Bob Goes Faster

Classical Mechanics Level 2

Scenario A: Bob attaches a mass $m$ at the end of a long string (length $L$ ) and holds the other end of the string, allowing the mass to swing like a pendulum, with amplitude $A$ . When the mass reaches a turning point, Bob quickly pulls on the string so that the swinging part of the string shortens to $\tfrac12 L$ . The pendulum now swings with a higher frequency.

Scenario B: Bob repeats the exact same situation: a pendulum length $L$ and mass $m$ is swinging with amplitude $A$ . This time, Bob quickly pulls on the string when the mass passes through the equilibrium position. Again, the string is shortened to $\tfrac12 L$ , and the pendulum swings with a higher frequency.

In which scenario, if any, will the pendulum have a greater amplitude after Bob shortens the string?

Assumptions: The size of the swinging mass is negligible. When Bob pulls on the string, he does this in a negligible amount of time. During the pull, the force is directed upward along the string.

The amplitude is greater in scenario A. The amplitude is greater in scenario B. The amplitudes will be the same. It depends on how exactly Bob applies the force.

2 solutions

Arjen Vreugdenhil
Feb 2, 2016

For now I will just give hints that will allow you to solve the problem in three different ways.

Method 1 : Consider the distance over which the mass is lifted during Bob's pull. In which case does the pendulum gain more potential energy? Why does the kinetic energy not change?

Method 2 : In situation A, the maximum swing angle $\theta$ does not change when Bob pulls. What remains constant in situation B? How does that affect the maximum swing angle?

Method 3 : Bob does work in the amount $W = F_T\:L/2$ , where $F_T$ is the tension in the string. This work increases the energy of the pendulum motion. Give two reasons why the tension force is greater in situation $B$ .

Mariano PerezdelaCruz
Feb 4, 2016

It is surprised me the small percentage of correct answers.Being an old man, in my childhood I use to swing at the playground, my older sister teach me that to get more ample swing I must stand up at the bottom and squat at the top. Every kid in those days knew, videogames may be the culprit of this knowloge erosion. Conceptually, by standing up at the bottom you increase the potencial energy of the system, by doing so you pump energy in every swing, if energy input is bigger than friction and drag you will increase the amplitude.

The interested ones can search on the web "Botafumeiro parametric pumping ". There are a few well written physics papers in the subject.

Botafumeiro a medieval huge incenser suspended from the cathedral ceiling in Santiago (Spain) that swings under same principle.

The book The Pendulum, G.L.Baker & J.A.Blackburn chapter 3 It has a very complete analysis of this problem.

Bob Goes Faster

2 solutions

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