Problems involving chains, cables, or ropes that are dropped, folded, or pass around pulleys attract ongoing interest, in part because they can become variable-mass situations if the chain is partitioned into sections for analysis. Less attention has been paid to trying to intentionally project the end of a string as far as possible. Here we…

Races between moving objects are an engaging way to teach dynamics to introductory physics students. One standard example consists in racing hollow and solid cylinders as they roll down an inclined plane. Another striking demonstration is a race between two marbles on side-by-side tracks that start and end together, but with one track taking a…

Stellar aberration is the phenomenon whereby the observed angular position of a star depends on the relative motion between the star and Earth. Specifically, a telescope must be tilted slightly into the direction of motion of Earth relative to the star. There are in fact three different angular positions of interest: the observed position of the…

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…

Some teenagers are exploring the outer perimeter of a castle. They notice a spy hole in its wall, across the moat a horizontal distance "x" and vertically up the wall a distance "y." They decide to throw pebbles at the hole. One girl wants to use physics to throw with the minimum speed necessary to hit the hole. What is the…

What trajectory in the laboratory frame does a marble follow if it is held inside a freely rotating pipe and then suddenly released so that it can slide frictionlessly outward along the pipe? A previously published solution is only valid for a pipe of small moment of inertia (so that it is either low in mass or short in length).

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.)

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…

A pair of masses or opposite-sign charges released from rest will move directly toward each other under the action of the inverse-distance-squared force of attraction between them. An exact expression for the separation distance as a function of time can only be found by numerically inverting the solution of a differential equation. A simpler,…

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,…

The collision of a ball with the end of a barbell illustrates the combined conservation laws of linear and angular momentum. This paper considers the instructive but unfamiliar case where the ball's incident direction of travel makes an acute angle with the barbell's connecting rod. The analysis uses the coefficient of restitution generalized to…