Download lecture 15 momentum and impulse

LECTURE 15
MOMENTUM AND IMPULSE
Lecture Instructor: Kazumi Tolich
Lecture 15
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Reading chapter 9-1 to 9-4
¤ Momentum
2nd law with momentum
n Conservation of momentum
n Newton’s
¤ Impulse
n Impulse-momentum
theorem
Momentum
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Linear momentum or just momentum is defined to be
𝐩 = 𝑚𝐯
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Momentum of a particle can be thought of as its quantity of motion, or
amount of effort needed to bring the particle to rest.
If a system consists of multiple particles, the total momentum of the system is
the vector sum of momentum of each particle:
𝐩%&%'( = 𝐩) + 𝐩) + 𝐩+ ⋯
Quiz: 1
4
Law of conservation of momentum/Demo: 1
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In Principia (1687), Newton presents the second law of motion in terms of momentum.
- 𝐅⃗ =
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∆𝐩
∆𝑡
This is equivalent to ∑ 𝐅⃗ = 𝑚𝐚 in less general case where 𝑚 is constant.
The law of conservation of momentum states:
If ∑ 𝐅⃗ = 𝟎, then 𝐩 is constant
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Multiple particles in a system can exert internal forces on each other, but since they always sum up to zero,
the total momentum of the system is conserved as long as there is no external force acting on the system.
Demo: Reaction Gliders on Air Track
Example: 1
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Meteor Crater in Arizona is thought to have
been formed by the impact of a meteor
with Earth some 50,000 years ago. The
mass of the meteor is estimated at
𝑚6 = 3 × 108 kg, and its speed at
𝑣6 = 1.3 × 104 m/s. What speed would
such a meteor impart to Earth in a head-on
collision?
Meteor Crater: 1200 m in diameter, 170 m deep
Example 2
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A railroad flatcar of weight 𝑊
can roll without friction along a
straight horizontal track. Initially a
man of weight 𝑤 is standing on the
car, which is moving to the right
with speed 𝑣: . What is the change
in velocity of the car if the man
runs to the left so that his speed
relative to the car is 𝑣;<( ?
Example 3
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A radioactive nucleus, initially at
rest, decays by emitting an
electron and a neutrino
perpendicular to each other. The
linear momentum of the electron is
𝐩< = 1.2 × 10-22 kg·∙m/s 𝐲>, and
that of the neutrino is
𝐩? = 6.4 × 10-23 kg·∙m/s 𝐱>. Find
the direction and magnitude of the
linear momentum of the nucleus as
it recoils from the decay.
Impulse
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When two objects collide, they usually exert
very large forces on each other for a very
brief time, and such forces are called
“impulsive forces.”
The impulse applied to an object during a
collision changes its momentum (Momentumimpulse theorem).
𝐈⃗ = 𝐅⃗'B ∆𝑡 = ∆𝐩
Quiz: 2 & 3
Long legs and jumping
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A frog making a jump wants to gain as much momentum, therefore imp
impulse, 𝐈⃗ = 𝐅⃗'B ∆𝑡, delivered to it, as possible before leaving the ground.
There is a maximum force that the muscle can exert, limiting 𝐅⃗'B .
The time interval ∆𝑡 over which the force is exerted can be increased by
having long legs.
Many good jumpers have long legs.
Example: 4
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In a typical golf swing, the
club is in contact with the
ball for about 1.0 ms. If the
45-g ball acquires a speed
of 67 m/s, estimate the
magnitude of the force
exerted by the club on the
ball.