Ball on a String
A ball of mass m is attached to a "non-stretchy"
string of length r. It is being whirled in a vertical circle (of
radius r). If the ball is going just fast enough so that the
string does not go slack at the top of the circle, how fast will
it be going at its lowest point?
The ultimate goal is to reach an analytic solution of the problem
- to express vbottom in terms of vtop, m, r,
and whatever else (if anything) matters in the situation. A
simulation can help you by:
- familiarizing you with the physical situation,
- helping you figure out what matters and what doesn't, and
- checking your final solution.
This simulation is easy to set up and run, but you may find that
it is difficult for a numerical simulation to provide extreme
accuracy - especially over a long time interval.
a method for setting it up:
- Open the Interactive PhysicsTM program.
- Create a
circle object to represent the ball.
- Create a rope
attaching one end to the center of the ball, and the other end to
- Attach a
velocity meter to the ball.
- Open the
ball's Properties Window, and give it an initial
- Set accuracy
Running the Simulation:
- Run the
the initial velocity of the ballto find the minimum velocity
that will keep the string taut. You will find that the ball will
have lost considerable speed if you let the simulation run until
the ball gets back to the top of the circle. This is caused by
numerical and round-off errors accumulating as the simulation
runs. To combat this:
- stop the simulation when it reaches the ball
reaches the bottom of its arc.
- try reducing
the animation step.
- use a more
accurate integrator (Runge-Kutta 4)
- When you have the simulation running acceptably, try
systematically varying one of the quantities that you think
affects the ball's speed at the bottom of the circle:
- Be sure to keep your data in data tables.
- When you have collected some data, you might want to use a
graphical analysis program such as Graphical AnalysisTM
or DataStudioTM to determine the relationship between
each quantity and vbottom.
last update January 17, 2001 by JL