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free/or 0.5$ |
| 55503 | The position of a pine wood derby car was observed at various times; the results are summarized in the following table. Find the average velocity of the car for
(a) The first second,
(b) The last 3 s, and
(c) The entire period of observation.
t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5 |
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| 55504 | The position of a particle moving along the x axis varies in time according to the expression x = 3t2, where x is in meters and t is in seconds. Evaluate its position
(a) At t = 3.00 s and
(b) At 3.00 s + ∆t
(c) Evaluate the limit of ∆x/ ∆t as ∆t approaches zero, to find the velocity at t = 3.00 s |
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| 55505 | The pioneers referred to in the last question found that a large tub of water placed in a storage cellar would prevent their food from freezing on really cold nights. Explain why this is so. |
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| 55506 | The pendulum of a certain pendulum clock is made of brass. When the temperature increases, does the period of the clock increase, decrease, or remain the same? Explain. |
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| 55507 | The passenger section of a jet airliner is in the shape of a cylindrical tube with a length of 35.0 m and an inner radius of 2.50 m. Its walls are lined with an insulating material 6.00 cm in thickness and having a thermal conductivity of 4.00 X 10-5 cal/s cm °C. A heater must maintain the interior temperature at 25.0°C while the outside temperature is -35.0°C. What power must be supplied to the heater? (Use the result of Problem 70.) |
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| 55508 | The particle P is acted upon by its weight of 3 lb and forces F1 and F2, where t is in seconds. If the particle originally has a velocity of v1 = {3i + 1j + 6k) ft/s, determine its speed after 2 s. |
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| 55509 | The Nova laser at Lawrence Livermore National Laboratory in California is used in studies of initiating controlled nuclear fusion (Section 45.4). It can deliver a power of 1.60 X 1013 W over a time interval of 2.50 ns. Compare its energy output in one such time interval to the energy required to make a pot of tea by warming 0.800 kg of water from 20.0°C to 100°C. |
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| 55510 | The New River Gorge bridge in West Virginia is a steel arch bridge 518 m in length. How much does the total length of the roadway decking change between temperature extremes of - 20.0°C and 35.0°C? The result indicates the size of the expansion joints that must be built into the structure |
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| 55511 | The melting point of gold is 1 064°C, and the boiling point is 2 660°C. (a) Express these temperatures in kelvins. (b) Compute the difference between these temperatures in Celsius degrees and kelvins. |
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| 55512 | The mass of a hot-air balloon and its cargo (not including the air inside) is 200 kg. The air outside is at 10.0°C and 101 kPa. The volume of the balloon is 400 m3. To what temperature must the air in the balloon be heated before the balloon will lift off? (Air density at 10.0°C is 1.25 kg/m3.) |
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| 55513 | The largest bottle ever made by blowing glass has a volume of about 0.720 m3. Imagine that this bottle is filled with air that behaves as an ideal diatomic gas. The bottle is held with its opening at the bottom and rapidly submerged into the ocean. No air escapes or mixes with the water. No energy is exchanged with the ocean by heat.
(a) If the final volume of the air is 0.240 m3, by what factor does the internal energy of the air increase?
(b) If the bottle is submerged so that the air temperature doubles, how much volume is occupied by air? |
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| 55514 | The intensity of solar radiation reaching the top of the Earth’s atmosphere is 1 340 W/m2. The temperature of the Earth is affected by the so-called greenhouse effect of the atmosphere. That effect makes our planet’s emissivity for visible light higher than its emissivity for infrared light, for comparison, consider a spherical object with no atmosphere, at the same distance from the Sun as the Earth. Assume that its emissivity is the same for all kinds of electromagnetic waves and that its temperature is uniform over its surface. Identify the projected area over which it absorbs sunlight and the surface area over which it radiates. Compute its equilibrium temperature. Chilly, isn’t it? Your calculation applies to
(a) The average temperature of the Moon,
(b) Astronauts in mortal danger aboard the crippled Apollo 13 spacecraft, and
(c) Global catastrophe on the Earth if widespread fires should cause a layer of soot to accumulate throughout the upper atmosphere, so that most of the radiation from the Sun were absorbed there rather than at the surface below the atmosphere. |
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| 55515 | The inside of a hollow cylinder is maintained at a temperature Ta while the outside is at a lower temperature, Tb (Fig. P20.70). The wall of the cylinder has a thermal conductivity k. Ignoring end effects, show that the rate of energy conduction from the inner to the outer surface in the radial direction is |
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| 55516 | The height of a helicopter above the ground is given by h = 3.00t 3, where h is in meters and t is in seconds. After 2.00 s, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground? |
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| 55517 | The graph shows the vertical reaction force of the shoe-ground interaction as a function of time. The first peak acts on the heel, and the second peak acts on the forefoot. Determine the total impulse acting on the shoe during the interaction. |
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| 55518 | The Golden Gate Bridge in San Francisco has a main span of length 1.28 km—one of the longest in the world. Imagine that a taut steel wire with this length and a cross-sectional area of 4.00 X 10-6 m2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day when the temperature of the wire is 35.0°C. (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10.0°C, what is the tension in the wire? Take Young’s modulus for steel to be 20.0 x 1010 N/m2. (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 X 108 N/m2. At what temperature would this happen? (c) What If? How would your answers to (a) and (b) change if the Golden Gate Bridge were twice as long? |
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| 55519 | The function Eint = 3.50nRT describes the internal energy of a certain ideal gas. A sample comprising 2.00 mol of the gas always starts at pressure 100 kPa and temperature 300 K. For each one of the following processes, determine the final pressure, volume, and temperature; the change in internal energy of the gas; the energy added to the gas by heat; and the work done on the gas.
(a) The gas is heated at constant pressure to 400 K.
(b) The gas is heated at constant volume to 400 K.
(c) The gas is compressed at constant temperature to 120 kPa.
(d) The gas is compressed adiabatically to 120 kPa. |
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| 55520 | “The first law of thermodynamics says you can’t really win, and the second law says you can’t even break even.” Explain how this statement applies to a particular device or process; alternatively, argue against the statement. |
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| 55521 | The exhaust temperature of a Carnot heat engine is 300°C. What is the intake temperature if the efficiency of the engine is 30.0%? |
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| 55522 | Help! One of our equations is missing! We describe constant acceleration motion with the variables and parameters vxi, vxf, ax, t, and xf - xi. Of the equations in Table 2.2, the first does not involve xf - xi . The second does not contain ax; the third omits vxf and the last leaves out t. So to complete the set there should be an equation not involving vxi. Derive it from the others. Use it to solve Problem 29 in one step. |
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