Which is heavier?

Can you correctly assess the weight difference between objects of different sizes?

Hold the two metal balls in your hands to determine which one feels heavier.

The balls you were holding are exactly the same weigh, but the smaller one feels heavier.

Our assumption is in conflict with reality; the smaller of two objects that actually weigh the same feels heavier. Everyday experience tells us that larger objects will be heavier and, therefore, we expect to need more muscle strength to lift those objects. This is what is known as a cognitive illusion.

Imagine that you work in an airport and are lifting suitcases onto a conveyor belt. What would it feel like if the largest suitcase were empty? What if the smallest and most delicate suitcase contained lead? Unusually heavy luggage is marked in order to avoid unfortunate surprises and accidents.

Fakir bed

Do you dare to lie on a bed of sharp nails?

Use the handle to raise the nails of the Fakir bed and touch their tips with your fingers. Lower the nails and lie down flat on the bed. Now lift the nails up once again. Keep your head on the pillow.

It is unlikely that you even felt the nails, much less their sharpness.

There are many nails in our bed, altogether 2,335 to be exact. The pressure exerted by the nails is distributed evenly over the entire body, thus ensuring that the pressure of any single nail is minimal. The pressure is approximately the same as that which is applied to the soles of your feet when you stand barefoot on an even platform. If, therefore, you are able to stand barefoot on the floor, you will have no problem lying on the Fakir bed either. You should also note that the soles of your feet have a much higher density of nerve cells that react to pressure than exist in your back. Thus, the feeling of pressure is less on your back.

The pressure that any single object exerts on the ground depends upon the weight of the object and the area of the part that touches the ground. Therefore, a person walking in high-heeled shoes could damage a floor much more than an elephant would. Despite the enormous weight of the elephant, the pressure exerted on the floor beneath the stiletto heel of a pump can actually be significantly greater than that of an elephant’s wide foot.

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Racetrack

Which ball will reach the bottom first?

Place the balls at the upper end of the tracks. Set the balls rolling down the tracks at the same time.

The ball rolling down the longer, curved track will be the first to reach the bottom.

The speed of both balls as they reach the bottom is the same, because they receive the same kinetic energy as they move the same distance on a vertical plane. The ball rolling down the curved track is faster at the start, because its speed of acceleration along the steep track is greater. Due to this fast initial acceleration, this ball will have a faster time, even though its acceleration at the gently sloped end of the track is slower and its track is longer than the straight track. In this race, it would be in vain to put your hopes in any final sprint for the finish line!

A track along which an object will descend the fastest or roll, as a result of gravitational pull, the distance between two points of differing heights without any frictional resistance is called a brachistochrone curve. The mathematical shape of the curve was studied – and explained – already during the 17th century by famous scientists including Newton. The curve is known as a cycloid.

A point on the circumference of a rolling circle draws a cycloid. If we attach a small lamp to a bicycle tire and drive with the bike in the dark, a camera that is set to a slow shutter speed will take an image in which it appears that the light from the lamp forms a cycloid pattern in the air.

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Racing wheels

Why is one wheel faster than the other?

Place both wheels at the top edge of the angled plane and release them simultaneously

The same wheel will always win the race. Can you find any differences between the wheels?

The wheels are the same size, the same weight and are made from the same materials. The only difference is the placement of the weight. One of the wheels has a heavy centre and the other wheel’s weight is located toward the outer rim. For this reason, the wheels have different moments of inertia.
The moment of inertia signifies the inertia of the object as it rotates, or, in other words, its ability to resist any change in the rotational speed. The wheel whose weight is located around its outer rim has a higher moment of inertia. Therefore, it accelerates slower as it rolls and falls behind the other wheel whose weight is located closer to its axis of rotation.

Many public bathrooms have very large toilet paper rolls in their stalls. Due to their high moment of inertia, these rolls spin slower as the paper is being pulled off the roll. If the paper is pulled too quickly, it will tear too soon. A knowledge of physics is an asset in this situation as well. In order to get a suitable amount of paper, it should first be pulled off of the big roll slowly. Then the paper can be torn off with a rapid tug without needing to use your other hand to hold the roll steady, as is necessary with a smaller roll.

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Car lift

Can you lift up a small car?

Pull on the rope and watch what happens to the car.

When you pull on the rope, you are able to easily lift the car into the air.

The Golden Rule of Mechanics states that “whatever you lose in distance, you gain in power.” We can use a block and tackle to illustrate this principle. Using a rope and a stationary pulley attached to an overhead beam, we can turn the downward pull on the rope into the necessary force to lift a car. The force is increased manifold when we introduce several mobile pulleys to the equation.
Each mobile pulley in Heureka’s tackle is attached to the stationary pulley that is attached to the beam. Using this system, each mobile pulley doubles the actual pulling force. Therefore, the lifting force is 26 = 64 times as great as the pulling force.
The distances that the ropes travel will be in the same proportion to one another, but reversed. So, in order to lift the car 10 cm, the rope must be pulled about 6 metres.

Simple pulleys have been used since before the common era. It has been said that Archimedes used a block and tackle to lift ships onto docks. He is believed to have said, “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world”; this statement is a fine illustration of the Golden Rule of Mechanics. In theory, it is possible to use this principle to achieve a limitless amount of force, but the practical realities, such as friction or material durability will cause problems long before such possibilities could be tested.

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Parabolic mirrors

Do the walls have ears?

Two people are needed for this task. One person speaks into the ring at the centre of one reflector and the other listens at the ring of the other reflector.

The person with his/her ear next to the ring in the other reflector can hear the voice of the speaker – even a whisper – over the noise of the room.

The reflectors are parabolic in shape. The sound waves exiting the focal point at the centre of the ring are projected off of the concave surface in a parallel fashion towards the other reflector. When they reach the other reflector, they are all projected towards that reflector’s focal point. Without the reflectors, the sound of the speaker’s voice would simply spread to the surroundings, and only a small portion of the sound waves, insufficient for the human ear, would reach the listener.

The same principle holds true for light and heat. With the help of two parabolic mirrors, we can light a match. We simply station the mirrors at a distance of tens of metres from one another, hold a match at the focal point of one of the mirrors, and place a small, hot halogen light bulb at the focal point of the other.

A satellite dish on a rooftop operates on the same principle. The micro head located at the focal point effectively catches the TV signal sent by a communications satellite and reflected off from the dish. Satellite dishes always face the same direction, because the communications satellites remain stationary, with respect to the Earth, on their orbits at a height of 36,000 km above the equator. So, you can have ears on your roof, not just on your walls!

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Bowling ball cannon

Can you make the tennis ball reach the ceiling?

Using the cord, pull the bowling ball up and let it drop. Observe the tennis ball in the other tube.

As the bowling ball begins to fall, the air below it is forced out through the holes in the larger tube. Once it’s beyond the holes, the bowling ball pushes the air below it towards the smaller tube, thereby blasting the tennis ball in the smaller tube towards the ceiling.

Without the holes in the large tube, the bowling ball would fall very slowly and the tennis ball would not rise particularly high. The slow fall is the result of the fact that the ball in the narrow tube combined with the air itself are very efficient in resisting the fall of the bowling ball. When the air is able to escape through the holes in the larger tube, no such air column resisting the fall of the bowling ball is created. The ball manages to achieve such a great speed so that it easily pushes the air in front of it, thereby sending the air with force into the smaller tube and launching the tennis ball to great heights. The rapidly falling bowling ball produces a much greater thrust than a slowly falling bowling ball. The speed of the tennis ball is further increased by the fact that the speed of the propulsive air increases as it is forced from a larger tube into one with a smaller diameter.

Some bicycle pumps have a small hole at the upper end of the cylinder. The point of the hole is to facilitate the initial speed of the piston, thereby easing the work of the person pumping the air.

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Slow motion with smoke