Transcript Momentum, Impulse, and Collisons 2

Momentum
•Linear Momentum
•Impulse
•Collisions
•One and Two
Dimensional Collisions
Linear
Momentum
 Momentum is a measure of how
hard it is to stop or turn a moving
object.
 p = mv
 P = Σpi
(single particle)
(system of particles)
Conservation of Linear Momentum
 The linear momentum of a system is conserved
– the total momentum of the system remains
constant
 Ptot = Σp = p1 + p2 + p3 = constant
 p1i + p2i = p1f + p2f
 Σpix = Σpfx, Σpiy = Σpfy, Σpiz = Σpfz
 “Whenever two or more particles in an isolated
system interact, the total momentum of the
system remains constant.”
 Practice Problem 1:
 How fast must an electron move to have the same
momentum as a proton moving at 300 m/s?
mp= 1.672 x 10-27 kg
me= 9.109 x 10-31 kg
ve= 5.507 x 105 m/s
 Practice Problem 2:
 A 90-kg tackle runs north at 5.0 m/s and a 75-kg
quarterback runs east at 8.0 m/s. What is the momentum
of the system of football players?
ptot= 750 kgm/s @ 53.1° N of E
Impulse
 An impulse is described as a change in
momentum:
 I = Dp
 Impulse is also the integral of force over a
period of time:
 I =  Fdt or I = FDt
 The change in momentum of a particle is
equal to the impulse acting on it
 Practice Problem 3:
 Show that Impulse actually comes from Newton’s 2nd Law
F=ma!!!
F = ma = m (Δv/Δt)
m(Δv) = FΔt
Δp = FΔt
Impulsive forces are generally of high magnitude
and short duration.
Force
time
Practice Problem 4:
 A 150-g baseball moving at 40 m/s 15o below the horizontal is
struck by a bat. It leaves the bat at 55 m/s 35o above the
horizontal. What is the impulse exerted by the bat on the ball?
 If the collision took 2.3 ms, what was the average force?
ptot= 2.12 kgm/s @ 62.8° above -x
 Practice Problem 5:
 An 85-kg lumberjack stands at one end of a floating 400-kg
log that is at rest relative to the shore of a lake. If the
lumberjack jogs to the other end of the log at 2.5 m/s
relative to the shore, what happens to the log while he is
moving?
The log will move at
.53 m/s in the
opposite direction of
the lumberjack
 Practice Problem 6:
 Two blocks of mass 0.5 kg and 1.5 kg are placed on a
horizontal, frictionless surface. A light spring is compressed
between them. A cord initially holding the blocks together is
burned; after this, the block of mass 1.5 kg moves to the right
with a speed of 2.0 m/s.
a) What is the speed and direction of the other block?
b) What was the original elastic energy in the spring?
a) v2f= -6 m/s
b) Us = 4.5 J
 Practice Problem 7: (1-D conservation of momentum)
 What is the recoil velocity of a 120-kg cannon that fires a
30-kg cannonball at 320 m/s?
Vcf = -80 m/s
Collisions
Elastic
Inelastic
Perfectly
Inelastic
Collisions:
 In all collisions, momentum is
conserved.
 Elastic Collisions: No deformation occurs
 Kinetic energy is also conserved
 Inelastic Collisions: Deformation occurs
 Kinetic energy is lost
 Perfectly Inelastic Collisions
 Objects stick together, kinetic energy is lost
 Explosions
 Reverse of perfectly inelastic collision, kinetic
energy is gained
Elastic Collisions
 Objects collide and return
to their original shape
 Kinetic energy remains the
same after the collision
 Perfectly elastic collisions
satisfy both conservation
laws shown below
Inelastic Collisions
 Momentum is Conserved:
 m1iv1i +m2iv2i = m1fv1f +m2fv2f
 Kinetic energy is less after the collision
 It is converted into other forms of energy
• Internal energy - the temperature is increased
• Sound energy - the air is forced to vibrate
 Some kinetic energy may remain after the collision, or it may
all be lost
Perfectly Inelastic Collisions
 Two objects collide and
stick together
 Two football players
 A meteorite striking the earth
 Momentum is conserved
 Masses combine
 Practice Problem 8: (1-D elastic collision)
 A proton, moving with a velocity of vi, collides elastically
with another proton initially at rest. If the two protons
have equal speeds after the collision, find
a)
b)
the speed of each in terms of vi and ...
the direction of the velocity of each
vf = ½ v1i
This plot illustrates the tremendous complexity
of the proton-Proton collisions that occur at the
Large Hadron Collider.
 Practice Problem 9: (1-D perfectly inelastic collision)
 A 1.5 kg cart traveling at 1.5 m/s collides with a stationary
0.5 kg cart and sticks to it. At what speed are the carts
moving after the collision?
Vf = 1.125 m/s
m1 = 1.5 kg
V1i = 1.5 m/s
m2 = .5 kg
V2i = 0 m/s
 Practice Problem 10: (1-D elastic collision)
 A 1.5 kg cart traveling at 1.5 m/s collides elastically with a
stationary 0.5 kg cart. At what speed are each of the carts
moving after the collision?
V1f = .75 m/s
V2f = 2.25 m/s
m1 = 1.5 kg
V1i = 1.5 m/s
m2 = .5 kg
V2i = 0 m/s
2-D
collisions
 Use conservation of momentum independently
for x and y dimensions
 You must resolve your momentum vectors into
x and y components when working the problem:
• m1v1ix + m2v2ix = m1v1fx + m2v2fx
• m1v1iy + m2v2iy = m1v1fy + m2v2fy
Practice Problem 11: (2-D collision)
A pool player hits a cue ball in the x-direction at 0.80 m/s. The cue
ball knocks into the 8-ball, which moves at a speed of 0.30 m/s at an
angle of 35o angle above the x-axis.
Determine the velocity and angle of deflection of the cue ball.
(assume m1 = m2)
V1f = .58 m/s @ 17.25° below -x