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- Question : 1P - Calculate the weight in pounds of an object whose mass is 3 slugs. Then convert the weight to newtons and the mass to kilograms.
- Question : 2P - Folklore has it that Sir Isaac Newton formulated the law of gravitation supposedly after being hit on the head by a falling apple. The weight of an apple depends strongly on its variety, but a typical weight is 1 newton! Calculate the total mass of 100 apples in kilograms. Then convert the total weight to pounds and the total mass to slugs.
- Question : 3P - A ball is thrown a distance of 50 feet, 5 inches. Calculate the distance in meters.
- Question : 4P - An American football field is 100 yards long. How long is it in meters?
- Question : 5P - How long is a 100-meter dash in feet?
- Question : 6P - Convert 50 feet per second to miles per hour
- Question : 7P - The speed limit in some countries is 100 kilometers per hour. How fast is that in miles per hour?
- Question : 8P - How many 60 watt lightbulbs are equivalent to one horsepower?
- Question : 9P - Convert the temperature of 70?F to ?C
- Question : 10P - Convert 30
- Question : 11P - A particular motor rotates at 3000 revolutions per minute (rpm). What is its speed in rad/sec, and how many seconds does it take to make one revolution?
- Question : 12P - The displacement of a certain object is described by y(t) = 23 sin 5t, where t is measured in seconds. Compute its period and its oscillation frequency in rad/sec and in hertz.
- Question : 13P - A car is driven at 40 miles per hour over a road whose surface is sinusoidal with a period of 30 feet. How many times per second will the car go over the peak of a bump?
- Question : 14P - The displacement in meters of a certain vibrating mass is described by x(t) = 0.005 sin 6t. What is the amplitude and frequency of its velocity x?(t)? What is the amplitude and frequency of its acceleration x
- Question : 15P - The distance a spring stretches from its
- Question : 16P - The following
- Question : 17P - Obtain two linear approximations of the function f (?) = sin ?, one valid near ? = ?/4 rad and the other valid near ? = 3?/4 rad.
- Question : 18P - Obtain two linear approximations of the function f (?) = cos ?, one valid near ? = ?/3 rad and the other valid near ? = 2?/3 rad
- Question : 19P - Obtain a linear approximation of the function f (h) = ?h, valid near h = 25.
- Question : 20P - Obtain two linear approximations of the function f (r) = r 2, one valid near r = 5 and the other valid near r = 10.
- Question : 21P - Obtain a linear approximation of the function f (h) = ?h, valid near h = 16. Noting that f (h) ? 0, what is the value of h below which the linearized model loses its meaning?
- Question : 22P - The flow rate f in m3/s of water through a particular pipe, as a function of the pressure drop p across the ends of the pipe (in N/m2) is given by f = 0.002?p. Obtain a linear model of f as a function of p that always underestimates the flow rate over the range 0 ? p ? 900.
- Question : 23P - In each of these problems, plot the data and determine the best function y(x) (linear, exponential, or power function) to describe the data. a. x 25 30 35 40 45 y 0 250 500 750 1000 b. x 2.5 3 3.5 4 4.5 5 5.5 6 7 8 9 10 y 1500 1220 1050 915 810 745 690 620 520 480 410 390 c. x 1000 2000 3000 4000 5000 y 41.2 18.62 8.62 3.92 1.86
- Question : 24P - The population data for a certain country are given here. Year 2005 2006 2007 2008 2009 2010 Population (millions) 9.8 10.5 11.3 12.0 12.9 13.8 Plot the data and obtain a function that describes the data. Estimate when the population will be double its 2005 size
- Question : 25P - The half-life of a radioactive substance is the time it takes to decay by half. The half-life of carbon-14, which is used for dating previously living things, is 5500 years. When an organism dies, it stops accumulating carbon-14. The carbon-14 present at the time of death decays with time. Let C(t)/C(0) be the fraction of carbon-14 remaining at time t. In radioactive carbon dating, it is usually assumed that the remaining fraction decays exponentially according to the formula C(t) C(0) = e?bt a. Use the half-life of carbon-14 to find the value of the parameter b and plot the function. b. Suppose we estimate that 90% of the original carbon-14 remains. Estimate how long ago the organism died. c. Suppose our estimate of b is off by
- Question : 26P - Quenching is the process of immersing a hot metal object in a bath for a specified time to improve properties such as hardness. A copper sphere 25 mm in diameter, initially at 300?C, is immersed in a bath at 0?C. Measurements of the sphere
- Question : 27P - The useful life of a machine bearing depends on its operating temperature, as shown by the following data. Plot the data and obtain a functional description of the data. Estimate a bearing
- Question : 28P - A certain electric circuit has a resistor and a capacitor. The capacitor is initially charged to 100 V. When the power supply is detached, the capacitor voltage decays with time as shown in the following data table. Find a functional description of the capacitor voltage v as a function of time t. Time (s) 0 0.5 1 1.5 2 2.5 3 3.5 4 Voltage (V) 100 62 38 21 13 7 4 2 3
- Question : 29P - Water (of volume 425 ml) in a glass measuring cup was allowed to cool after being heated to 207?F. The ambient air temperature was 70?F. The measured water temperature at various times is given in the following table. Time (sec) 0 300 600 900 1200 1500 Temperature (?F) 207 182 167 155 143 135 Time (sec) 1800 2100 2400 2700 3000 Temperature (?F) 128 123 118 114 109 Obtain a functional description of the relative water temperature ( T = T ? 70) versus time.
- Question : 30P - Consider the milk container of Example 1.4.2 (Figure 1.4.7). A straw 19 cm long was inserted in the side of the container. While adjusting the tap flow to keep the water height constant, the time for the outflow to fill a 250-ml cup was measured. This was repeated for several heights. The data are given in the following table. Height (cm) 11 10 9 8 7 654321 Time (s) 7 7 7 8 9 10 11 13 15 17 23 Obtain a functional description of the volume outflow rate f through the straw as a function of water height h above the hole.
- Question : 31P - Consider the milk container of Example 1.4.2 (Figure 1.4.7). A straw 9.5 cm long was inserted in the side of the container. While adjusting the tap flow to keep the water height constant, the time for the outflow to fill a 250-ml cup was measured. This was repeated for several heights. The data are given in the following table. Height (cm) 11 10 9 8 7 6 5 4321 Time (s) 6 6 6 7 8 9 9 11 13 17 21 Obtain a functional description of the volume outflow rate f through the straw as a function of water height h above the hole.

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