Physics Online
Collisions
When two objects collide, they exert forces on one another. If we know the exact forces and
time of contact, then we can use Newton’s second law and kinematics equations to predict
the subsequent motion of the objects. But the exact forces exerted can be extremely difficult
to measure, and they often vary over the course of the collision, so a different method of
analysis is preferred. The preferred analysis uses the law of conservation of momentum. The
purpose of this lab is to test this law.
Momentum can be calculated with the following definition:
[1]
p = mv
p = momentum
m = mass
v = velocity
Newton’s second law can be rewritten in terms of momentum as follows:
[2]
[3]
[4]
[5]
ΣF = ma
ΣF = m(Δv/Δt)
ΣF = Δ(mv)/Δt
ΣF = Δp/Δt
(Newton’s second law)
(definition of acceleration)
(assumption of constant mass)
(definition of momentum)
The second law can be stated as “the net force is the rate of change in momentum.”
If we analyze a pair of objects that do not interact significantly with the outside world (no
net external force), then we can use equation [5] and Newton’s third law to prove
conservation of momentum.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
F21 = Δp1/Δt
(equation [5] applied to object 1)
F12 = Δp2/Δt
(equation [5] applied to object 2)
F21 = -F12
(Newton’s third law)
F21 + F12 = 0
Δp1/Δt + Δp2/Δt = 0 (equations [6] and [7] in equation [9])
Δp1 + Δp2 = 0
(multiply by Δt)
(p1f - p1i) + (p2f - p2i) = 0 (definition of Δ)
p1i + p2i = p1f + p2f
For a system with no significant net external force, the total momentum before an
event equals the total momentum after an event. This is called “conservation of
momentum.” This analysis can be extended to more than two objects. In this lab, we will
test the motion of two objects in one dimension. Conservation of momentum in one
dimension is written as follows:
[14]
[15]
p1i + p2i = p1f + p2f
m1v1i + m2v2i = m1v1f + m2v2f
If two objects stick together after a collision, the collision is called “completely inelastic.”
The conservation of momentum equation can be rewritten with a common final velocity as
follows:
[16]
[17]
m1v1i + m2v2i = m1vf + m2vf
m1v1i + m2v2i = (m1 + m2)vf
Physics is fun!
Equipment You Procure
 digital camera
 metric tape measure
 horizontal surface with sharp edge and above
the ground
 duct tape (the stickier the better) or strong
magnet
Equipment from Kits
 inclined plane
 4” x 6” card
 solid metal spheres (2)
 rings (2)
 bubble level
 scale
Experimental Procedures
Launch Speed Calculation (Note: these are similar to the projectile motion lab, please see that lab for the
relevant kinematics equations)
1) Select a horizontal surface. Use the bubble level to
check if the surface is horizontal. If the surface is not
horizontal, then correct this or select another surface.
2) Raise the inclined plane to an angle of about 30
degrees.
Δy
3) Tape the 4”x6” card to the end of the inclined plane.
An inch or two of the card should overlap the end of
Δx
the inclined plane.
4) Place the inclined plane on the horizontal surface so
that the non-taped end of the card is a few inches
from the edge of the horizontal surface.
5) Measure the vertical distance between the top of the surface and the floor, Δy.
6) Place the solid metal ball about halfway up the ramp. Mark its starting point on the
ramp.
7) Roll the ball down the ramp and the card. Note its approximate landing place.
8) Tape down a piece of paper near the landing place.
9) Draw all over the metal ball.
10) Roll the metal ball down the ramp from the same starting point. The ball should land
on the paper and make a mark.
11) Measure the horizontal distance between the edge of the surface and the landing
place, Δx1.
12) Use kinematics in the y-direction to derive a symbolic solution for the time to
impact, t, in terms of Δy and g.
13) Use kinematics in the x-direction to derive a symbolic solution for vix in terms of
Δx1, Δy, and g.
Collision
14) Measure the mass of the sphere used in the launch speed calculation, m1.
15) Obtain a ring and measure its mass. It should be no less than 1/3 the mass of the
sphere and no more than 3 times the mass of the sphere.
16) Place a big wad of tape on one side of the ring and measure its mass again, m2.
17) Use equation [17] and the symbolic solution derived in step 13 to obtain a
symbolic solution for the velocity after the collision, vf, in terms of m1, m2, Δx1, Δy,
and g. This will be the initial velocity, vix, for the projectile motion.
18) Use kinematics in the y-direction to derive a symbolic solution for the time to
impact, t, in terms of Δy and g.
19) Use kinematics in the x-direction and your results from steps 17 and 18 to derive a
symbolic solution for the new horizontal distance, Δx2, in terms of m1, m2, and Δx1
alone. Please check your work with me if you are unsure of your symbolic solution.
If you use an incorrect symbolic solution, then you may have your report returned
for resubmission.
20) Use your symbolic solution from step 19 to predict a horizontal distance. Note that
this is the first and only time you will calculate anything.
21) Place the ring near the edge of the horizontal surface. The sticky side should face the
ramp.
22) Roll the sphere down the ramp from the same point as you used to calculate the
launch speed. The sphere must smash into the ring and stick. If it does not stick,
then you should use more tape (weigh it again) or roll the sphere from a shorter
distance up the ramp (measure Δx1 again).
23) Measure the horizontal distance between the edge of the surface and the landing
place, Δx2.
24) Compare your experimental and theoretical displacements. Did this experiment
support the law of conservation of momentum?
25) Repeat this experiment with a different sphere, ring, or initial velocity (different ramp
angle or starting point). Complete this experiment a total of four times.