PHYS 201 FINAL EXAM 12/12/07 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 = (15 m, 68°)

B = (12 m, 159°)

C = (9 m, 307°)

(11.02 m, 90.9^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) A jet on an aircraft carrier accelerates from rest up to a speed of 88 m/s (67 mph) in a time of 2.2 seconds.

a) What is the average acceleration of the jet during the 2.2 seconds?

40 m/s²

b) How far does the jet go during the 2.2 seconds assuming its acceleration is constant?

96.8 m

4) A ball of mass 0.25 kg is thrown from the top of a building 15 meters above the ground with an initial speed of 25 m/s at an angle of 69° 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?

47.81 m

b) How long a time is the ball in the air?

5.34 sec.

5) Consider a weight hung from a combination of a rod attached to the left side wall and a rope attached to a ceiling at a point that is left of where the rod and rope meet. The angle the rope makes with the ceiling is 70^o. The angle the rod makes with the wall is 53^o, and the rod is free to rotate up and down. The weight is 200 Nt.

a) Does the rod push up and to the right, or down and to the left?

Up and to the right

b) What is the magnitude of the tension in the rod?

71.53 Nt.

c) What is the tension in the rope?

167.03 Nt.

6) A 25 kg satellite is to be put into orbit around Mars (radius of Mars = 3,400 km; mass of Mars = 6.4 x 10²³ kg ) at a height of 1,000 km above Mars' surface (or radius of 3,400 km + 1,000 km = 4,400 km).

a) What will the speed of the satellite have to be to maintain this orbit?

3,115 m/s.

b) How long will it take the satellite to orbit once around Mars (that is, what is its period)?

8,876 sec = 2 hours, 27 minutes and 56 seconds.

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

55.1 Nt.

d) What is the weight of the satellite on the EARTH's surface?

245 Nt. 

7) Consider a jet of mass 30,000 kg. It can accelerate from zero to 88 m/sec in 2.2 seconds.

a) What is the final kinetic energy of the jet?

1.16 x 10⁸ Joules

b) Assuming the catapult on the aircraft carrier was the source of this final kinetic energy, what is the average power of the catapult (neglecting that needed to overcome friction and air resistance) during the acceleration

in Watts? 5.28 x 10⁷ Watts

in horsepower? 70,777 hp.

c) If the catapult provided constant POWER, did the force of the catapult on the jet: [increase with increasing speed, stay constant with increasing speed, or decrease with increasing speed] ?

decrease with increasing speed.

8) Object #1 (mass₁ = 35 g) moving North with a speed of 188 m/s crashes into object #2 (mass₂ = 7,500 g) moving South with a speed of 2.5 m/s.

a) If the two objects stick together, what will their speed be immedicately after the crash?

-1.62 m/s.

b) Will the balls be moving North or South?

South.

9) a) A ring of mass 400 grams and radius 7 cm slides on its side down a slick incline (neglect friction) of height 90 cm that makes an angle of 25^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?

4.2 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 ring of part a above now rolls (without slipping) down the incline. If the object started from rest, and if neglect air resistance, how fast will the ring be going at the base of the incline?

2.97 m/s.

10) a) If you apply a force of 7 lbs on a cylinder of area 0.18 in², what is the gauge pressure on the fluid behind the cylinder?

in lb/in² : 38.89 lb/in² ; in Nt/m²: 2.68 x 10⁵ Nt/m²

b) If the fluid under the above pressure pushes on another cylinder of area 12 in², what will be the force on this cylinder?

in lbs: 466.67 lbs; in Nt: 2079 Nt.

11) A small artery of inside DIAMETER 1.0 mm and length 2 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) expressed

in m³/sec: 4.89 x 10^-7 m³/sec;

in cc/sec: .489 cc/sec.

12) A house with a width of 30 ft and a length of 50 ft (for a total square footage of living space of 1500 ft²) with 8 ft ceilings, ahs thermal insulation due to brick and fiberglassd with a total value of R = 14 ft²*^oF*hr/BTU.

a) If the average inside temperature is 72^oF and the average outside temeprature is 48^oF, what is the average heat loss per time (in Watts) due to conduction through the four outside walls?

692 Watts.

b) If the cost of energy is $.07 / kW*hr, what will the cost be for a month to replace the energy lost by conduction?

$32.36 .

13) A source of sound (assume it is a point source) emits a power of 45 microWatts (sound, not electrical). What is the intensity at a distance of 1 meter from the source

a) in Watts/m²: 3.58 x 10^-6 Watts/m²; in dB: 65.5 dB

If the source is 8 meters away, what will be the intensity:

b) in Watts/m² : 5.60 x 10^-8 Watts/m²; in dB: 47.5 dB

14) A certain piano string has a length of 0.90 meters and a mass density of 0.42 grams/meter. A tension of 33 Nt. is applied to it.

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

280.3 m/s.

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

155.7 Hz.

c) If a fundamental frequency of 280 cycles/sec is desired, what should the tension in the string be?

106.7 Nt.

d) If a different string of the same length but a smaller mass density is used, and if the original tension of 33 Nt is applied, will the fundamental frequency for this string be higher, the same, or lower than for the string in part (b)?

Higher.

15) For this problem, assume the speed of sound in the air around the train and car is 345 m/s. Answers to all parts must be at least to the nearest Hz. Do not round your answers more than that. A train moving West at a speed of 25 m/s approaches a person in a stopped car.

a) If the train emits a sound of frequency 3,000 Hz. what will the car observer measure for the frequency as the car approaches the train? (Assume no wind.)

3,234.4 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.)

2,797.3 Hz.

c) A second car going 33 m/s West approaches the rear of the train (which is still going West). If the train again blows its horn (3,000 Hz with respect to the train), what will the person in the second car measure for the frequency of the horn? (Again assume no wind.)

3,064.9 Hz.

d) If there is a West wind (blowing from the West towards the East) with a speed of 11 m/s for part c, what will the frequency the car observer measure for the horn?

3,063 Hz.

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