7.0 - Introduction
“The more things change, the more they stay the same” is a well-known French
saying.
However, though witty and perhaps true for many matters on which the French have
great expertise, this saying is simply not good physics.
Instead, a physicist would say: “Things stay the same, period. That is, unless acted
upon by a net force.” Perhaps a little less joie de vivre than your average
Frenchman, but nonetheless the key to understanding momentum.
What we now call momentum, Newton referred to as “quantity of motion.” The linear
momentum of an object equals the product of its mass and velocity. (In this chapter,
we focus on linear momentum. Angular momentum, or momentum due to rotation,
is a topic in another chapter.) Momentum is a useful concept when applied to
collisions, a subject that can be a lot of fun. In a collision, two or more objects exert
forces on each other for a brief instant of time, and these forces are significantly
greater than any other forces they may experience during the collision.
At the right is a simulation í a variation of shuffleboard í that you can use to begin
your study of momentum and collisions. You can set the initial velocity for both the blue and the red pucks and use these velocity settings to
cause them to collide. The blue puck has a mass of 1.0 kg, and the red puck a mass of 2.0 kg. The shuffleboard has no friction, but the pucks
stop moving when they fall off the edge. Their momenta and velocities are displayed in output gauges.
Using the simulation, answer these questions. First, is it possible to have negative momentum? If so, how can you achieve it? Second, does
the collision of the pucks affect the sum of their velocities? In other words, does the sum of their velocities remain constant? Third, does the
collision affect the sum of their momenta? Remember to consider positive and negative signs when summing these values. Press PAUSE
before and after the collisions so you can read the necessary data. For an optional challenge: Does the collision conserve the total kinetic
energy of the pucks? If so, the collision is called an elastic collision. If it reduces the kinetic energy, the collision is called an inelastic collision.
7.1 - Momentum
Momentum (linear):Mass times velocity.
An object’s linear momentum equals the product of its mass and its velocity. A fast
moving locomotive has greater momentum than a slowly moving ping-pong ball.
The units for momentum are kilogram·meters/second (kg·m/s). A ping-pong ball with a
mass of 2.5 grams moving at 1.0 m/s has a momentum of 0.0025 kg·m/s. A 100,000 kg
locomotive moving at 5 m/s has a momentum of 5×10^5 kg·m/s.
Momentum is a vector quantity. The momentum vector points in the same direction as
the velocity vector. This means that if two identical locomotives are moving at the same
speed and one is heading east and the other west, they will have equal but opposite
momenta, since they have equal but oppositely directed velocities. Momentum
Moving objects have momentum
Momentum increases with mass,
velocity