Transcript 1 PHYSICS 231 Lecture 12: Keeping momentum

PHYSICS 231
Lecture 12: Keeping momentum
Remco Zegers
Walk-in hour: Thursday 11:30-13:30 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 player’s
length is negligible (i.e. the ball is thrown from a vertical height of
0.0 m).
40 m/s
40o
40sin(40o)
40cos(40o)
Horizontal direction
(0)t+½at2
X(t)=x(0)+vx
d=0+40cos(40o)t+0
d=31t
d=31*5.2=161.2 m
d
Vertical direction
Y(t)=Y(0)+vy(0)t+½at2
0=0+40sin(40o)t-½gt2
25.7t-½gt2=0
(25.7-½gt)t=0 so
t=0 (start) or t=25.7/(½g)=5.2
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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?
Cancel!
velocity of
can parallel of
the train
(-25 km/h)
N
Train (25 km/h)
W
E
velocity of the can
S
perpendicular to
the train (to the south) (10
km/h)
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X-t and v-t graph
Xx
tt
Xv
tt
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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
10kg
10 kg
mass 10.0 kg by a string over a
massless pulley (see figure).
What is the acceleration of the
bigger mass?
Use Newton’s second law for each object separately!
40 kg
10 kg
T=40a (only hor. direction) -T+10g=10a
-T+98.1=10a
-40a+98.1=10a
98.1=50a so a=98.1/50=1.96 m/s2
40 kg
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Tail of chapter 5
30o
h
L=5m
If relieved from rest, what is
the velocity of the ball at the
lowest point?
(PE+KE)=constant
PErelease=mgh (h=5-5cos(30o))
=6.57m J
KErelease=0
PEbottom=0
KEbottom=½mv2
½mv2=6.57m so v=3.6 m/s
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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 step=1.5 m long)
What is the force the person exerts on the
road?
W=Fx
P=W/t=Fv
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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
(Newton’s 3rd law: Fwall-bullet=-Fbullet-wall).
Fwall-bullet=mbulletabullet
Fbullet-wall=mwallawall
Mbullet << Mwall
|abullet|>> awall
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Is it only the mass???
Vbullet=100 m/s
Vbullet=200 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-bullet=mbulletabullet=mbulletvbullet/t
The force also depends on the velocity of the bullet!
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More general…and formal.
F=ma
Newton’s 2nd law
F=mv/t
a=v/t
F=m(vfinal-vinital)/t
Define p=mv
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
p=Ft
Definition:
F2
F1
Force=change in (mv) per time
period (t).
The change in momentum equals
the force acting on the object times
how long you apply the force.
p=Impulse
What if the force is not constant within the time
period t?
p=Ft=(F1s+F2s+F3s)=
= t(F1s+F2s+F3s)/t
= tFaverage
F3
s s s
t
p=Faverage t
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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 v=50 km/h
(about 30 miles/h). Is he to be trusted?
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