Download Study Notes Lesson 14 Momentum

Physics Study Notes
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Lesson 14 Momentum
Momentum
a.
Momentum: The concept of inertia in motion, or the mass of an object multiplied by its velocity.
b.
Formula:
momentum = mass x velocity
or
p = mv
or
p = mv
If direction is not an important factor,
momentum = mass x speed
c.
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For objects moving at the same velocity, the one having more mass will have more momentum.
For objects of the same mass, the higher the velocity, the more the momentum. An object at rest
has no momentum.
Impulse Changes Momentum
a.
Impulse-momentum relationship: If the momentum of an object changes, either the mass or the
velocity or both change. Since velocity change due to acceleration, and acceleration occurs due to
force, we define impulse:
impulse = force x time interval
or
J = FΔ t
According to Newton’s second law and the definition of acceleration,
a=
F and
Δv ,
a=
m
t
so,
F Δv
=
m
t
Ft = Δ (mv)
or
impulse = change in momentum
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b.
Increasing Momentum: To increase the momentum of an object, you can apply the greatest force
€
€ involved in impulses usually vary from instant to
possible for as€long as possible. Since the force
instant, when we speak of such impact forces, we mean the average force of impact. Impact refers
to a force and measured in newtons. (while impulse is impact force x time and is measured in
newton-seconds.)
c.
Decreasing momentum: The impact time is the time during which your momentum is F
brought to zero. A longer impact time reduces the force of the impact and decreases
the resulting deceleration.
Bouncing
a.
4
t
Impulses are greater when an object bounces since there is additional impulse required to “throw it
back again”. The curved blades of the Pelton wheel cause water to bounce and make a U-turn,
producing a large impulse that turns the wheel.
Conservation of Momentum
a.
Change momentum: To change momentum of an object, you need to exert an impulse on it. The
impulse must be exerted by something outside the object. Internal foces won’t work since they
come in balanced pairs that cancel within the object. If no external push or pull is present, no
change in momentum is possible. If no net force or net impulse acts on a system, the momentum
of that system cannot change.
b.
Law of conservation of momentum:
In the absence of an external force, the momentum of a system remains unchanged.
c.
The impulse the cannon exerts on the cannonball is equal and opposite to the impulse the
cannonball exerts on the cannon.
Mr. Lin
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Physics Study Notes
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Lesson 14 Momentum
Collisions
a.
Conservation of momentum: Whenever there is no external net force, the net momentum of both
objects before collision equals the net momentum of both objects after collision.
net momentum before collision = net momentum after collision
b.
pbefore = Pafter
Elastic collision: When objects collide without being permanently deformed and without
generating heat, the collision is called an elastic collision. Colliding objects bounce perfectly in
perfect elastic collisions, and the sum of the momentum vectors is the same before and after the
collision.
Collision
Before Collision
c.
or
After Collision
Inelastic collision: Whenever colliding objects become tangled or coupled together, a totally
inelastic collision occurs. The momentum of the freight car on the left is shared with the freight
car on the right.
m1v 1
m1v1 + m2•0= (m1 + m2)v,
or
v=
(m1 + m2 )
v1
v2 = 0 m/s
m1
m2
€
v
m1 + m2
m1v1 + m2 v2= (m1 + m2)v,
or
v1
v=
v2
m1
m 1v 1 + m 2 v 2
(m1 + m2 )
m2
€
m1 + m2
Mr. Lin
v
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Physics Study Notes
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Lesson 14 Momentum
Momentum Vectors
a.
Momentum vectors: Momentum is a vector quantity. Momentum is conserved even when
interacting objects do not move along the same straight line. Vector techniques will be used to
analyze momentum in any direction.
b.
Combined momentum:
c.
Resolved momentum: When an object bursts, the vector sum of the momenta of its fragments add
up to the object’s momentum just before bursting.
mv
m1v1
m2v2
mv
Momentum and Impulse Problems:
1.
Assume an 8 kg bowling ball moving at 2 m/s bounces off a spring at the same speed that it had before bouncing.
(a) What is its change in momentum? (b) If the interaction with the spring occurs in 0.5 s, calculate the average
force the spring exerts on it.
2.
Cart A and cart B (initially at rest) are pushing apart by a spring that exerts an average force of 50 N for a period
of 0.2 s. (Assume frictionless conditions.) (a) What is the impulse applied
by the spring on cart A? (b) What is the magnitude of the impulse acting
2 kg
1 kg
on cart B? (c) What is the average acceleration of cart A during the 0.2 s
A
B
interaction? (d) What is the velocity of cart B at the end of the 0.2 s? (e)
What is total momentum of the carts after spring is released?
Mr. Lin
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Physics Study Notes
Lesson 14 Momentum
3.
Silvia, whose mass is 45.0 kg, is ice skating with a constant speed of 7.00 m/s when she hits a rough patch of ice
with a coefficient of friction of 0.08. How long will it take before Silvia coasts to a stop?
4.
A block of M kg free-falling from H meters high hit the ground and stopped without bouncing. If the impact time
is T, what is the average impact force during the impact?
5.
Person A and B stand still on the frictionless surface and person A hold a ball with mass m. The mass of person A
is mA and the mass of person B is mB. (a) If person A throw the ball horizontally to person B at speed v, and
person B catch it, what is the speed of A (vA) and B (vB) respectively at the end of this action? (b) What’s the ratio
between vA and vB? (c) If person B then throw the ball horizontally back to person A at speed v, and person A
catch it, what is the velocity of A (vA’) and B (vB’) respectively at the end of this second action? (d) What’s the
ratio between vA’ and vB’?
Mr. Lin
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