Problem 1 Using dimensional equations, convert: (a) 102 km/day to in/sec (b) 5 k

Question

Problem 1 Using dimensional equations, convert: (a) 102 km/day to in/sec (b) 5 kg/cm2 to pounds/ft? (c) 24 km/day to insec Problem 2 Using the table of conversion factors on the inside of the front cover, convert (a) 3.3 x 1013 ergs/hr to hp sec to mi (c) 158 lbf cm to J Problem 3 Let us assume that the normal Olympic athlete has, on average, a normal basal metabolic rate of 4000 kcal day. Using a dimensional cquation, and assuming no loss of cncrgy in conversion, estimate the number of 40 W lightbulbs that 25 average' olympians could keep lit? Problem 4 Calculate (a) The mass of an object in kg that exerts a force of 125. N (b) The weight of an object in lbrthat has a mass of35 kg (c) The weight of an object in Ibm ft/mina that has a mass of 32. metric tons Problem 5 Perform the following calculations; For each part, first make a good cstimation without your calculator. Then use your calculator, paying close attention to significant digits. (a) 9.464 2227.2 (b) 9.274 x 2.2 x 10 (c) 202 x 103 5.3223 (d) 201.57686 -2.3

Explanation / Answer

1)

a) we know that 1km = 1000m = 39.3701 X 10^3 inches

1 day = 24 hours = 24 X 60 minutes = 24 X 60 X 60 seconds

So 102 Km / day = 102 X 39.3701 X 10^3 inches / 24 X 60 X 60 = 46.48 inch / seconds

b) 1 Kg = 2.205 pounds

1cm2 = 0.00108 ft2

5kg / cm2 = 5 X 2.206 / 0.00108 = 10212.96 pounds / ft2

c) 1km = 1000m = 39.3701 X 10^3 inches

1 day = 24 hours = 24 X 60 minutes = 24 X 60 X 60 seconds

24 km /day2 = 24 X 39.3701 X 10^3 inches / 24 X 60 X 60 X 24 X 60 X 60 sec2 = 1.266 X 10^-4 inches / sec2

2) 1 erg / hour = 3.725 × 10-14 hp

3.3 X 10^13 erg / hour = 3.3 X 10^13 X 3.725 × 10-14hp = 1.229 hp

b) 1 m/ second = 2.237 miles / hour

50m/sec = 50 X 2.237 miles / hour = 111.85 miles / hour

c) 1lbf *cm = 0.0444 Joules

158lbf *cm = 0.0444 X 158 Joules = 7.015 joules

3) metabolic rate = 4000 Kcal / day

4000 Kcal / day = 4000 Kcal / 24 hours = 166.67 KCal / hour

1 Kcal / hour = 1.163 Watts

166.67 Kcal / hour = 1.163 X 166.67 watts =193.84 watts

Energy by 25 athletes = 25 x 193.84 watts = 4846 watts

Power of bulb = 40 W

Number of bulbs which can be lit = 4846 / 40 = 121.15 (appro)

4) a) 1 N 1 kgm/s2

125 N = 125 Kg / m/s2 = mass X acceleration due to gravity

Mass = force / g = 125 / 9.8 = 12.76 Kg

b)1Kg = 2.205 lbf

35 Kg = 35 x 2.205 lbf = 77.16 lbf

5 a) 9.464 + 2227.2 = 2236.664

b) for multiplication the least number of significant figures determines the number of significant figure in answer

20.4 X 10^4

c) for division the least number of significant figures determines the number of significant figure in answer

37.9 X 10^-3

d) 199.27686

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