PHYSICS 231 Lecture 12: Keeping momentum

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PHYSICS 231Lecture 12 Keeping momentum

• Remco Zegers
• Walk-in hour Thursday 1130-1330 am
• Helproom

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The 3 most difficult exam problems

• The Football player (28 correct)
• Can out of the train (40 correct)
• x-t and v-t graph block-pulley (47 correct)

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The football player
A football player throws a ball with an initial
velocity of 40 m/s and an angle of 40o with
respect to the field. At what distance from the
player will the ball hit the field? Assume that
the players length is negligible (i.e. the ball
is thrown from a vertical height of 0.0 m).
40 m/s
40sin(40o)
40o
d
40cos(40o)
Vertical direction
Horizontal direction
Y(t)Y(0)vy(0)t½at2 0040sin(40o)t-½gt2 25.7t-½
gt20 (25.7-½gt)t0 so t0 (start) or
t25.7/(½g)5.2
X(t)x(0)vx(0)t½at2 d040cos(40o)t0 d31t
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Can out of the train
A train is moving with a speed of 25 km/h to the
east. An environment-unfriendly passenger throws
a can out of the window. The velocity with which
he throws the can relative to the moving train is
25 km/h toward the back of the train the (west)
and 10 km/h away from the train toward the south.
To an onlooker standing on the ground (south of
the track), what is the observed direction of
motion of the can?
N
Cancel!
W

Train (25 km/h)
E
velocity of can parallel of the train (-25 km/h)
velocity of the can perpendicular to the train
(to the south) (10 km/h)
S
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X-t and v-t graph
X
x
t
t
X
v
t
t
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Pulley
40 kg
A block of mass 40.0 kg sliding on a frictionless
table is attached to another block of mass 10.0
kg by a string over a massless pulley (see
figure). What is the acceleration of the bigger
mass?
40 kg
10kg
10 kg
Use Newtons second law for each object
separately!
40 kg
10 kg
-T10g10a -T98.110a -40a98.110a 98.150a so
a98.1/501.96 m/s2
T40a (only hor. direction)
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Tail of chapter 5
If relieved from rest, what is the velocity of
the ball at the lowest point?
30o
L5m
(PEKE)constant PEreleasemgh (h5-5cos(30o))
6.57m J KErelease0 PEbottom0 KEbotto
m½mv2 ½mv26.57m so v3.6 m/s
h
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A running person
While running, a person dissipates about 0.60 J
of mechanical energy per step per kg of body
mass. If a 60 kg person develops a power of 70
Watt during a race, how fast is she running (1
step1.5 m long) What is the force the person
exerts on the road? WF?x PW/?tFv
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Chapter 6 Momentum Collisions
When a bullet hits the wall, its velocity is very
much reduced. The wall does not move, although
the force on the ball is the same as the force on
the wall (Newtons 3rd law Fwall-bullet-Fbullet
-wall).
Fwall-bulletmbulletabullet Fbullet-wallmwallawal
l
Mbullet ltlt Mwall
abulletgtgt awall
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Is it only the mass???
Vbullet100 m/s
Vbullet200 m/s
When the bullet gets stopped in the wall, it
deaccelerates from its initial velocity to 0. So,
its acceleration is vbullet/?t, with ?t some
small time (independent of v).
Second law Fwall-bulletmbulletabulletmbulletvbu
llet/?t The force also depends on the velocity of
the bullet!
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More generaland formal.
Fma Newtons 2nd law Fm?v/?t
a?v/?t Fm(vfinal-vinital)/?t Define pmv p
momentum (kgm/s) F(pfinal-pinitial)/?t F?p/?t
The net force acting on an object equals the
change in momentum (?p) in a certain time period
(?t). Since velocity is a vector, momentum is
also a vector, pointing in the same direction as
v.
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Impulse
F?p/?t Forcechange in (mv) per time period
(?t). ?pF?t The change in momentum equals the
force acting on the object times how long you
apply the force. Definition ?pImpulse
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Some examples
A tennis player receives a shot approaching him
(horizontally) with 50m/s and returns the ball in
the opposite direction with 40m/s. The mass of
the ball is 0.060 kg. A) What is the impulse
delivered by the ball to the racket? B) What is
the work done by the racket on the ball?
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Child safety
A friend claims that it is safe to go on a car
trip with your child without a child seat since
he can hold onto your 12kg child even if the car
makes a frontal collision (lasting 0.05s and
causing the vehicle to stop completely) at v50
km/h (about 30 miles/h). Is he to be trusted?