PHYS 201 FINAL EXAM 12/12/16
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 10^{24}kg; RADIUS OF EARTH = 6378 km.

1) Add the following three
vectors and express your answer in POLAR form:

A = (32 m, 35°)

B = (43 m, 155°)

C = (34m, 215°)

** (44.03 m, 157.3 ^{o} )**

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 x_{o }<_{
}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/s ^{2}.**

** **

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 75^{o} with the ceiling and the right rope making an
angle of 50^{o} with the ceiling.
The weight is 300 Nt.

a)
Is the magnitude of the tension 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 rope: [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?

**335.4 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 1,222 km (760 miles) so the
radius of orbit = 7,600 km).

a) What will the period of orbit
of this satellite be?

**6,581 sec = 109 minutes
and 41 seconds. **

b) What speed should this satellite
have to maintain this circular orbit?

**7,257 m/s .**

c) What is the force of
gravity on the satellite when it is orbiting at this radius?

**485 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 122 meters?

**83,692 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 244 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 1,222 kilometers?

**7.06 x 10 ^{8}
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 2,444
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 60 cm that makes an angle of
50^{o} 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?

**3.43
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?

**2.90 m/s.**

d) Since there now is friction (to make the ball
roll), is there any energy lost to this friction?

**No.**

10)
A submersible vehicle dives to a depth of 400 feet (122 meters) in the
ocean. It has a viewing port of diameter
8 inches (area = 200 in^{2} = 0.129 m^{2}).

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/m^{2}: **1.19 x
10 ^{6} Nt/m^{2}** ; in lb/in

b)
What is the net force on the viewing plate due to the water pressure:

in Nt: ** 154,280 Nt**
. in lb: **34,800
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/m^{2} ?

**1,595 Nt/m ^{2}**

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 m^{3}/sec: **2.45
x 10 ^{-7} m^{3}/sec; **

in cc/sec: **.245 cc/sec.**

** **

12) Assume a house has 1,500 ft^{2} 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 house?

In
ft^{3}? **12,000 ft ^{3}; **in m

Now assume the temperature in
the room is set to be 68^{o}F.

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 41^{o}F to 68^{o}F ?

**6.15 x 10 ^{6} J =
1.71 kW*hr.**

d) At $.095/kW*hr,
what would this amount of 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/m^{2}:** 1.59 x 10 ^{-7}
Watts/m^{2}; **in dB:

If
the source is 400 meters away, what will be the intensity:

b)
in Watts/m^{2}** **:** 9.95
x 10 ^{-13} Watts/m^{2}; **in
dB:

14) A certain piano string has a length of 0.37
meters and a mass density of 0.60 grams/meter.
A tension of 50 Nt. is applied to it.

a) What will be the speed of
the wave on the string?

**289 m/s.**

b) What will be the
fundamental frequency when it is plucked?

**390 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?

**63.6 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 a second car going North at 30 m/s approaching
the front of the train and the train still going 15 m/s South, what will the
person in the second car measure for the frequency of the horn? (Again assume no wind.)

** 5,692 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 approaching car measure for the horn?

**5,668
Hz.**