Uniform Circular Motion
- Warning! This is one of the few mechanics experiments that
can seriously injure you. Keep your hands and loose clothing well
away from the quickly rotating cage.
- We will determine the force required to stretch a spring of unknown
force constant a given distance in two ways:
- Record the number of grams stamped into the mass.
The manufacturer does not quote an error estimate. What is
probably the error in this quantity?
- Measure the distance from the center of rotation (marked by a small
line on one side of the cage) to the center of the mass (marked by
a line around the cylindrical mass) when the spring is extended
just enough to trip the indicator. Record an error estimate.
You may find that it easier to measure this length while the cage
is attached to the table during method 2.
- Attach the cage to the motor and increase the speed of rotation
until the indicator trips. Make sure the speed is as low as
possible while still tripping the indicator.
- Record the number of revolutions on the counting wheel before
engaging the gears. One partner should use the stopwatch to time
30 seconds during which time the other partner should engage the
gears of the counting wheel. Record the final number of revolutions
and subtract from the initial count. Record a timing error estimate.
Remember that just because the stopwatch display has two decimal places
does not mean that the timing error is 0.01 seconds. Look back at
the Kinematics Lab if you are
- From these data, determine the force (in newtons) required to trip
the indicator. Include an error estimate. (Do not get a
numerical value for the speed, and do not solve for the error in
the speed. You want a formula for the force in terms of only the
quantities that you measure in lab and speed is not one of them.)
- Attach the table clamp to the lab bench. Attach
the cage to the table clamp. Hang masses from the string attached
to the mass until the indicator just trips. For the error in the
hanging mass, decide how much mass you can add or subtract from the
hanger without noticing a difference.
- Determine the force (in newtons), with an error estimate,
required to trip the indicator.
Remember that the mass of the hanger is 50 grams. Should you include
the mass of the spinning cylinder? Why or why not?
- Do the two forces determined have overlapping error estimates?
- Which determination of the critical force is more reliable? Why?
- Assume that the equilibrium position of the spring is at the center
of rotation. What is the spring constant of the spring in MKS units?
No error estimate is required here.
- In Method 2, should you include the mass of the spinning cylinder?
Why or why not?
- Identify at least two sources of statistical error.
- Identify at least two sources of systematic error.
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