PHYS 201 FINAL EXAM 12/14/09 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 = (41 m, 38°)

B = (21 m, 248°)

C = (51m, 328°)

(70.95 m, -17.4^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 ball is dropped (released from rest) from the top of a building. It takes 3.5 seconds for the ball to hit the ground. Neglect air resistance.

a) How high is the building (above the ground)?

60.0 m

b) How fast will the ball be going when it reaches the ground?

34.3 m/sec

4) A ball of mass 0.52 kg is thrown from the top of a building 14 meters above the ground with an initial speed of 42 m/s at an angle of 63° 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?

152.4 m

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

7.99 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 55^o. The angle the rod makes with the wall is 50^o, and the rod is free to rotate up and down. The weight is 120 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?

69.09 Nt.

c) What is the tension in the rope?

92.28 Nt.

6) A 120 kg satellite is to be put into orbit around the earth at a height above the earth of 23,620 km (14,680 miles) so the radius of orbit = 30,000 km).

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

51,609 sec = 14 hours, 20 minutes and 8 seconds.

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

3,652 m/s.

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

53.4 Nt.

d) What is the force of gravity on the satellite on the earth's surface?

1,176 Nt. 

7) Consider a 13 kg object.

a) How much energy will it take to lift the object from the earth’s surface up to a height of 25 meters?

3,185 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 50 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 5,000 kilometers?

3.58 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 10,000 kilometers

Significantly less than twice.

8) An astronaut with a mass of 55 kg and wearing a belt of tools that have a combined mass of 5 kg (so initial total mass = 60 kg) is floating beside a space station 13 meters away. The safety line has been cut by someone closing a door and catching the line in the door.

a) Can the astronaut “swim” back to the station?

No.

b) Explain your answer to part a above:

Assume the astronaut and tools are initially stationary. To get back to the space station, the astronaut throws a wrench of mass 0.35 kg away from the space station with a velocity of 23 m/s.

c) What will the final velocity of the astronaut be after the throw?

0.135 m/s.

d) How long a time will it take the astronaut to float back to the station after the astronaut throws the wrench?

96.3 seconds.

9) a) A ring of mass 320 grams and radius 6 cm slides on its side down a slick incline (neglect friction) of height 70 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?

3.70 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 we neglect air resistance, how fast will the ring be going at the base of the incline?

2.62 m/s.

10) a) What is the gauge pressure at a depth of 150 feet (46 meters) under water:

in Nt/m²: 4.51 x 10⁵ Nt/m² ; in lb/in² : 65.6 lb/in² ; in atmospheres: 4.46 atmospheres .

b) If a planet had oceans of liquid methane (density of 0.422 gm/cm³) instead of liquid water, and if the acceleration due to gravity on that planet were 4.9 m/s², what would the gauge pressure at the same depth (46 meters) be?

95,119 Nt/m² .

11) A small artery of inside DIAMETER 1.2 mm and length 5 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 20 mm of Hg, what is the pressure drop expressed in Nt/m² ?

2,658 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: 6.76 x 10^-7 m³/sec;

in cc/sec: .676 cc/sec.

12) A house with 2,400 ft² of floor (and ceiling) space has thermal insulation due to sheetrock and fiberglass with a total value of R = 22 ft²*^oF*hr/BTU. Assume the average inside temperature is 72^oF and the average outside temperature is 18^oF. Ignore other sources of heat loss such as through the walls, through the floor, via convection and radiation.

a) What is the average heat loss per time (in Watts) due to conduction through the ceiling?

1,728 Watts.

b) If the cost of energy is $.09 / kW*hr, what will the cost be for a month to replace the energy lost by conduction?

$111.96 .

13) A source of sound (assume it is a point source) emits a power of 7 microWatts (sound, not electrical). What is the intensity at a distance of 1 meter from the source

a) in Watts/m²: 5.57 x 10^-7 Watts/m²; in dB: 57.5 dB

If the source is 50 meters away, what will be the intensity:

b) in Watts/m² : 2.23 x 10^-10 Watts/m²; in dB: 23.5 dB

14) A certain piano string has a length of 0.55 meters and a mass density of 0.38 grams/meter. A tension of 21 Nt. is applied to it.

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

235 m/s.

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

213.7 Hz.

c) If a fundamental frequency of 350 cycles/sec is desired, what should the tension in the string be?

56.3 Nt.

15) For this problem, assume the speed of sound in the air around the train and car is 340 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 East at a speed of 18 m/s approaches a person in a stopped car.

a) If the train emits a sound of frequency 4,000 Hz. what will the car observer measure for the frequency as the car approaches the train? (Assume no wind.)

4,223.6 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.)

3,798.9 Hz.

c) The car now starts approaching the rear of the train with the car going 30 m/s East and the train still going 18 m/s East. If the train again blows its horn (4,000 Hz with respect to the train), what will the person in the car now measure for the frequency of the horn? (Again assume no wind.)

4,134.1 Hz.

d) If there is an East wind (blowing from the East towards the West) with a speed of 12 m/s for part c, what will the frequency the car observer measure for the horn?

4,129.7 Hz.

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