Tuesday, 5 January 2016

WAVES AND STRING

1.Two waves travel on the same string. Is it possible for them to have (a) different frequencies; (b) different wavelengths; (c) different speeds; (d) different amplitudes; (e) the same frequency but different wavelengths? Explain your reasoning.
2. Under a tension F, it takes 2.00 s for a pulse to travel the length of a taut wire. What tension is required (in terms of F) forthe pulse to take 6.00 s instead?
3. What kinds of energy are associated with waves on a stretched string? How could you detect such energy experimentally?
4. The amplitude of a wave decreases gradually as the wave travels down a long, stretched string. What happens to    the energyof the wave when this happens?
5. For the wave motions discussed in this chapter, does the speed of propagation depend on the amplitude? What makes you say this?
6. The speed of ocean waves depends on the depth of the water; the deeper the water, the faster the wave travels.  Use this toexplain why ocean waves crest and “break” as they near the shore
7. Is it possible to have a longitudinal wave on a stretched string? Why or why not? Is it possible to have a transverse   Wave on a steel rod? Again, why or why not? If your answer is yes in either case, explain how you would create  such a wave.
8. An echo is sound reflected from a distant object, such as a wall or a cliff. Explain how you can determine how far away theobject is by timing the echo.
9. Why do you see lightning before you hear the thunder? A familiar rule of thumb is to start counting slowly, once per second,when you see the lightning; when you hear the thunder, divide the number you have reached by 3 to obtain your distance from the lightning in kilometers (or divide by 5 to obtain your distance inmiles). Why does this work, or does it?
10. For transverse waves on a string, is the wave speed the same as the speed of any part of the string? Explain the difference between these two speeds. Which one is constant?
11. Children make toy telephones by sticking each end of a long string through a hole in the bottom of a paper cup and knotting it so it will not pull out. When the spring is pulled taut, sound can be transmitted from one cup to the other. How does this work? Why is the transmitted sound louder than the sound traveling through air for the same distance?
12. The four strings on a violin have different thicknesses, but are all under approximately the same tension. Do waves travel faster on the thick strings or the thin strings? Why? How does the fundamental vibration frequency compare for the thick versus the thin strings?
13. A sinusoidal wave can be described by a cosine function, which is negative just as often as positive. So why isn’t the averagepower delivered by this wave zero?


Monday, 4 January 2016

velocity , acceleration Problems

1. After an airplane takes off, it travels 10.4 km west, 8.7 km north, and 2.1 km up. How far
   is it from the takeoff point?

2. Two ropes in a vertical plane exert equal-magnitude forces on a hanging weight but pull with an angle of  86.0° between them. What pull does each one exert if their resultant pull is 372 N directly upward?

3. You are hungry and decide to go to your favorite neighborhood fast-food restaurant. You leave your apartment and take the elevator 10 flights down (each flight is 3.0 m) and then go 15 m south to the apartment exit. You then proceed 0.2 km east, turn north, and go 0.1 km to the entrance of the restaurant. (a) Determine the displacement from your apartment to the restaurant. Useunit vector notation for your answer, being sure to make clear yourchoice of coordinates. (b) How far did you travel along the path you took from your apartment to the restaurant, and what is the magnitude of the displacement you calculated in part (a)?

4. While following a treasure map, you start at an old oak tree. You first walk 825 m directly south, then turn and walk 1.25 km at 30.0° west of north, and finally walk 1.00 km at 40.0° north of east, where you find the treasure: a biography of Isaac Newton! (a) To return to the old oak tree, in what direction should you head and how far will you walk? Use components to solve this problem. (b) To see whether your calculation in part (a) is reasonable, check it with a graphical solution drawn roughly to scale.

5. A ship leaves the island of Guam and sails 285 km at 40.0° north    of west. In which direction must it now head   and how far must it sail so that its resultant displacement will be 115 km directly east of Guam?

6. A one-euro coin is dropped from the Leaning Tower of Pisa and falls freely from rest. What are its position and velocity after 1.0 s, 2.0 s, and 3.0 s?

7. A flowerpot falls off a windowsill and falls past the window below. You may ignore air resistance. It takes the pot 0.420 s to pass from the top to the bottom of this window, which is 1.90 m high. How far is the top of the window below the windowsill from which the flowerpot fell?

8. A juggler performs in a room whose ceiling is 3.0 m above the level of his hands. He throws a ball upward so that it just reaches the ceiling. (a) What is the initial velocity of the ball? (b) What is the time required for the ball to reach the ceiling? At the instant when the first ball is at the ceiling, the juggler throws a second ball upward with two-thirds the initial velocity of the first. (c) How long after the second ball is thrown do the two balls pass each other? (d) At what distance above the juggler’s hand do they pass each other?
9.A physics teacher performing an outdoor demonstration suddenly falls from rest off a high cliff and simultaneously shouts “Help.” When she has fallen for 3.0 s, she hears the echo of her shout from the valley floor below. The speed of sound is (a) How tall is the cliff? (b) If air resistance is neglected, how fast will she be moving just before she hits the ground? (Her actual
speed will be less than this, due to air resistance.)
10. A helicopter carrying Dr. Evil takes off with a constant upward acceleration of Secret agent Austin Powers jumps on just as the helicopter lifts off the ground. After the two men struggle for 10.0 s, Powers shuts off the engine and steps out of the helicopter. Assume that the helicopter is in free fall after its engine is shut off, and ignore the effects of air resistance.
 (a) What is the maximum height above ground reached by the helicopter?
(b) Powers deploys a jet pack strapped on his back 7.0 s after leaving the helicopter, and then he has a constant downward acceleration with magnitude How far is Powers above the ground when the helicopter crashes into the ground?


Sunday, 3 January 2016

Measurement and vectors Questions

1. You are writing an adventure novel in which the hero escapes across the border with a billion dollars’ worth of gold
   in his suitcase. Could anyone carry that much gold? Would it fit in a suitcase?

2. A cross-country skier skis 1.00 km north and then 2.00 km east on a horizontal snowfield. How far and in what
  direction is she fromthe starting point?
3. After an airplane takes off, it travels 10.4 km west, 8.7 km north, and 2.1 km up. How far is it from the takeoff point?
4. How many correct experiments do we need to disprove a theory?How many do we need to prove a theory? Explain.
5. A guidebook describes the rate of climb of a mountain trail as 120 meters per kilometer. How can you express this
  as a number with no units?
6. Suppose you are asked to compute the tangent of 5.00 meters.Is this possible? Why or why not?
7. A highway contractor stated that in building a bridge deck he poured 250 yards of concrete. What do you think he
  meant?
8. What is your height in centimeters? What is your weight in newtons?
9. What physical phenomena (other than a pendulum or cesium clock) could you use to define a time standard?
10. Describe how you could measure the thickness of a sheet of paper with an ordinary ruler.
11. What are the units of volume? Suppose another student tellsyou that a cylinder of radius r and height h has
    volume given byr 3h. Explain why this cannot be right.
12 Three archers each fire four arrows at a target. Joe’s fourarrows hit at points 10 cm above, 10 cm below, 10 cm to
    the left,and 10 cm to the right of the center of the target. All four of Moe’s arrows hit within 1 cm of a point 20 cm
   from the center, and Flo’s four arrows all hit within 1 cm of the center. The contest judge says that one of the    
    archers is precise but not accurate,another archer is accurate but not precise, and the third archer is both accurate
   and precise. Which description goes with whicharcher? Explain your reasoning.
13. A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the
   track from the north side to the south side? When she makes one complete circle around the track? Explain your   
   reasoning.
14. Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are
      required for three vectors to have a vector sum of zero? Explain your reasoning.
15. One sometimes speaks of the “direction of time,” evolving from past to future. Does this mean that time is a vector
     quantity?Explain your reasoning.
16. Air traffic controllers give instructions to airline pilots telling them in which direction they are to fly. These
    instructions are called “vectors.” If these are the only instructions given, is the name “vector” used correctly? Why
   or why not?
17. Can you find a vector quantity that has a magnitude of zero but components that are different from zero? Explain.
    Can themagnitude of a vector be less than the magnitude of any of its components? Explain.
18. (a) Does it make sense to say that a vector is negative? Why? (b) Does it make sense to say that one vector is
     the negative of another? Why? Does your answer here contradict what you said in part (a)?
19. How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to
      remember.)
20. How many years older will you be 1.00 gigasecond from  now? (Assume a 365-day year.)
21.With a wooden ruler you measure the length of a rectangular piece of sheet metal to be 12 mm. You use micrometer calipers to measure the width of the rectangle and obtain the value 5.98mm. Give your answers to the following questions to the correct number of significant figures. (a) What is the area of the rectangle? (b) What is the ratio of the rectangle’s width to its length? (c) What is the perimeter of the rectangle? (d) What is the difference

between the length and width? (e) What is the ratio of the length to the width?

Saturday, 2 January 2016

MEASUREMENT

1.An automobile company displays a die-cast model of its first car, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in solid gold from the original dies. What mass of gold is needed to make the new model?
2.  A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 10-27 kg. Determine the density of the proton

3. Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five   
   times greater. Find its radius.
4. What mass of a material with density r is required to make a hollow spherical shell having inner radius   r1  and outer radius r2?
5. On an interstate highway in a rural region of Gujarat, a car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit of 75.0 Km/h?
6. Estimate the number of breaths taken during an average human lifetime.
7. What if the average lifetime were estimated as 80 years instead of 70? Would that change our final estimate?
8. A carpet is to be installed in a rectangular room whose length is measured to be 12.71 m and whose width is measured to be 3.46 m. Find the area of the room.
9. The mass of a copper atom is 1.06 10-25 kg, and the density of copper is 8 920 kg/m3 . (a) Determine the number of atoms in 1 cm3 of copper. (b) Visualize the one cubic centimeter as formed by stacking up identical cubes,  with one copper atom at the center of each. Determine the volume of each cube. (c) Find the edge dimension of each   cube, which represents an estimate for the spacing between atoms.