College Physics: Introduction

Chapter 1

3. Even when simplified models do not exactly match real conditions , they can still provide insight into the features of a physical system . Often a problem would become too complicated if one attempted to match the real conditions exactly, and an approximation can yield a result that is close enough to the exact one to still be useful.

13. Trends in a set of data are often the most interesting aspect of the outcome of an experiment. Such trends are more apparent when data is plotted graphically rather than listed in numerical tables .

15. Order -of-magnitude estimates provide a quick method for obtaining limited precision solutions to problems. Even if greater accuracy is required, order-of-magnitude calculations are still useful as they provide a check as to the accuracy of the higher precision calculation.

16. After solving a problem , it is a good idea to check that the solution is reasonable and makes intuitive sense. It may also be useful to explore other possible methods of solution as a check on the validity of the first.

1. Strategy Relate the surface area S to the radius r using .

Solution Find the ratio of the new radius to the old.

 

The radius of the balloon increases by 7.7%.

2. Strategy Relate the surface area S to the radius r using .

Solution Find the ratio of the new radius to the old.

8. Strategy The volume of the rectangular room is given by Let the original and final volumes be and respectively.

Solution Find the factor by which the volume of the room increased.

12.
(a) Strategy Rewrite the numbers so that the power of 10 is the same for each. Then add and give the answer with the number of significant figures de termined by the less precise of the two numbers . Solution Write your answer using the appropriate number of significant figures.

(b) Strategy Add and give the answer with the number of significant figures determined by the less precise of the two numbers. Solution Write your answer using the appropriate number of significant figures.
702.35 km+1897.648 km= 2600.00 km

(c) Strategy Multiply and give the answer with the number of significant figures determined by the number with the fewest significant figures. Solution Write your answer using the appropriate number of significant figures.
5.0 m×4.3 m= 22 m²

(d) Strategy Find the quotient and give the answer with the number of significant figures determined by the number with the fewest significant figures.
 
Solution Write your answer using the appropriate number of significant figures.

(e) Strategy Find the quotient and give the answer with the number of significant figures determined by the number with the fewest significant figures.

Solution Write your answer using the appropriate number of significant figures.
 

19.
(a) Strategy Divide the length of the roadway by the distance between reflectors. There are 1760 yards in one mile. Solution Find the distance between reflectors.

(b) Strategy Divide the length of the roadway by the distance between reflectors. There are 1000 meters in one kilometer.

Solution Find the distance between reflectors.

20. Strategy There are 1000 watts in one ki lowatt and 100 centimeters in one meter.

Solution Convert 1.4 kW/m² to W/cm².

28.
(a) Strategy Replace each quantity in ma an ks with its dimensions.

Solution Show that the dimensions of are equivalent . and ma an ks

are equivalent. ma has dimensions and ks has dimensions

Since  the dimensions are equivalent.

(b) Strategy Use the results of part (a).

Solution Since and F=ma, F=kx the dimensions of the force unit are .

29. Strategy Replace each quantity in with its dimensions.

Solution Show that the equation is dimensionally correct. T² has dimensions  [T]² and has dimensions .

Since the equation is dimensionally correct.

34. Strategy and Solution A normal heart rate is about 70 beats per minute and a person lives for about 70 years, so the heart beats about times per lifetime, or about 3×10⁹.

41. Strategy Use the two temperatures and their corresponding times to find the rate of temperature change with respect to time (the slope of the graph of temperature vs. time). Then, write the linear equation for the temperature with respect to time and find the temperature at 3:35 p.m.

Solution Find the rate of temperature change. Use the slope- intercept form of a graph of temperature vs. time to find the temperature at 3:35 P.M.

48. Strategy The weight is proportional to the mass and inversely proportional to the square of the radius , so Thus, for Earth and Jupiter, we have and.

 Solution Form a proportion.

On Jupiter, the apple would weigh .

54. Strategy Use the conversion factors from the inside cover of the book.

(a)

(b)

71. (a) Strategy There are 7.0 leagues in one pace and 4.8 kilometers in one league.

Solution Find your speed in kilometers per hour.

(b) Strategy The circumference of the earth is approximately 40,000 km. The time it takes to march around the Earth is found by dividing the distance by the speed.

Solution Find the time of travel.

72. Strategy Use the fact that

Solution Calculate the ratio of P_B to P_A