Momentum, p (kg*m/s)
• Momentum is the product of Mass (m) and Velocity (v)
> p = mv
• It is a vector quantity
> the direction of the momentum vector is the same as the
direction as the velocity
Example: A 1,200 kg car is driving on the highway with a velocity of
25 m/s. What is its momentum?
Example 2: A 6,000 kg truck is driving such that it has the same
momentum as the car mentioned above. What is its velocity?
Change in Momentum, ∆p
• ∆p = pf - p0 = mvf - mv0
Example: A 0.20 kg baseball is pitched with a velocity of 35 m/s,
when it is struck with a bat such that its final velocity is -50 m/s.
What is the change in momentum of the baseball?
Example 2: A 0.6 kg basketball is dropped from a height of 1.6 m
above the ground. It rebounds off the floor, such that its speed
after hitting the floor is 90% of the speed before it hits. What is the
change in momentum of the basketball?
Conservation of Momentum: When an object, or a system of
objects, is subject to no Net External Force, we can say that the
Momentum of that object, or system, is Conserved (implying the
total Momentum will not change).
[Why? Because if there is no Net External Force, there is no
acceleration, and so the velocity remains the same.]
In these cases, we will say that p0 = pf
If there are two or more objects involved, we will need to add their
individual momenta (as vectors); the sum of their combined
momenta must be constant.
So, if there are 2 objects, we say that: p0 = pf
p01 + p02 = pf1 + pf2
In a 1-dimensional case, we will just deal with the vectors as being
Positive or Negative. If we have a 2-dimensional case, we will need
to decompose vectors into x- and y-components, and then apply
Conservation of Momentum in each direction separately.
Example: A 100 kg Physics teacher is holding a 5 kg medicine ball,
standing on a skateboard, initially at rest. He throws the medicine
ball away from himself with a velocity of +8 m/s. What is his
velocity? [This is often referred to as a Recoil velocity]
Example 2: An atomic nucleus has a mass of 197 u (this symbol
stands for Atomic Mass Unit; it is the mass of 1 proton = 1.67 E-27 kg)
is at rest when it emits a neutron, with a mass of ~ 1 u. If the
neutron has a velocity of -6,000 m/s, what is the recoil velocity of
the nucleus? [*Note: the mass of the nucleus is now just 196 u]
Collisions: A collision in Physics is considered to be any
interaction that occurs between two (or more) objects that
1.
Occur over a short period of time;
2.
Result in the objects exerting relatively large forces on each other
Examples:
• A moving car crashes into a stationary truck; vice versa
• A baseball player swings his bat, and the bat strikes the ball
• One ball on a Newton's cradle smacks into a second ball
• The magnets on one dynamics cart pushes on a second cart
• A firecracker explodes into multiple pieces (not what we normally
think of as a collision, but explosions satisfy the definition above)