Linear Momentum

Momentum
CONTENTS:
Center of Mass
Impulse
Momentum
Change in Momentum
Change in Momentum from representations
Graph of net external force vs. time and change in momentum vs. time
Open and Closed Systems
Center of Mass motion during collisions/explosions
Elastic & Inelastic Collisions
Using Conservation of Momentum and Energy to make predictions
momentum interact
Linear conservation
momentum
collision Internal force
explode Elastic collision
Inelastic collision External force
impulse impulse-
momentum
theorem
Center of Mass net external force
Conservation of
Momentum
momentum 动量 interact 相互作用
Linear 线性动量 conservation 守恒
momentum
collision 碰撞 Internal force 内力
explode 爆炸 Elastic collision 弹性碰撞
Inelastic collision 非弹性碰撞 External force 外力
impulse 冲量 impulse- 动量定理

momentum
theorem
Center of Mass 质心 net external force 合外力
Conservation of 动量守恒
Momentum
Center of Mass (CM)
The center of mass is the point where all of the mass of an object can be considered
to be concentrated
What do you think the center of mass is related to?

Calculate Center of Mass (CM)
1,On a lightweight (air-filled)“banana boat,” three people of roughly equal mass m
sit along the x axis at positions and measured from the left-hand end as shown in Fig.
7–23. Find the position of the CM. Ignore the mass of the boat
xcm=4.0m
2,Find the center of mass of the three-mass system shown in Fig. 7–37 relative to the
1.00-kg mass.
xcm=0.438 m
3,The CM of an empty 1250-kg car is 2.40 m behind the front of the car. How far
from the front of the car will the CM be when two people sit in the front seat 2.80 m
from the front of the car, and three people sit in the back seat 3.90 m from the front?
Assume that each person has a mass of 65.0 kg.
xcm=2.62 m
4,A (lightweight) pallet has a load of ten identical cases of tomato paste (see Fig.
7–39),each of which is a cube of length �.Find the center of gravity in the horizontal
plane,so that the crane operator can pick up the load without tipping it.
xcm=1.15�
ycm=0.9�
Impulse
Impulse is the product of the average force on an object and the time interval over
which it acts
The area under a force vs. time graph represents the impulse
Classroom examples
Calculate the work done of each force.

Calculate the impulse of each force.
Calculate and Rank the magnitude of the impulse applied to the box by the force
during each 2-second interval indicated below:
A. 0–2 seconds B. 2–4 seconds C. 4–6 seconds D. 6–8 seconds E. 8–10 seconds
Defining linear momentum
The linear momentum of an object is defined as the product of its mass and
its velocity.
Momentum is a vector quantity , its direction is the same as the

direction of the object’s velocity
Note: Since velocity is a vector quantity (has a magnitude and direction),

then momentum is also a vector quantity
5,A compact car, with mass 725 kg, is moving at 115 km/h toward the east. Sketch the
moving car.
a. Find the magnitude and direction of its momentum. Draw an arrow on your
sketch showing the momentum.
b. A second car, with a mass of 2175 kg,has the same momentum. What is its
velocity?
a,2.32×104 kg.m/s eastward
b,10.7m/s eastward
Change in Momentum
Change of momentum (ΔP )

what do you guess is the cause of the change in momentum ?
Momentum and Newton’s laws
Newton’s first law of motion
An object will remain at rest or keep travelling at constant
velocity unless it is acted on by a resultant force .
Hence the first law is really saying that the momentum of an

object remains the same unless the object experiences an
external force
NEWTON’SECOND LAW :
The rate of change of momentum of an object is equal to the net force
applied to it.
Impulse-Momentum Theorem
The impulse of the force acting on an object equals the change in momentum
of that object
Newton’s third law of motion
Force pairs equal in magnitude, opposite in direction
Scenario
Two stationary ice skaters push off .Both skaters exert equal forces on each
other and for the same time.
One gains momentum to the left while the other gains equal momentum
to the right .
What do you think the relationship of their momentums
Under what conditions is the momentum of the system of
two balls conserved?
For all systems under all circumstances, energy, charge, linear momentum, and
angular momentum are conserved. For an isolated or a closed system, conserved
quantities are constant. An open system is one that exchanges any conserved quantity
with its surroundings.
Open vs Closed systems (momentum)

An open system is one in which there is a force applied to that system by something
outside the system
A closed system is one in which there are no forces applied to that system by something
outside the system
Conservation of momentum
Within a closed system , the total momentum in any direction is
constant
If no net external force acts on a system, the total momentum of
the system is a conserved quantity.
Problem solving strategies
Make sure you have a good diagram of the event pre and post collision
Always start by writing down the law of conservation of momentum
List the momenta of each object before and after the collision
Remember the direction of each object is going...rigth(+) and left (-)
Non-SI units are OK as long as all the mass units are the same and all the velocity
units are the same.
11,Two lab carts are pushed together with a spring mechanism compressed between
them. Upon release, the 5.0-kg cart repels one way with a velocity of 0.12 m/s, while
the 2.0-kg cart goes in the opposite direction. What is the velocity of the 2.0-kg cart?
-0.30 m/s
12,A 50.0-g projectile is launched with a horizontal velocity of 647 m/s from a 4.65-kg
launcher moving in the same direction at 2.00 m/s. What is the launcher’s velocity
after the launch?
-4.94 m/s, or 4.94 m/s backwards
13,A 2575-kg van runs into the back of an 825-kg compact car at rest. They move
off together at 8.5 m/s. Assuming that the friction with the road is negligible,
calculate the initial speed of the van.
11 m/s
Two types of collision
What’s the difference between these two kinds of collisions ?
There is no loss of kinetic energy in an elastic collision

Kinetic energy is reduced in an inelastic collision
Two types of collision
When objects hit each other, the resulting collision can be considered to be either
elastic or inelastic. Momentum and total energy are always conserved in both cases.
In an Inelastic collision some of the kinetic energy is converted to other

forms of energy (often heat & sound)
At the atomic level the collisions of atoms and molecules are often elastic.
But in the “macroscopic” world of ordinary objects, an elastic collision is
an ideal that is never quite reached,
If two objects stick together as a result of a collision, the collision is

said to be completely inelastic.
Elastic Collisions Inelastic Perfectly Inelastic
Collisions Collisions
Visual description objects bounce off objects bounce off objects stick
one another one another together
Momentum conserved conserved conserved
Kinetic Energy conserved not conserved not conserved

elastic collision
Collisions in two dimensions
Momentum is a vector quantity and so we can split it into components

in order to solve problems
Momentum is conserved both in the X-direction and in the Y-direction
*velocity of center of mass

Linear Momentum

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Momentum

explode Elastic collision

Inelastic collision External force

explode 爆炸 Elastic collision 弹性碰撞

Inelastic collision 非弹性碰撞 External force 外力

impulse 冲量 impulse- 动量定理

What do you think the center of mass is related to?

Calculate the work done of each force.

Momentum is a vector quantity , its direction is the same as the

Note: Since velocity is a vector quantity (has a magnitude and direction),

Change of momentum (ΔP )

Hence the first law is really saying that the momentum of an

Open vs Closed systems (momentum)

-4.94 m/s, or 4.94 m/s backwards

What’s the difference between these two kinds of collisions ?

There is no loss of kinetic energy in an elastic collision

In an Inelastic collision some of the kinetic energy is converted to other

If two objects stick together as a result of a collision, the collision is

Momentum conserved conserved conserved

Kinetic Energy conserved not conserved not conserved

Momentum is a vector quantity and so we can split it into components

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