Transcript Physics 131: Lecture 14 Notes
Physics 151: Lecture 17 Today’s Agenda
Today’s Topics : Momentum (Chapter 9) Conservation of Momentum Introduce Collisions (Elastic and Inelastic) Physics 151: Lecture 17, Pg 1
ACT- 2
Objects A and B , of mass M a distance d and 2M respectively, are each pushed straight up an inclined plane by a force F parallel to the plane. The coefficient of kinetic friction between each mass and the plane has the same value . At the highest point , 1.
2.
3.
4.
5.
K A > K B .
K A = K B .
K A < K B .
The work done by F on A is greater than the work done on B.
The work done by F on A is less than the work done on B.
Physics 151: Lecture 17, Pg 2
Lecture 16,
Example
Skateboard
. .
Let’s suppose that the surface is not frictionless and the same skateboarder reach the speed of skateboarder ? 7.0 m/s at bottom of the hill. What was the work done by friction on the m = 25 kg Conservation of Total Energy : W f W f + K 1 + U 1 = K 2 + 0 + mgR = 1/2mv + U 2 2 + 0 W f = 1/2mv 2 - mgR
R=3 m
W f = (1/2 x25 kg x (7.0 m/s 2 ) 2 - 25 kg x 10m/s 2 3 m) -
. .
W f = 613 - 735 J = - 122 J Total mechanical energy decreased by 122 J !
Physics 151: Lecture 17, Pg 3
Chapter 9 Linear Momentum
Definition:
For a single particle, the momentum defined as:
p = mv
(
p
vector).
p
is is a vector since
v
is a So
p x = mv x
etc.
Newton’s 2nd Law:
F = ma
m dv dt
d dt ( m
v
)
Units of linear momentum are
kg m/s
.
F
d
p
dt
Physics 151: Lecture 17, Pg 4
F
EXT
d
P
dt
Momentum Conservation
d
P
0 dt
F
EXT
0
The concept of momentum conservation is one of the most fundamental principles in physics.
This is a component (vector) equation.
We can apply it to any direction in which there is no external force applied.
You will see that we often have momentum conservation even when (mechanical) energy is not conserved.
Physics 151: Lecture 17, Pg 5
Elastic vs. Inelastic Collisions
A collision is said to be momentum is conserved before and after the collision.
K before
= K after elastic
when energy as well as Carts colliding with a spring in between, billiard balls, etc.
v
i
A collision is said to be before and after the collision, but momentum is conserved.
K before
K after inelastic
when energy is not conserved Car crashes, collisions where objects stick together, etc.
Physics 151: Lecture 17, Pg 6
Lecture 17, ACT 1
Collision in 1-D
Winter in Storrs
ice (no friction) Physics 151: Lecture 17, Pg 7
V 0
M = 2m
Lecture 17, ACT 1
Collision in 1-D
m
initially
v = 0
ice (no friction)
finally
vf = ?
V f = A) 0 B) V o /2 C) 2V o /3 D) 3V o /2 E) 2V o Physics 151: Lecture 17, Pg 8
Lecture 17,
Review problem: numerical
High-speed stroboscopic photographs show that the head of a golf club of mass 200 grams is traveling at 55 m/s just before it strikes a the collision, the clubhead travels (in the same direction) at 40 m/s 46-gram golf ball at rest on a tee. After . Find the speed of the golf ball just after Physics 151: Lecture 17, Pg 9
Inelastic collision in 1-D: Example 1
A block of mass
M
is initially at rest on a frictionless horizontal surface. A bullet of mass
m
is fired at the block with a muzzle velocity (speed) speed
V.
In terms of
m, M
, and
V
:
v
. The bullet lodges in the block, and the block ends up with a What is the initial speed of the bullet
v
?
What is the initial energy of the system ?
What is the final energy of the system ?
Is energy conserved ?
x v V
before See example 12-6 after Physics 151: Lecture 17, Pg 10
Lecture 19,
ACT 2 Let’s do some rocket engineering !
A rocket engine consumes 450 kg of fuel per minute . If the exhaust speed of the ejected fuel is 5.2 km/s , what is the thrust of the rocket ?
» a. 48 kN » b. 39 kN » c. 55 kN » d. 32 kN initial v g final m M+m M v v+ D v Physics 151: Lecture 17, Pg 11
Lecture 17,
ACT 3
Momentum Conservation
Two balls of equal mass are thrown horizontally with the same initial velocity. They hit identical stationary boxes resting on a frictionless horizontal surface. The ball hitting box 1 bounces back, while the ball hitting box 2 gets stuck.
Which box ends up moving fastest ?
(a)
Box 1
(b)
Box 2
(c)
same
1 2 Physics 151: Lecture 17, Pg 12
Lecture 17
Review problem: more involved
A 3.0-kg 0.40 m mass is sliding on a horizontal frictionless surface with a speed of 3.0 m/s when it collides with a initially at rest as shown in the figure. The masses stick together and slide up a frictionless circular track of radius . To what maximum height, h, above the horizontal surface will the masses slide?
1.0-kg mass Physics 151: Lecture 17, Pg 13
Lecture 17
Ballistic Pendulum
Physics 151: Lecture 17, Pg 14
Lecture 17
ACT 4
The law of conservation of momentum applies to a collision between two bodies if: a. they exert forces on each other respectively proportional to their masses.
b. they exert forces on each other respectively proportional to their velocities.
d. their accelerations are proportional to their masses.
e. they exert equal and opposite forces on each other.
Physics 151: Lecture 17, Pg 15
Inelastic collision in 2-D
Consider a collision in 2-D (cars crashing at a slippery intersection...no friction).
v
1
V
m 1 + m 2 m 1 m 2
before
v
2
after Physics 151: Lecture 17, Pg 16
Inelastic collision in 2-D...
There are no net external forces acting.
Use momentum conservation for both components.
P x , a
P x , b
m 1
x V x
m 1 m
1 m 2
v 1 P y , a
P y , b 2
m 1
y V y
m 1 m
2 m 2
v 2
v
1 m 1 m 2
v
2
V
=
(
V x ,V y
)
m 1 + m 2
Physics 151: Lecture 17, Pg 17
Inelastic collision in 2-D...
So we know all about the motion after the collision !
V
=
(
V x ,V y
)
V x V y V x
m 1 m
1 m 2
v 1 V y
m 1 m
2 m 2
v 2
p
1
P p
2
P
p
1
p
2 tan
V V x y
m 2 v 2 m 1 v 1
p 2 p 1
Physics 151: Lecture 17, Pg 18
Comment on Energy Conservation
We have seen that the total kinetic energy of a system undergoing an inelastic collision is not conserved.
Energy is lost: » Heat » Bending of metal (crashing cars) Kinetic energy
is not
the collision !
conserved since
work
is done during Momentum along a certain direction
is
there are no external forces conserved when acting in this direction.
In general, easier to satisfy than energy conservation.
Physics 151: Lecture 17, Pg 19
Recap of today’s lecture
Momentum and Collisions Ch. 9.1-9.4 (part of 9.4) Physics 151: Lecture 17, Pg 20