10 Problems

January 3, 2020

You should do all of these problems, but at a minimum do: 1, 2, 3, 7, 11, 20, 21, 24, 28, 29.  If you find any errors in any of these questions in particular the posted answers, contact Jennifer Kirkey for bonus marks.  kirkeyj@douglascollege.ca.  You are expected to do these problems as homework.  You do not have to hand them in, yet it is possible (likely) that there will be in class work, quizzes and tests that are very similar to these assigned problems.

Problems

  1. What is the weight in newtons at the surface of the Earth of  an object that has a mass of (a) 7.77 kg  (b) 0.0333 mg, and (c) 888 Mg?  Assume that g = 9.81 m/s2 (Answers a) 76.2 N b) 0.327 mN c) 8.71 MN)

  2. Represent each of the following combinations  of units in the correct SI form a)  b) MN/ms b) mg/μN c)  kN/(kg•ms)  (Answers a) GN/s  b) kg/N c) MN/(kg•s) )
  3. Use standard engineering notation to represent each of the following as a number between 0.1 and 1000 using an appropriate prefix: (a)  45600 kN, (b) 567 x 105  mm, and (c) 0.00345 mg. (Answer: 45.6 MN b) 56.7 km c) 3.45 μg)
  4. Represent each of the following quantities in the correct SI form using an appropriate prefix: a) 0.000 123 kg b) 34.5(103) N = 34.5 x 103 N c) 0.002 34 km (Answers a) 0.123 g b) 34.5 kN c) 2.34 m )
  5. Round off the following numbers to three significant figures and use the appropriate prefix: (a) 58322 m, (b) 65.432 s, (c) 3453 N, and (d) 8555 kg. (Answers a) 58300 m = 58.3 km b) 65.4 s c) 3450 N = 3.45 kN d) 8560 kg = 8.56 Mg)
  6. Convert: (a) 300 lb•ft to N•m b) 600 lb/ ft3 to kN/m3 , (c) 4 ft/h to mm/s. Give your final answer to three significant figures as usual and use the appropriate prefix. (Answer: a) 407 N•m b) 94.3 kN/m3 c) 0.339 mm/s )
  7. The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this? (Answer (a) 27.8 m/s  b) 62.1 miles per hour or mph)
  8. A car is traveling at a speed of 33 m/s.  What is its speed in kilometres per hour? Is it exceeding the 90 km/h speed limit?   (Answer 118.8 km/h so yes it is speeding)
  9. Show that 1.0 m/s=3.6 km/h. Hint: Show the explicit steps involved in converting 1.0 m/s=3.6 km/h.  (Answer [latex]\frac{1.0 \:  m } {s} = \frac {1.0 \:  m }{s} \times \frac{ 3600 \:  s}{1 \: { hr}}  \times \frac{1\: { km}}{1000 \: { m}}[/latex]  = 3.6  km/h. )
  10. American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? Remember that 1 yard = 3 feet and 1 foot = 0.3048 m.  (Answer 91.4 m).
  11. Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? Remember that 1 meter equals 3.281 feet. (Answer length: 377 ft; 4.53 x 1 = 3 in    width =  280 ft ; 3.3 x 103 inches )
  12. What is the height in meters of a person who is 6 ft 1.0 in. tall? Remember that 1 meter equals 39.37 in. and there are 12 inches in one foot. (Answer: 1.85 m)
  13. Mount Everest, at 29,031.7 feet, is the tallest mountain on the Earth. What is its height in kilometers? (Assume that 1 kilometer equals 3,281 feet.). (Answer 8.84886 km) 
  14. The speed of sound is measured to be 342 m/s on a certain day. What is this in km/h? (Answer 1120 km/h)
  15.  Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?  (Answer (a) 1.3 x 10-9 m (b) 40 km/My or mega year.) 
  16. Represent each of  the following in the correct SI form using an appropriate prefix: a)  8765 ms, (b) 8888 N, (c) 0.893kg  c) 0.987 kg (Answers: 8.765 s b) 8.888 kN c) 987 g )
  17. Represent each of  the following combinations of units in the correct SI form using an appropriate prefix: a) Mg/mm b) mN/μs c) μm•Mg (Answers: a) Gg/m b) kN/s c) mm•kg)
  18. Represent each of  the following combinations of units in the correct SI form using an appropriate prefix: a) m/ms b) μkm  c)  ks/mg d) km•μN (Answers: a) km/s b) mm c) Gs/kg d) mm•N )
  19. Represent each of  the following combinations of units in the correct SI form using an appropriate prefix: a) GN•μm b) kg/μm c) N/mm2 d) kN/μs (Answers: a)  kN•m b) Gg•m c) MN/m2 d) GN/s)
  20. Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix:  a)  (654 mm) / (43 μs), b) (22 ms)(0.0345 Mm)/(555 mg)  c) (3.45 mm)(456 Mg)  (Answers: a) 15.2 km/s b)  1.37 Mm•s/kg c) 1.57 km•kg)
  21. Density is defined to be mass/volume. The density of copper is 17.4 slugs/ft3.  To three significant figures, what is its density in SI units? Use the appropriate prefix. (Answers: 8970 kg/m3 = 8.97 Mg/m3)
  22. Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: a) (56700 ms)2 b) (234 mN)2 b) c)  (897 (106) ) 1/2 ms.  Remember that 897 (106) ) 1/2 ms = [latex]\sqrt { 897 (10^6)  }[/latex] ms. (Answers a) 3214.9 s2  = 3.2149(103) s2 3b)  0.054756 N2 = 54.8(10-3) N2  c) 29.9 s ) 
  23. a) Show that the equation for the gravitation force [latex]F = G \frac {m_1 m_2 } {r^2}[/latex] is a “dimensionally homogeneous equation” that will give you the force in newtons. b) Use the equation above to find the magnitude of the gravitational force between two spheres of radius 200 mm that are touching each other.  Each sphere has a mass of 300 kg. (Answer b) 37.5 μN)
  24. The pascal Pa is the SI derived unit of pressure. It is actually very small.  Show this by converting 1 Pa = 1 N/m2 to lb/ft2.  STP which is Standard Temperature and Pressure assumes that the air pressure at sea level is 1 atmosphere = 14.7 lb/in2 = 2116.2 lb/ft2 .  Convert this into pascals.  (Answer: 101.3 kPa)
  25. Water has a density of 1.94 slug/ft3. What is the density expressed in SI units? Express the answer to three significant figures. (Answer: 1000 kg/m3 = 1.00 Mg/m3).
  26. Evaluate each of the following to three significant figures. Use SI units and the appropriate prefix. a) (0.00345 Mg) (199 ms) b) (456 mg)(78 km)/(0.0123 kN)  c) (789 kN)/(23.4 mm) (Answer: a)  0.687 kg·s b) 2.89 kg·s/N c) 33.7 GN/m)
  27. A cylindrical column of concrete is 3 metres high and it has a diameter of 400 mm.  Assume the density which is mass/volume of the concrete to be 2.34 Mg/m3.   Find the a) volume b) mass in kg c) weight in pounds. (Answers a) 0.377 m3 b) 882 kg c) 1940 pounds or 1.94 kip)
  28. The first woman in space was the Soviet cosmonaut Valentina Tereshkova.  She had a weight of 170 pounds when she was on the surface of the earth.  What was a) her weight in newtons? b) her mass in slugs? c) her mass in kilograms?  While she never made it to the Moon where the acceleration due to gravity g = 5.30 ft/s2 as opposed to the Earth’s 32.2 ft/s2, let us pretend she had.  What would have  her d) mass in kilograms on the Moon and e) her weight in pounds? (Answers a) 756 N b) 5.28 slugs c) 77.1 kg d) 77.1 kg e) 28.0 lb. )
  29. Two particles have a mass of 9 kg and 8 kg, respectively. If the centres of the two particles are 700 mm apart, what is the force of gravity acting between them? What is the weight of each particle in newtons?   (Answers 9.80 nN, 88.3 N, 78.5 N.)

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