A common homework problem in many introductory physics courses is similar to the following. "A car drives at constant speed over a hill on a road in the shape of a vertical circular arc. What is the maximum speed the car can have and not lose contact with the road at the crest of the hill?" Unfortunately this problem is flawed, because…

The role of work and mechanical energy in classical relativity has been a subject of renewed interest in this publication. Here we present a problem that illustrates the relationship between impulse and kinetic energy for a rocket-powered object that can also change its gravitational potential energy. The same introductory physics principles lead…

A Genecon is an inexpensive hand-cranked dc electric generator. You can use it to charge a one-farad supercapacitor. If you stop cranking the handle, the capacitor will discharge, sending a current into the Genecon and thereby causing the handle to start turning as an electric motor. How does the current direction compare before and after you stop…

Suppose a block of mass "m"[subscript 1] traveling at speed "v"[subscript 1] makes a one-dimensional perfectly inelastic collision with another block of mass "m"[subscript 2]. What else does one need to know to calculate the fraction of the mechanical energy that is dissipated in the collision? (Contains 1 figure.)

In the late 18th and throughout the 19th century, lead shot for muskets was prepared by use of a shot tower. Molten lead was poured from the top of a tower and, during its fall, the drops became spherical under the action of surface tension. In this article, we ask and answer the question: "How does the size of the lead shot depend on the height…

A simple model is developed that predicts the coefficient of rolling friction for an undriven laboratory cart on a track that is approximately independent of the mass loaded onto the cart and of the angle of inclination of the track. The model includes both deformation of the wheels/track and frictional torque at the axles/bearings. The concept of…

Resistance to motion often includes a dry frictional term independent of the speed of an object and a fluid drag term varying linearly with speed in the viscous limit. (At higher speeds, quadratic drag can also occur.) Here, measurements are performed for an aluminium disc mounted on bearings that is given an initial twist and allowed to spin…

Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A…

Basic laws of thermodynamics and mechanics are used to analyse an air gun. Such devices are often employed in outdoor physics demonstrations to launch potatoes using compressed gas that is here assumed to expand reversibly and adiabatically. Reasonable agreement is found with reported muzzle speeds for such homebuilt cannons. The treatment is…

A pair of objects on an inclined plane are connected together by a string. The upper object is then connected to a fixed post via a spring. The situation is first analysed as a classroom exercise in using free-body diagrams to solve Newton's second law for a system of objects upon which many different kinds of force are acting (string tension,…