A child who drops a toy from a high chair, a juggler who catches three balls and a driver who brakes for a stop light all rely on a built-in sense of how objects move and how heavy they are. This kind of knowledge is called intuitive physics. Studies of babies show that some of it is present within months, such as the expectation that an object does not pass through another and does not float in mid-air. Yet adults make telling mistakes when asked to predict motion explicitly, and these mistakes show how the system works.
What we do well
For events that are short, familiar and seen on a human scale, people are good. Catching, hitting a ball and predicting where a thrown object lands are done with remarkable accuracy, partly through the eyes' ability to track and partly through well-trained timing. Experiments have also found that people judge stability well: how far a stack of blocks can lean before it falls is predicted with an error of just a few degrees in several studies. Researchers such as Peter Battaglia, Jessica Hamrick and Joshua Tenenbaum have suggested that the brain runs something like a noisy "physics engine", which simulates the scene a few steps ahead and with limited precision.
What we do badly
- Curved paths. In 1980 Michael McCloskey and colleagues asked students to draw the path of a ball leaving a curved tube. A large part drew a path that continued to curve. In reality it leaves in a straight line. This "curvilinear impetus" belief resembles the medieval impetus theory.
- Falling. Many people think heavier objects fall faster. In a vacuum, all fall at the same rate; in air only the drag differs. Galileo is credited with the argument, and in 1971 an Apollo 15 astronaut dropped a hammer and a feather on the Moon to show it.
- Long times and big heights. Falling time is not proportional to the height. In free fall, the time is the square root of 2 times the height divided by 9.8, which gives 0.45 seconds for 1 metre, 1.4 seconds for 10 metres and 4.5 seconds for 100 metres. Because the height grows much faster than the time, the guesses for tall buildings are often too long.
- Heaviness. In the size-weight illusion, described by Augustin Charpentier in 1891, the smaller of two objects with the same weight feels heavier. It persists even when you know that they are equal.
Falling objects in numbers
Ignoring air resistance, an object falls a distance of about 5 metres in the first second, 20 metres in two seconds and 45 metres in three. The speed at the end of the first second is about 10 metres per second, or 36 kilometres per hour. A useful rule of thumb is that the height in metres is about 5 times the square of the time in seconds. If you hear a stone splash after 3 seconds, the well is roughly 45 metres deep, with a small correction for the sound travelling back. Air resistance matters for light, wide objects such as a feather or a sheet of paper, and for very long falls, but it hardly changes a steel ball falling from a few metres.
Balance and tipping
A block tips when the line of its centre of gravity falls outside its base. For a uniform rectangular block with a width w and a height h, that happens at a tilt of the angle whose tangent is w/h, measured from the upright. A tall thin block tips at a small angle and a low broad one at a large angle. For a lever, the rule is that the torque, which is the weight times the distance from the pivot, must be equal on both sides. People usually take the weights into account and forget the distances, or the other way round. When they are told to use both, the estimate improves a lot, which tells that the knowledge is available but not always applied.
Improving your feel
- Get feedback. A quick answer with an immediate reveal teaches more than a lecture. The physical games on this site show the true value after each round, and some animate it.
- Learn a few anchors. A litre of water weighs a kilo, a pack of butter is 250 grams, a tennis ball 58 grams, and you can lift a weight of 20 kilos with some effort. A newton is roughly the weight of a small apple.
- Simulate. Before answering, imagine the scene and run it forward in your mind for a moment. The people who do best are the ones who see the outcome.
- Check units. Many errors are factor-of-ten slips between grams and kilograms, or between metres and feet.
Physical intuition is not the same as knowing the formulas. A craftsperson or an athlete may be much better than a physics student at predicting what will happen with real objects, and a physics student may be better at the rules. The best result comes from both: the gut feeling to find the answer and the formula to check it.