Experimental Competition: 14 July 2011
Problem 2 Page 1 of 2
2. Mechanical Blackbox: a cylinder with a ball inside
A small massive particle (ball) of mass m is fixed at distance z below the top of a long hollow
cylinder of mass M . A series of holes are drilled perpendicularly to the central axis of the cylinder.
These holes are for pivoting so that the cylinder will hang in a vertical plane.
Students are required to perform necessary nondestructive measurements to determine the numerical
values of the following with their error estimates:
i. position of centre of mass of cylinder with ball inside.
Also provide a schematic drawing of the experimental set-up for measuring the centre of
mass. [1.0 points]
ii. distance z [3.5 points]
M
iii. ratio . [3.5 points]
m
iv. the acceleration due to gravity, g . [2.0 points]
Equipment: a cylinder with holes plus a ball inside, a base plate with a thin pin, a pin cap, a ruler, a
stopwatch, thread, a pencil and adhesive tape.
z
O pivot
x
CM
Base plate
R to be clamped
to a table top
CM L
Thin pin
m for pivoting
M x is the distance from the top of the cylinder to the
CM
centre of mass.
R is the distance from the pivoting point to the centre of
mass.
Experimental Competition: 14 July 2011
Problem 2 Page 2 of 2
Cylinder with holes
Adhesive
plus ball inside
tape
Pin cap
Stopwatch Thread Base plate Ruler
(for balancing)
Caution: The thin pin is sharp. When it is not in use, it should be protected with a pin cap for safety.
Useful information:
d2
1. For such a physical pendulum, M m R2 I g M m R , where I is
CM dt2 CM
the moment of inertia of the cylinder with a ball about the centre of mass and is the angular
displacement.
2. For a long hollow cylinder of length Land mass M , the moment of inertia about the centre of
2
1 L
mass with the rotational axis perpendicular to the cylinder can be approximated by M .
3 2
3. The parallel axis theorem: I I Mx2, where x is the distance from the rotation
centre of mass
point to the centre of mass, and M is the total mass of the object.
4. The ball can be treated as a point mass and it is located on the central axis of the cylinder.
5. Assume that the cylinder is uniform and the mass of the end-caps is negligible.