Chapter 7
Momentum and Collisions
Linear Momentum
Momentum is the mass times velocity.
SI unit: 
Example 7-1
(a) A 1180 kg car drives along a city street at 30.0 mph (13.4 m/s). What is the magnitude of the car's momentum?
(b) A major league pitcher can give a 0.142 kg baseball a speed of 101 mph (45.1 m/s). Find the magnitude of the baseball's momentum?
Example 7-2
The figure shows a 2.0 kg toy race car before
and after taking a turn on a track. Its speed is 0.50 m/s before the turn and
0.40 m/s after the turn. What is the change 
in
the linear momentum of the car due to the turn?
Impulse and Momentum Change
The Law of Conservation of Momentum
If no net external force acts on objects in a system,
the total linear momentum  |
Newton's Second Law was written in momentum form at first.
Newton's Second Law The time rate change of the momentum of a particle is equal to the net force acting on the particle and is in the direction of that force.
|
Example 7-3
The figure gives the linear momentum versus time for a particle moving along an axis. A force directed along the axis acts on the particle. (a) Rank the four regions indicated according to the magnitude of the force, greatest first. (b) In which region is the particle slowing?
Example 7-4
At a city park, a person throws some bread into a duck pond. Two 4.00 kg ducks and a 9.00 kg goose paddle rapidly toward the bread, as in the figure. If the ducks swim at 1.10 m/s, and the goose swims with a speed of 1.30 m/s, find the magnitude and direction of the total momentum of the three birds.
Impulse
Impulse = change in momentum
A given impulse will produce a specific change in momentum no matter what the mass or speed of the recipient body.
Example 7-5
A 0.144 kg baseball is moving toward home
plate with a speed of 43.0 m/s when it is bunted (hit softly). The bat exerts
an average force of 
on
the ball for 1.30 ms. The average force is directed toward the pitcher, which
we take to be positive x direction. What is the final speed of the ball?
Example 7-6
A person stands under an umbrella during a rain shower. A few minutes later the rain drops turn to hail–though the number of "drops" hitting the umbrella per time and the speed remains the same. Is the force required to hold the umbrella in the hail (a) the same as (b) more than, or (c) less than the force required in the rain?
Example 7-7
After winning a prize on a game show, a 72 kg contestant jumps for joy. (a) If the jump results in an upward speed of 2.1 m/s, what is the impulse experienced by the contestant? (b) Before the jump, the floor exerts an upward force of mg on the contestant. What additional average upward force does the floor exert if the contestant pushes down on it for 0.36 sec during the jump?
Conservation of Momentum
Example 7-8
Two groups of canoeists meet in the middle of a lake. After a brief visit, a person in canoe 1 pushes on canoe 2 with a force of 46 N to separate the canoes. If the mass of canoe 1 and its occupants is 130 kg, and the mass of canoe 2 and its occupants is 250 kg, find the momentum of each canoe after 1.20 s of pushing.
Example 7-9
In example 7-8, the final momentum of the system (consisting of the two conoes and their occupants) is equal to the initial momentum of the system. Is the final kinetic energy (a) equal to, (b) less than, or (c) greater than the initial kinetic energy?
Example 7-10
A honeybee with a mass of 0.150 g lands
on one end of a floating 4.75 g popsicle stick. After sitting at rest for a
moment, it runs toward the other end with a velocity 
relative
to the still water. The stick moves in the opposite direction with a speed
of 0.120 cm/s. What is the velocity of the bee? (Let the direction of the bee's
motion be the positive x direction.)
Example 7-11
A ballot box with mass m = 6.0 kg slides
with speed v = 4.0 m/s across a frictionless floor in the positive x direction
on an x axis. It suddenly explodes into two pieces. One piece, with mass 
,
moves in the positive direction of the x axis with speed 
.
What is the velocity of the second piece, with mass 
?
Example 7-12
A firecracker placed inside a coconut of
mass M, initially at rest on a frictionless floor, blows the coconut into three
pieces that slide across the floor. See the figure below. Piece C, with mass
0.30M, has final speed 
.
(a) What is the speed of piece B, with mass 0.20M?
(b) What is the speed of piece A?
of
the system cannot change.
