PC1141 Physics I
Conservation of Momentum in Collisions
1
Purpose
•
Determination of the velocity and this momentum of each glider before and after the
collision from which the total momentum of the system before and after the collision is
obtained
•
Evaluation of the extend to which the total momentum of the system before the collision
is equal to the total momentum of the system after the collision
2
Equipment
•
Air track, air blower, two gliders, fork with rubber band, holder with plate, wax and
needle
3
•
Smart Timer and picket fence
•
Photogates
•
Various weights
•
Laboratory balance
Theory
The momentum of an object of mass
m
moving with a velocity
~v
is dened to be
p~ = m~v
Momentum is a vector quantity because it is the product of a scalar
(m)
with a vector
(~v ).
It
can be shown for a system of particles that the total momentum of the system is constant if
there are no external forces acting on the system. The forces exerted between the particles of
the system are called internal force and they cannot change the momentum of the system.
A collision between two objects is an example of a case in which momentum is conserved
because the forces that the two objects exert on each other are internal to the system. If p
~i1
f
f
i
and p
~2 stand for the initial momenta of particles 1 and 2 and p~1 and p~2 stand for their nal
momenta after the collision, then
p~1i + p~2i = p~1f + p~2f
Page 1 of 5
(1)
Conservation of Momentum in Collisions
Page 2 of 5
In the most general case, equation (1) implies that each of the components of the momentum is conserved. In this experiment, two gliders will undergo collisions on a linear air track
and hence these are one dimensional collisions. The vector nature of the problem is specied
by writing momenta to the right as positive and momenta to the left as negative.
Equation (1) is strictly valid only if there are no external forces on the system. Friction
on the gliders of an air track will be an external force.
Therefore, frictional eects on the
gliders will tend to invalidate equation (1) if the frictional forces are comparable to the forces
of collision on the gliders.
When two gliders collide with each other, the total momentum of both gliders is conserved
regardless of elastic or inelastic collision. Both elastic and inelastic (completely) collisions will
be investigated in this experiment. An elastic collision is one in which the two gliders bounce
o of each other with no loss of kinetic energy accomplished through the use of the fork
with rubber band and holder with plate in this experiment. A completely inelastic collision
is one in which the two gliders hit and stick to each other accomplished in this experiment
using the wax and needle on one end of each glider.
Three dierent proles for collision will be investigated in this experiment. There are:
Collision I:
Place one of the gliders at rest in the middle of the track. Give the other glider
an initial velocity toward the stationary glider.
Collision II:
Start both gliders at one end of the track. Give the rst glider a slow velocity
and the second glider a faster speed so that the second glider catches the rst glider.
Collision III:
Start both gliders at opposite ends of the track toward each other.
Figure 1: Apparatus setup
In this experiment, the measurements will involve determination of the velocities of two
gliders before the collision and after the collision. Each of these four velocities is a constant
velocity. The value of a velocity will be determined by Smart Timer when the glider passes
the photogate.
PC1141 Physics I
Semester I, 2007/08
Conservation of Momentum in Collisions
4
Page 3 of 5
Experimental Procedure
1.
Level the track by setting a glider on the track to see which way it rolls. Adjust the
leveling screw at the bottom of the track to raise or lower that end until a glider placed
at rest on the track will remain at rest.
2.
Put a picket fence into the slots in the top of each glider and place the collision gliders so
the wax and needle face each other. Position the two photogates just far enough apart so
the collision can take place between the photogates. Adjust the height of the photogates
so the 1-cm ag will block the photogate infrared beams. Connect the photogates to
the Smart Timer.
Figure 2: Conneting the photogate to
the Smart Timer
Figure 3: Smart Timer picket
fences
3.
Setup the Smart Timer to measure
Speed: collision (cm/s).
Press
Start/Stop
to
activate the Smart Timer.
Note:
If the ag does not go through the photogate beams twice, the Smart Timer will
not complete the timing cycle and display velocities automatically.
press
Start/Stop
You will need to
to stop timing manually. The completed timing measurements will
be displayed and the uncompleted measurements will be registered as
0.
The display
will present the results in the following format:
1: Input Jack 1, initial speed 1, nal speed 1
2: Input Jack 2, initial speed 2, nal speed 2
The rst number represents the input jack and the following two numbers indicate the
initial and nal speeds respectively.
If the glider passes through the photogates just
once, take the non-zero reading as the velocity of the glider when the glider passes
through the corresponding photogate. Press
1
or
2
to scroll back and forth between the
registered velocities from respective photogates.
PC1141 Physics I
Semester I, 2007/08
Conservation of Momentum in Collisions
4. Equal Masses.
Page 4 of 5
Perform each of the following completely inelastic collisions FIVE
times.
(a)
Collisions I.
Record your data in the Data Table 1.
(b)
Collision II.
Record your data in the Data Table 2.
Note: M1 , M2
are the respective masses of the gliders and
initial velocities (positive if moving towards right).
5. Unequal Masses.
(a)
(1M ).
are the respective
is the nal velocity of the gliders.
Put the weights on the steel pegs mounted on the sides of the gliders
so that the mass of one glider
glider
~v
~u1 , ~u2
(2M )
is approximately two times the mass of the other
Perform each of the following completely inelastic collisions FIVE times.
Collisions I.
Let
1M
be the stationary glider at middle of the track. Record your
data in the Data Table 3.
(b)
Collision II.
Let
1M
be the rst glider and
2M
be the second glider. Record your
data in the Data Table 4.
(c)
6.
Collision III.
Record your data in the Data Table 5.
Set up the gliders so the fork with rubber band and holder with plate face each other,
so the gliders will repel each other when they collide.
7. Equal Masses.
Perform each of the following elastic collisions FIVE times.
(a)
Collisions I.
(b)
Collision III.
Note: M1 , M2
Record your data in the Data Table 6.
Record your data in the Data Table 7.
are the respective masses of the gliders,
velocities (positive if moving towards right) and
8. Unequal Masses.
(a)
(1M ).
are the respective initial
are the respective nal velocities.
Put the weights on the steel pegs mounted on the sides of the gliders
so that the mass of one glider
glider
~v1 , ~v2
~u1 , ~u2
(2M )
is approximately two times the mass of the other
Perform each of the following elastic collisions FIVE times.
Collisions I.
Let
2M
be the stationary glider at middle of the track. Record your
data in the Data Table 8.
(b)
Collision II.
Let
2M
be the rst glider and
1M
be the second glider. Record your
data in the Data Table 9.
(c)
Collision III.
PC1141 Physics I
Record your data in the Data Table 10.
Semester I, 2007/08
Conservation of Momentum in Collisions
5
D1.
Page 5 of 5
Data Analysis
Enter your data in the Data Table 15 into the Excel spreadsheet. For each of the cases,
calculate the the momentum for each of the gliders before and after the collision in the
spreadsheet. Let momenta to the right be positive and momenta to the left be negative.
D2.
For each case, calculate the total momentum of both gliders before and after the collision
in the spreadsheet. Note that momentum is a vector quantity.
D3.
Calculate the percentage dierence between the total momentum before the collision
and the total momentum after the collision for each of the cases in the spreadsheet.
Hint:
The percentage dierence is dened as
Percentage dierence
D4.
=
|~pi | − |~pf |
× 100%
(|~pi | + |~pf |)/2
Calculate the best experimental value of the percentage dierence between the total
momentum before the collision and the total momentum after the collision as well as
its corresponding uncertainty. Do your results indicate that momentum is conserved for
inelastic collision?
D5.
Enter your data in the Data Table 610 into the Excel spreadsheet.
For each of the
cases, calculate the momentum for each of the gliders before and after the collision in
the spreadsheet.
D6.
For each case, calculate the total momentum and total kinetic energy of both gliders
before and after the collision in the spreadsheet.
D7.
Calculate the percentage dierence between the total momentum before the collision and
the total momentum after the collision for each of the cases in the spreadsheet. Perform
the similar calculations for the percentage dierence between the total kinetic energy
before the collision and the total kinetic energy after the collision in the spreadsheet.
D8.
Calculate the best experimental values of the percentage dierence between the total
momentum and total kinetic energy before the collision and the total momentum and total kinetic energy after the collision as well as their corresponding uncertainties. Do your
results indicate that momentum and kinetic energy are conserved for elastic collision?
PC1141 Physics I
Semester I, 2007/08