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24 The mass values of specified volumes of pure gold nuggets are given in Table 1-4 a Plot mass versus volume from the values given in the table and draw the curve that best fits all points b Describe the resulting curve c According to the graph, what type of relationship exists between the mass of the pure gold nuggets and their volume d What is the value of the slope of this graph Include the proper units e Write the equation showing mass as a function of volume for gold f Write a word interpretation for the slope of the line

Table 1-4

Mass of Pure Gold Nuggets Volume (cm3) 10 20 30 40 50 Mass (g) 194 386 581 774 965

Figure 1-19 Computer animators use mathematical models of the real world to create a convincing fictional world They need to accurately portray how beings of different sizes move, how hair or clothing move with a character, and how light and shadows fall, among other physics topics

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+ (NSSet *)keyPathsForValuesAffectingStringEncodingName { return [NSSet setWithObjects:@"filePath", @"fileWrapper", @"chosenEncoding", nil]; } - (NSString *)stringEncodingName { if (!filePath) return nil; if (self.chosenEncoding != 0) { return [[self encodingNames] objectForKey: [NSString stringWithFormat:@"%u", self.chosenEncoding]]; } else { NSStringEncoding encoding = 0; NSError *err = nil; [NSString stringWithContentsOfFile:filePath usedEncoding:&encoding error:&err]; if (encoding==0) { return @"No encoding detected. Perhaps a binary file "; } return [[self encodingNames] objectForKey: [NSString stringWithFormat:@"%u", encoding]]; } } - (void)setStringEncodingName:(NSString *)name { NSString *key = [[[self encodingNames] allKeysForObject:name] lastObject]; self.chosenEncoding = [key longLongValue]; }

When scientists discover relations like the ones shown in the graphs in this section, they use them to make predictions For example, the equation for the linear graph in Figure 1-16 is as follows: y (008 cm/g)x 137 cm

Relations, either learned as formulas or developed from graphs, can be used to predict values you haven t measured directly How far would the spring in Table 1-3 stretch with 49 g of mass y (008 cm/g)(49 g) 18 cm It is important to decide how far you can extrapolate from the data you have For example, 49 kg is a value far outside the ones measured, and the spring might break rather than stretch that far Physicists use models to accurately predict how systems will behave: what circumstances might lead to a solar flare, how changes to a circuit will change the performance of a device, or how electromagnetic fields will affect a medical instrument People in all walks of life use models in many ways One example is shown in Figure 1-19 With the tools you have learned in this chapter, you can answer questions and produce models for the physics questions you will encounter in the rest of this textbook 137 cm

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1 A soccer ball is kicked from a 22-m-tall platform It lands 15 m from the base of the platform What is the net displacement of the ball 2 If the net displacement is 32 m for the same situation, as described in problem 1, how far from the platform base must the ball land 3 For any single force vector, there is only one angle for which its x- and y-components are equal in size a What is that angle b How many times bigger is a vector at this particular angle than either of its components

a What is the magnitude of the resultant of the sum of these three vectors b What is the size of the angle, , that the resultant makes with the horizontal c Into which quadrant does the resultant point

6 A 90-kg crate sits on a level, rough floor A 61-N force is needed just to start it moving What is the size of the coefficient of maximum static friction 7 Given the graph below answer the following questions a What is the value of k for this system b If the frictional force is 15 N, what is FN c Does tripling FN triple Fapplied d Do Fapplied and FN act in the same direction Explain why or why not

Finally, fileStringValue and its matching keyPathsForValuesAffectingFileStringValue method. Here we also have a couple of primary code paths. In the first case, where

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