Concept explainers
Using proportions A proportion is defined as an equality between two ratios; for instance, a/b = c/d. Proportions can be used to determine the expected change in one quantity when another quantity changes Suppose, for example, that the speed of a car doubles By what factor does the stopping distance of the car change? Proportions can also be used to answer everyday questions, such as whether a large container or a small container of a product is a better buy on a cost-per-unit-mass basis.
Suppose that a small pizza costs a certain amount. How much should a larger pizza of the same thickness cost? If the cost depends on the amount of ingredients used, then the cost should increase in proportion to the pizza s area and not in proportion to its diameter:
Let us rearrange Eq. (3.10) so the two variable quantities (cost and radius) are on the right side of the equation and the constants are on the left:
This equation should apply to any size pizza. If r increases, the cost should increase so that the ratio Cost/r2 remains constant. Thus, we can write a proportion for pizzas of different sizes:
For example, if a 3.5-in. -radius pizza costs $4.00, then a 5.0-in. radius pizza should cost.
This process can be used for most equations relating two quantities that change while all other quantities remain constant.
You decide to open a pizza parlor The ingredients require that you charge $4.50 for a 7.0-in -diameter pizza How large should you make a pizza whose price is $10.00, assuming the cost is based entirely on the cost of ingredients?
a. 1.4 in.
b. 3.1 in.
c. 7.0 in.
d. 10 in.
e. 16 in.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
College Physics
Additional Science Textbook Solutions
Physics (5th Edition)
Lecture- Tutorials for Introductory Astronomy
Applied Physics (11th Edition)
Modern Physics
University Physics Volume 1
Essential University Physics (3rd Edition)
- In 1898, the world land speed record was set by Gaston Chasseloup-Laubat driving a car named Jeantaud. His speed was 39.24 mph (62.78 km/h), much lower than the limit on our interstate highways today. Repeat the calculations of Example 2.7 (acceleration for first 6 miles, time of timed mile, acceleration for last 6 miles) for the Jeantaud car. Compare the results of the ThrustSSC to Jeantaud.arrow_forwardThe culling tool on a lathe is given two displacements, one of magnitude 4 cm and one of magnitude 3 cm, in each one of five situations (a) through (e) diagrammed in Figure OQ3.4. Rank these situations according to the magnitude of the total displacement of the tool, putting the situation with the greatest resultant magnitude first. If the total displacement is the same size in two situations, give those letters equal ranks.arrow_forwardTask VI: As a technical engineer in the army, you are part of a team in charge of testing and commissioning a new tank recently purchased by the artillery. 1010100 Field testing has revealed the following information: 1) The tank moves from rest to a speed of 70 km/hr in 10 seconds. 2) Using the breaking system, the tank is brought to a complete stop from a speed of 70 km/hr in 5 seconds. You are required to address all the questions below providing all calculations, graphs, and explanations as appropriate to back your answers.arrow_forward
- As a technical engineer in the army, you are part of a team in charge of testing and commissioning a new tank recently purchased by the artillery. Field testing has revealed the following information: 1) The tank moves from rest to a speed of 70 km/hr in 10 seconds. 2) Using the breaking system, the tank is brought to a complete stop from a speed of 70 km/hr in 5 seconds. You are required to address all the questions below providing all calculations, graphs, and explanations as appropriate to back your answers. First: Motion of the tank: a) Find the average driving acceleration of the tank. b) Calculate the average breaking acceleration of the tank. c) For parts (a) and b above parts report your answers in US Customary Units (mile/hr) so that the information could be shared with experts from the US.arrow_forwardtcos(angle) x-x0 1.4 28 1.8 36 2.1 42 2.2 45 2.15 44 1)plot a graph of x-x0 vs tcos(angle) 2)Find the value of the initial speed. Show your steps of calculation. Compare the value of initial speed obtained and the value used in the simulation.arrow_forwardReview I Constants I P A car has a mass of 1500 kg. If the driver applies the brakes while on a gravel road, the maximum friction force that the tires can provide without skidding is about 7000 N. Part A If the car is moving at 26 m/s, what is the shortest distance in which the car can stop safely? Express your answer to two significant figures and Include the approprlate units. HA Az = Value Units Submit Previous Answers Request Answer X Incorrect; Try Again; 2 attempts remaining Provide Feedback FEB 13 J O stvNarrow_forward
- Lisa takes her dog to the local dog park every morning. She walks with her dog 6 blocks north, 6 blocks west, and 6 blocks south in order to get to the park. What is her total distance traveled? Answer: blocks hparrow_forwardA physics student took a 4 hours car trip to visit a friend. In the first hour, he traveled 100 km at constant speed. In the two hours, he stopped after his car developed some trouble. In the last hour, he traveled 90 km.What was his average speed during a. first hour b. the last two hours c. the entire trip?arrow_forwardh The graph above shows the height h, in feet, of a ball t seconds after it was thrown from the top of a building. 40+ Which of the following must be true? 30+ A) The ball was thrown downward from a height of 20 feet. 10+ B) The ball was thrown upward from a height 20 feet. 0- C) The ball was thrown horizontally from a height of 20 feet. 1 3 D) The ball was thrown upward with a velocity of 20 feet per second. 20arrow_forward
- Elisha Graves Otis invented the elevator brake in the mid-1800s, making it possible to build tall skyscrapers with fast elevators. Todays skyscrapers are a large fraction of a mile tall; for example. Taipei 101 in Taiwan has 101 stories and is 515 m (0.32 miles) tall. The top speed of the elevator in the Taipei 101 tower is roughly three times greater than the ascent rate of a commercial jet airplane. The position and time data in the table are based on such an elevator. a. Working in SI units, make a position-versus-time graph for the elevator. (You may wish to use a spreadsheet program.) b. Describe the motion of the elevator in words. c. Find the highest speed of the elevator. When is the elevator going at this speed? d. What sort of considerations would the engineers need to make to ensure the comfort of the passengers?arrow_forwardTowns A and B in Figure P4.64 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/h. If the cars arrive simultaneously at the lake, what is the speed of car 2?arrow_forwardReview. The graph in Figure P7.20 specifies a functional relationship between the two variables u and v. (a) Find abudv. (b) Find baudv. (c) Find abvdu. Figure P7.20arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University