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free/or 0.5$ |
| 55823 | A car is approaching a hill at 30.0 m/s when its engine suddenly fails just at the bottom of the hill. The car moves with a constant acceleration of -2.00 m/s2 while coasting up the hill.
(a) Write equations for the position along the slope and for the velocity as functions of time, taking x = 0 at the bottom of the hill, where vi=30.0 m/s.
(b) Determine the maximum distance the car rolls up the hill. |
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| 55824 | A car has an initial velocity v0 when the driver sees an obstacle in the road in front of him. His reaction time is ∆tr, and the braking acceleration of the car is a. Show that the total stopping distance is sstop = vo ∆tr – vo2/2a. Remember that a is a negative number. |
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| 55825 | Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than the average velocity over a time interval containing the instant? Can it ever be less? |
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| 55826 | Can the equations of kinematics (Eqs. 2.9–2.13) be used in a situation where the acceleration varies in time? Can they be used when the acceleration is zero? |
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| 55827 | Can a heat pump have a coefficient of performance less than unity? Explain. |
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| 55828 | Calculate the R value of
(a) a window made of a single pane of flat glass ⅛ in. thick, and
(b) A thermal window made of two single panes each ⅛ in. thick and separated by a ¼ in air space.
(c) By what factor is the transfer of energy by heat through the window reduced by using the thermal window instead of the single pane window? |
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| 55829 | Calculate the change in internal energy of 3.00 mol of helium gas when its temperature is increased by 2.00 K. |
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| 55830 | Calculate the change in entropy of 250 g of water heated slowly from 20.0°C to 80.0°C. (Suggestion: Note that dQ = mc dT) |
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| 55831 | A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0°C. Assuming the average coefficients of linear expansion are constant, (a) To what temperature must this combination be cooled to separate them? Is this attainable? (b) What If? What if the aluminum rod were 10.02 cm in diameter? |
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| 55832 | A box with a total surface area of 1.20 m2 and a wall thickness of 4.00 cm is made of an insulating material. A 10.0-W electric heater inside the box maintains the inside temperature at 15.0°C above the outside temperature. Find the thermal conductivity k of the insulating material. |
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| 55833 | A biology laboratory is maintained at a constant temperature of 7.00°C by an air conditioner, which is vented to the air outside. On a typical hot summer day the outside temperature is 27.0°C and the air conditioning unit emits energy to the outside at a rate of 10.0 kW. Model the unit as having a coefficient of performance equal to 40.0% of the coefficient of performance of an ideal Carnot device.
(a) At what rate does the air conditioner remove energy from the laboratory?
(b) Calculate the power required for the work input.
(c) Find the change in entropy produced by the air conditioner in 1.00 h.
(d) What If? The outside temperature increases to 32.0°C. Find the fractional change in the coefficient of performance of the air conditioner. |
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| 55834 | A bimetallic strip is made of two ribbons of dissimilar metals bonded together. (a) First assume the strip is originally straight. As they are heated, the metal with the greater average coefficient of expansion expands more than the other, forcing the strip into an arc, with the outer radius having a greater circumference (Fig. P19.54a). Derive an expression for the angle of bending - as a function of the initial length of the strips, their average coefficients of linear expansion, the change in temperature, and the separation of the centers of the strips (Δr = r2 - r1). (b) Show that the angle of bending decreases to zero when ΔT decreases to zero and also when the two average coefficients of expansion become equal. (c) What If? What happens if the strip is cooled? (d) Figure P19.54b shows a compact spiral bimetallic strip in a home thermostat. The equation from part (a) Applies to it as well, if Ө is interpreted as the angle of additional bending caused by a change in temperature. The inner end of the spiral strip is fixed, and the outer end is free to move. Assume the metals are bronze and Invar, the thickness of the strip is 2Δr = 0.500 mm, and the overall length of the spiral strip is 20.0 cm. Find the angle through which the free end of the strip turns when the temperature changes by one Celsius degree. The free end of the strip supports a capsule partly filled with mercury, visible above the strip in Figure P19.54b. When the capsule tilts, |
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| 55835 | A beaker made of ordinary glass contains a lead sphere of diameter 4.00 cm firmly attached to its bottom. At a uniform temperature of - 10.0°C, the beaker is filled to the brim with 118 cm3 of mercury, which completely covers the sphere. How much mercury overflows from the beaker if the temperature is raised to 30.0°C? |
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| 55836 | A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.00 s for the ball to reach its maximum height. Find
(a) Its initial velocity and
(b) The height it reaches. |
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| 55837 | A bar of gold is in thermal contact with a bar of silver of the same length and area (Fig. P20.43). One end of the compound bar is maintained at 80.0°C while the opposite end is at 30.0°C. When the energy transfer reaches steady state, what is the temperature at the junction? |
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| 55838 | A ball starts from rest and accelerates at 0.500 m/s2 while moving down an inclined plane 9.00 m long. When it reaches the bottom, the ball rolls up another plane, where, after moving 15.0 m, it comes to rest.
(a) What is the speed of the ball at the bottom of the first plane?
(b) How long does it take to roll down the first plane?
(c) What is the acceleration along the second plane?
(d) What is the ball’s speed 8.00 m along the second plane? |
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| 55839 | A ball is thrown directly downward, with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does the ball strike the ground? |
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| 55840 | A ball is dropped from rest from a height h above the ground. Another ball is thrown vertically upwards from the ground at the instant the first ball is released. Determine the speed of the second ball if the two balls are to meet at a height h/2 above the ground. |
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| 55841 | Automotive engineers refer to the time rate of change of acceleration as the “jerk.” If an object moves in one dimension such that its jerk J is constant,
(a) Determine expressions for its acceleration ax (t), velocity vx (t), and position x (t), given that its initial acceleration, velocity, and position are axi , vxi , and xi , respectively.
(b) Show that ax2 = axi2 + 2J (vx – vxi). |
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| 55842 | An automobile tire is rated to last for 50 000 miles. To an order of magnitude, through how many revolutions will it turn? In your solution state the quantities you measure or estimate and the values you take for them. |
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