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 1024kg; 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, 157.3o )

Draw a quick diagram showing the above three vectors and the resultant:

 

v vs t diagram for problem 22) To the right is a graph of v(t). On the graphs below it, sketch x(t) and a(t) assuming that xo < 0.

 

 

 

 

 

x vs t diagram for problem 2 

 

 

 

 

 

a vs t diagram for problem 2 

 

 

 

 

 

 

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 50o 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 108 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 50o 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 in2 = 0.129 m2). 

  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:  1.19 x 106 Nt/m2 ;   in lb/in2 : 174 lb/in2 ;  in atmospheres:  11.8  atmospheres .

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/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 house?

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 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/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 0.37 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.

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