Conservation of momentum in 2D-collisions EXPERIMENTS
::
E-303
Let one steel ball roll down the track from the start posi-
tion – it should fall freely to the floor without hitting the
holder for the other ball. Use the spot where the ball hits
the floor together with the point O to define the direction
of the x-axis and to determine the initial, vertical velocity
v
x0
of the rolling ball. Calculate the initial x-momentum,
p
x0
, as well.
Draw a y-axis perpendicular to the x-axis. The initial
velocity along this axis, v
y0
, is clearly zero.
Now place the holder with the second steel ball in a posi-
tion such that the two balls collide and fall freely to each
side of the x-axis. From the dots on the paper you can
calculate the momentum of each ball along the x - and y-
axes – independently and respecting the sign of the y-
position. (The y components of the momentum of the
Purpose
two balls will always have different signs.)
In this experiment we want to verify the conservation of
Adding the x components of the two balls’ momentum
momentum in two dimensions.
should give the initial x-momentum, p
x0
.
Theory
Adding the y components of the two balls’ momentum
should give a result close to zero.
Unlike for instance energy, velocity, v, has not only a
magnitude but also a direction – it is a vector. Defining
the momentum pof a particle of mass m as p= m·vimpli-
es that the same is true for momentum. The total
momentum of an isolated physical system is therefore
Required Equipment
independently conserved along any of the three axes x, y
1992.20 Curved ball track 1,00 Pcs
and z.
1992.10 Easily smudged carbon paper 1,00 Pcs
The system we are studying in this experiment is not iso-
lated; the two balls are subjected to gravity. The total
momentum of the balls is therefore not conserved along
the z-axis but only along the x- and y-axes.
In this experiment, the balls fall freely after the collision –
with no initial vertical velocity. The time it takes to fall a
distance h is therefore given by
where g is the acceleration of gravity.
When a ball moves the horizontal distance x along the x-
axis in the time t, the x component of the velocity is
simply given by
A similar expression can be used for the y component.
Procedure
Place a large piece of paper where the balls will hit the
floor. To determine the precise spots where the balls hit,
sheets of carbon paper are placed there. Write numbers
immediately next to the dots and keep a log of the who-
le exercise.
Mark the position O directly under the collision spot
using the string and bob. Measure the vertical distance h
from the floor to the bottom of the balls when they are on
the small horizontal (lower) part of the track. Use h to cal-
culate the fall time t of the balls.
®
Science Equipment for Education Physics
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