Conservation of Linear Momentum
Melissa Polewczak
, Kassi Xifo, and Melissa Eppler
PHYS 2115-009
November 1, 2012
ABSTRACT
When two objects are in motion and they collide, that linear momentum of the system
remains unchanged, but instead is transferred equally and oppositely throughout the two objects.
To measure this, objects placed on an air track were collided in elastic and inelastic collisions,
and their velocities and masses were measures. The average of the first two collisions showed a
∆ P system of -0.023, and -0.027. The average of the inelastic collision showed a ∆ P system of
0.094. Overall, the momentum in all three systems was conserved with slight room for
uncertainty.
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INTRODUCTION
Newton’s first law generally states that an object in motion will stay in motion, unless
acted on by an outside force. Without any other force acting on the object, including friction, the
objects speed and direction will remain constant. In other terms this means that the object’s
velocity vector will remain the same from the initial moment that it begins to move. In most
cases, an object’s mass will also remain constant throughout time. This constant mass combined
with its constant velocity makes up linear momentum. Linear momentum is defined as the
continued constant movement of an object over time and it can be found with the equation
mv
.
Newton’s second law Is a major factor when more than one object is involved. The total
amount of force exerted on the object is equal to the mass times the acceleration. The
acceleration of an object is the change in velocity over the change in time so that would then be
related to the total force. The equation F = M * Δv/Δt is then derived from the previous
information. These equations though only tell what the impulse and linear momentum is, while
Newton’s third law is needed to find the momentum after objects collide.
When two objects collide their momentum is transferred to each other. This is known as
the conservation of linear momentum. This law can be defined by this following equation:
M
A
V
Ai
+ M
B
V
Bi =
M
A
V
Af
+
M
B
V
Bf
. The total momentum in a system will remain constant because
each of the objects will have equal but opposite momentum before and after the collision.
Momentum is always conserved but the only thing not conserved is the total mechanical
energy in the system when the two objects stick together rather than bouncing off of each other.
This can be measured by the kinetic energy equation: KE = ½mv for the initial and final
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