. blackberry) and titanium dioxide. This type of cell is called a Grätzel cell. Make such a cell and investigate the necessary parameters to obtain maximum efficiency.

可以使用导电玻璃片、碘、果汁（例如黑莓）和二氧化钛来制造功能太阳能电池。这种电池被称为Grätzel电池。制造这样一个电池，并调查获得最大效率所需的参数。

Take several identical fidget spinners and attach neodymium magnets to their ends. If you place them side by side on a plane and rotate one of them, the remaining ones start to rotate only due to the magnetic field. Investigate and explain the phenomenon.

取几个相同的手指旋转器，并在它们的末端附上钕磁铁。如果你将它们并排放在一个平面上并旋转其中一个，其余的将仅由于磁场开始旋转。调查并解释这一现象。

A simple water pump can be made using a straw shaped into a triangle and cut open at the vertices. When such a triangle is partially immersed in water with one of its vertices and rotated around its vertical axis, water may flow up through the straw. Investigate how the geometry and other relevant parameters affect the pumping speed.

可以使用塑造成三角形并在顶点处剪开的吸管制作一个简单的水泵。当这样的三角形部分浸没在水中，并围绕其垂直轴旋转时，水可能会通过吸管流动。调查几何形状和其他相关参数如何影响抽水速度。

Lower a compressed slinky into a soap solution, pull it out and straighten it. A soap film is formed between the turns of the slinky. If you break the integrity of the film, the front of the film will begin to move. Explain this phenomenon and investigate the movement of the front of the soap film.

将一个压缩的弹簧玩具放入肥皂溶液中，拉出并拉直。弹簧玩具的转动之间形成了肥皂膜。如果你破坏了膜的完整性，膜的前端将开始移动。解释这一现象并调查肥皂膜前端的运动。

A rubber band may fly a longer distance if it is non-uniformly stretched when shot, giving it spin. Optimize the distance that a rubber band with spin can reach.

如果在射击时非均匀拉伸橡皮筋，使其旋转，它可能飞行更长的距离。优化旋转橡皮筋可以达到的距离。

Place a ruler on the edge of a table, and throw a ball at its free end. The ruler will fall. However, if you cover a part of the ruler with a piece of paper and repeat the throw, then the ruler will remain on the table while the ball will bounce off it. Explain this phenomenon, and investigate the relevant parameters.

将尺子放在桌子的边缘，并朝其自由端扔球。尺子会掉下来。但是，如果你用纸张覆盖尺子的一部分并重复投掷，则尺子将保持在桌子上，而球将从上面弹起。解释这一现象，并调查相关参数。

Gently place a piece of tracing paper on the surface of water. It rapidly curls into a scroll and then slowly uncurls. Explain and investigate this phenomenon.

轻轻地将一张描图纸放在水面上。它迅速卷成卷轴，然后慢慢展开。解释并调查这一现象。

Place an object on a large air cushion and drop several other objects in such a way that the first object is catapulted away. Investigate how the exit velocity depends on relevant parameters.

将物体放在一个大的气垫上，并以这样的方式投放其他几个物体，使第一个物体被弹射出去。调查出口速度如何取决于相关参数。

If you put a flame with table salt added in front of a vapor sodium lamp, the flame casts a shadow. The shadow can become lighter if the flame is put into a strong magnetic field. Investigate and explain the phenomenon.

如果你在蒸气钠灯前点燃一支加了食盐的火焰，火焰会投下阴影。如果将火焰放入强磁场中，阴影可能变浅。调查并解释这一现象。