PHYS 201 FINAL
EXAM 12/12/11 Dr. Holmes NAME
DO ALL 15 PROBLEMS. THE WORTH OF EACH PART
OF EACH PROBLEM IS MARKED NEXT TO THE SLOT FOR THE ANSWER. SHOW YOUR WORK FOR
PARTIAL CREDIT.
INFORMATION: MASS OF EARTH = 6.0 x 1024kg;
RADIUS OF EARTH = 6378 km.
1) Add the following three vectors and
express your answer in POLAR form:
A = (22 m, 35°)
B = (33 m, 155°)
C = (24m, 215°)
(34.04 m, 157.9o )
Draw a quick diagram showing the above three
vectors and the resultant:
2) To the right is a graph of v(t). On the graphs
below it, sketch x(t) and a(t) assuming that xo < 0.
3) An airplane takes off from an aircraft
carrier. Assume the airplane undergoes
constant acceleration during the take-off.
The distance for take-off (length of deck) is 90 meters. The initial velocity of the aircraft is zero,
and the final lift-off speed (after going 90 meters ) is 80 m/s.
a) How long a time did it take to launch the
aircraft?
2.25 sec.
b) What was the average acceleration during
the launch?
35.56 m/s2.
4)
A ball of mass 0.45 kg is thrown from the top of a building 15
meters above the ground with an initial speed of 39 m/s at an angle
of 57° above the horizontal. The object
then hits the ground (assume a level surface and assume no air resistance).
a) How far away from the thrower does the
object land?
150.9 m
b) How long a time is the ball in the air?
7.1 sec.
5) Consider a
weight hung from the ceiling with two ropes with the left rope making an angle
of 75o with the ceiling and the right rope making an angle of 40o
with the ceiling. The weight is 300 Nt.
a) Is the
magnitude of the tenion in the left rope plus the magnitude of the tension in
the right rope: [the same as, more than, or less than] the weight?
More than
b) Is the magnitude of the tension in the left roope:
[less than, the same as, or more than] the magnitude of the tension in the
right rope?
More than
c) What is the magnitude of the tension in the left
rope?
253.6 Nt.
6) A 70 kg satellite is to be put into a circular
orbit around the earth (info on earth is at the top of the first page) at a
height above the earth’s surface of 1,122 km (857 miles) so the radius of orbit
= 7,500 km).
a) What will the period of orbit of this
satellite be?
6,451 sec = 107 minutes and 31 seconds.
b) What speed should this satellite have to maintain
this circular orbit?
7,305 m/s = 16,363 mph.
c) What is the force of gravity on the
satellite when it is orbiting at this radius?
498 Nt.
d) What is the
force of gravity on the satellite on the earth's surface?
686 Nt.
7) Consider a 70 kg object.
a)
How much energy will it take to lift the object from the earth’s surface
up to a height of 85 meters?
58,310 Joules.
b) Will it take {significantly less than
twice, about twice, or significantly more than twice} the energy to lift the
object to twice the height (from the surface up to 170 meters)? [Here,
“about” means a difference of less than 10%; significantly more means a
difference of more than 10%.]
About twice.
c)
How much energy will it take to lift the object from the earth’s surface
up to a height of 8,500 kilometers?
2.51 x 109 Joules.
d) Will it take {significantly less
than twice, about twice, or significantly more than twice} the energy to lift
the object to twice the height (from the surface up to 17,000 kilometers
Significantly less than twice.
8)
Object #1 with a mass of 1,800 kg moving East with a speed of 27 m/s
crashes into object #2 with a mass of 2,400 kg also moving East with a speed of
9 m/s.
a) If
the two objects stick together, what will their speed be immediately after the
crash?
16.7 m/s.
b) Will the objects be moving East or West?
East.
c) Was momentum conserved in the crash? If the answer is no, then tell where the
momentum went to or came from.
Yes.
d)
Was the kinetic energy (total for both objects) the same before and
after the crash? If the answer is no,
then tell where it went to or came from.
No,
some of the kinetic energy went into deforming the objects so that they would
stick together.
9) a) A ball (solid sphere) of mass 1,420 grams
and radius 5 cm slides on its side
down a slick incline (neglect friction) of height 80 cm that makes an angle of
70o with the horizontal. If
the object started from rest, and if we neglect air resistance and friction,
how fast will the object be going at the base of the incline?
3.96 m/s.
b) If the object had an initial speed of 2 m/s
at the top of the inline, would the speed at the base of the incline after it
slid without friction be: [less than 2 m/s more, 2 m/s more, more than 2 m/s
more] than the answer to part a?
Less than.
c)
The ball of part a above now rolls
(without slipping) down the incline. If
the object started from rest, and if we neglect air resistance, how fast will
the object be going at the base of the incline?
3.35 m/s.
d)
Since there now is friction (to make the cylinder roll), is there any
energy lost to this friction?
No.
10) A
submersible vehicle dives to a depth of 450 feet (137 meters) in the
ocean. It has a viewing port of diameter
8 inches (area = 200 in2).
a) Assuming that inside the submersible the
pressure is regular atmospheric, what is the gauge pressure on the viewing port
at that depth:
in
Nt/m2: 1.34 x 106 Nt/m2 ; in lb/in2 : 195.4 lb/in2
; in atmospheres: 13.3 atmospheres .
b) What is the
net force on the viewing plate due to the water pressure:
in Nt: 174,090 Nt . in lb:
39,080 lb.
11) A small artery of inside DIAMETER 1.0 mm
and length 4 cm carries blood. Assume the beginning and ending of the artery
are at the same height.
a) If the pressure drop from the front to
the back of the artery is 12 mm of Hg, what is the pressure drop expressed in
Nt/m2 ?
1,595 Nt/m2
b) Assuming there is the above pressure
drop, and given that the viscosity of the blood is 4 x 10-3 Pl
(about four times that of water), what is the volume flow of blood per time
through the artery? (Assume laminar flow.)
in m3/sec: 2.45 x 10-7
m3/sec;
in cc/sec: .245 cc/sec.
12)
Assume a house has 1,500 ft2 of floor space (50 ft x 30 ft)
all of it with 8 ft ceilings.
a)
What is the volume of air space in this hourse?
In ft3? 12,000 ft3; in m3: 340 m3.
Now assume the temperature in the room is
set to be 68oF.
b) calculate the number of moles of air in
this house:
14,120
.
c) Given that the molar heat capacity of air (at
constant pressure) is (7/2)*R, how much energy would it take to heat up the air
in this house from 41oF to 68oF ?
6.15 x 106 J = 1.71 kW*hr.
d) At $.095/kW*hr, what would this amoun tof
energy cost?
$0.16
13) A source of sound (assume it is a point
source) emits a power of 2 microWatts (sound, not electrical). What is the intensity at a distance of 1
meter from the source
a) in Watts/m2: 1.59 x 10-7 Watts/m2; in dB:
52.0 dB
If the source
is 400 meters away, what will be the intensity:
b) in Watts/m2
: 9.95 x 10-13 Watts/m2; in dB:
0 dB
14) A
certain piano string has a length of 0.33 meters and a mass density of 0.55
grams/meter. A tension of 50 Nt. is
applied to it.
a) What will be the speed of the wave on the
string?
301 m/s.
b) What will be the fundamental frequency
when it is plucked?
457 Hz.
c) If a fundamental frequency of 440
cycles/sec (note A above middle C) is desired, what should the tension in the
string be?
46.4 Nt.
15) For this problem, assume the speed of sound in the air
around the train and car is 340 m/s. The
frequency of the train horn is 5,000 Hz when the train is stationary and the
observer is also stationary. Answers to
all parts must be at least to the nearest 1 Hz.
Do not round your answers more than that.
a) If the train is moving South at a speed of 15
m/s and it approaches a person in a stopped car, what will the car observer measure for the
frequency? (Assume no wind.)
5,231 Hz.
b) After the
train passes the car and starts heading away, what will the car observer
measure for the frequency? (Again assume no wind.)
4,789 Hz.
c) If the car now starts going South at 30 m/s
approaching the rear of the train and the train still going 15 m/s South, what
will the person in the car now measure for the frequency of the horn? (Again assume no wind.)
5,211 Hz.
d) If there is a North wind (blowing from the
North towards the South) with a speed of 12 m/s, what will the frequency the
person in the car measure for the horn?
5,219 Hz.