Momentum and Collisions
Momentum and Collisions
Physics 2053Lecture Notes
Momentum and Collisions
6-01 Momentum and Impulse
6-02 Conservation of Momentum
6-03 Collisions
Topics
Momentum and Collisions
mm
iv
F
tavv if
mF
fv
if mvmvtF
ImpulsetΔF )p( omentumMmv
Momentum is a vectormvtF
mvtF ptmF
vv if
pΔtΔF
Momentum and Impulse
Momentum and Impulse
t
Momentum and Collisions
A block moving with an initial velocity vi is acted on by
a constant force F for a time t.
maF
tΔmvΔ
F net
Momentum and Impulse
Newton’s 2nd Law
netFtΔvΔ
p
tΔvΔ
mF net
tΔpΔ
F net
Momentum and Impulse
Momentum and Collisions
A 12 kg hammer strikes a nail at a velocity of 8.5 m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail?
(b) What is the average force acting on the nail?
hamernail ppI
if mvmvI m/s 8.5 kg 120I m/skg 102
tp
Favg
s 0080.0
m/skg 102 N 750,12
Momentum and Collisions Problem
Momentum and Collisions
v
m
The area under the curve on a Force versus time (F vs. t) graph represents
A) impulse.
B) momentum.
C) work.
D) kinetic energy.
Momentum and Collisions 07-01
Momentum and Collisions
M m
FMFm
Fm = FM
Fmt = FMt
pm = pM
m(u2 u1) = M(v2 v1)
Conservation of
Momentum
v1 u1
M m
v = u
M m
v2 u2
mu2 m u1 = Mv2 Mv1
Mv1 + m u1 = Mv2 mu2
p(before) = p(after)
Conservation of Momentum
Collision between to moving objects
Momentum and Collisions
M m
v
before
after
mMMv
V
M m
V = ?
afterbefore PP
Mv VmM
VmMMv
Conservation of Momentum
Collision with a stationary block
Momentum and Collisions
A 9,300 kg boxcar traveling at 15.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s. What is the mass of the second car?
Momentum and Collisions 07-08
Momentum and Collisions
Mv
m
before after
V
mMmv
V
afterbefore PP
mv (M + m)V
VmMmv
Conservation of Momentum
Bullet fired into a block which is initially at rest.
Momentum and Collisions
A freight car moves along a frictionless level railroad track at constant speed. The car is open on top. A large load of coal is suddenly dumped into the car.What happens to the velocity of the car?
A) It increases.
B) It remains the same.
C) It decreases.
D) cannot be determined from the information given
Momentum and Collisions 07-01
Momentum and Collisions
Collisions
Elastic Collisions
Inelastic Collisions
Momentum and Kinetic Energy are both conserved
Only Momentum is conserved
Momentum and Collisions
m1 m2
v1
m1 m2
vf
before
after
An Inelastic Collision
v2
21
2211f mm
vmvmv
afterbefore pp
2211 vmvm f21 vmm
f212211 vmmvmvm
Collisions
Momentum and Collisions
In an inelastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy?
A) Kinetic energy is also conserved.
B) Kinetic energy is gained.
C) Kinetic energy is lost.
D) none of the above
Momentum and Collisions 07-01
Momentum and Collisions
Two objects collide and stick together. Kinetic energy
A) is definitely conserved.
B) is definitely not conserved.
C) is conserved only if the collision is elastic.
D) is conserved only if the environment is frictionless.
Momentum and Collisions 07-01
Momentum and Collisions
1 Eq vmm
m2v
mm
mmv 1B
BA
B1A
BA
BA2A
2 Eq vmm
mmv
mm
m2v 1B
BA
AB1A
BA
A2B
mBmA
vA1 vB1
mBmAvA2 vB2
Elastic Collision (General Equations)
Collisions
Momentum and Collisions
1BBA
B1A
BA
BA2A v
mm
m2v
mm
mmv
Elastic Collision (vB1 = 0) Ball B is initially at rest.
0 vmm
mmv 1A
BA
BA2A
mBmA
vA1
mBmAvA2 vB2
1BBA
AB1A
BA
A2B v
mm
mmv
mm
m2v
0 vmm
m2v 1A
BA
A2B
Collisions
Momentum and Collisions
mmvA1
mm
VB2
Elastic Collision (vB1 = 0 and mA= mB)
1ABA
BA2A v
mm
mmv
1ABA
A2B v
mm
m2v
0v 2A
1A2B vv
Collisions
Momentum and Collisions
In an elastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy?
A) Kinetic energy is also conserved.
B) Kinetic energy is gained.
C) Kinetic energy is lost.
D) none of the above
Momentum and Collisions 07-01
Momentum and Collisions
When is kinetic energy conserved?
A) in inelastic collisions
B) in any collision in which the objects do not stick together
C) in all collisions
D) in elastic collisions
Momentum and Collisions 07-01
Momentum and Collisions
When a light beach ball rolling with a speed of 6.0 m/s collides with a heavy exercise ball at rest, the beach ball's speed after the collision will be, approximately,
A) 0.
B) 3.0 m/s.
C) 6.0 m/s.
D) 12 m/s.
Momentum and Collisions 07-01
Momentum and Collisions
Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be their speeds after the collision?
Momentum and Collisions Problem
Momentum and Collisions
Ballistic Pendulum
m
vo M h
v
Cons. Momentum Cons. Energy
Collisions
Momentum and Collisions
Ballistic Pendulum
m
v M h
V
Cons. Momentum
VMmmv Mmmv
V
Find the speedof the bullet
afterbefore pp
Collisions
Momentum and Collisions
Ballistic Pendulum
M h
V
Cons. Energy
gh2 m
Mmv
Mm
mvV
0KU
2
Mmmv
21
gh
2
VMmgh Mm
2
Collisions
Momentum and Collisions
A 28 g rifle bullet traveling 230 m/s buries itself in a 3.6 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement.
Momentum and Collisions Problem
Momentum and Collisions
A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s how high will the block rise after the bullet becomes embedded in it?
Momentum and Collisions Problem
Momentum and Collisions
Two objects collide and bounce off each other.Linear momentum
A) is definitely conserved.
B) is definitely not conserved.
C) is conserved only if the collision is elastic.
D) is conserved only if the environment is frictionless.
Momentum and Collisions 07-01
Momentum and Collisions
A 100 kg football linebacker moving at 2.0 m/s tackles head-on an 80 kg halfback running 3.0 m/s. Neglecting the effects due to digging in of cleats,
A) the linebacker will drive the halfback backward.
B) the halfback will drive the linebacker backward.
C) neither player will drive the other backward.
D) this is a simple example of an elastic collision.
Momentum and Collisions 07-01
Momentum and Collisions
cm
xcm
x1
x2
x
y
m1
m2
21
2211cm mm
xmxmx
ii
iii
cm m
xm
x
Center of Mass (cm)
Momentum and Collisions
21
2211cm mm
xmxmx
Location of the cm of the Earth-Moon system
xcmmemm
me
mmcm mm
Rmx
kg10x 7.3kg10x 6.0
m10x 3.8kg10x 7.3x
2224
822
cm
m10x 4.6 6
Rm
x
Center of Mass (cm)
Momentum and Collisions
Find the center of mass of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass.
Momentum and Collisions Problem
0.5 m 0.25 m
1.0 kg 1.5 kg 1.1 kgx
y
Momentum and Collisions
Consider two unequal masses, M and m. Which of the following statements is false?
A) The center of mass lies on the line joining the centers of each mass.
B) The center of mass is closer to the larger mass.
C) It is possible for the center of mass to lie within one of the objects.
D) If a uniform rod of mass m were to join the two masses, this would not alter the position of the center of mass of the system without the rod present.
Momentum and Collisions 07-01
Momentum and Collisions
Two cars collide head-on on a level friction-free road. The collision was completely inelastic and both cars quickly came to rest during the collision. What is true about the velocity of this system's center of mass?
A) It was always zero.
B) It was never zero.
C) It was not zero, but ended up zero.
D) none of the above
Momentum and Collisions 07-01
Momentum and Collisions
mvp Momentum :
vΔmtΔF Impules:
Newton’s second law: tΔpΔ
F net
Total momentum of an isolated system of objects is conserved.
0pΔ
afterbefore pp
Momentum is conserved during collisions.
Chapter 7 Summary
Momentum and Collisions
In an elastic collision, total kinetic energy is also conserved
In a completely inelastic collision, the two objects stick together after the collision.
The center of mass of a system is the point at which external forces can be considered to act.
In an inelastic collision, some kinetic energy is lost.
Chapter 7 Summary
Momentum and Collisions
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