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)
- A hockey puck struck by a hockey stick is given an initial speed v0 in the positive x-direction. The coefficient of kinetic friction between the ice and the puck is k. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of part (a) to obtain an expression for the distance d the puck slides. The answer should be in terms of the variables v0, k, and g only.arrow_forwardA basketball player dribbles the ball while running at a constant speed straight across the court. Think about the velocity and acceleration of the ball and then sketch a motion diagram for the ball. Explain how you arrived at your sketch.arrow_forwardIn this chapter, you've encountered a large number of concepts it related to forces and motion. Organizing a concept map might help clarify the meanings of many of these concepts for you. As a stall, you examine Concept Map 2.2 pertaining to the concept of "net force" created by a student who had previously taken an introductory physics course. Unfortunately, this student had some misconceptions about this topic, so there are some blatant errors in the concept map. Locate and correct as many of these errors as you can. (hint: Carefully inspect the linking words used to connect the concepts and consider the meanings of the "propositions" they make.)arrow_forward
- Review. A hockey puck struck by a hockey stick is given an initial speed i in the positive x direction. The coefficient of kinetic friction between the ice and the puck is k. (a) Obtain an expression for the acceleration of the puck as it slides across the ice. (b) Use the result of part (a) to obtain an expression for the distance d the puck slides. The answer should be in terms of the variables k and g only.arrow_forwardWhen you learn to drive, you discover that you need to let up slightly on the brake pedal as you come to a stop or the car will stop with a jerk. Explain this in terms of the relationship between static and kinetic friction.arrow_forwardConsider a child holding a helium balloon in a closed car at rest. What would the child observe the balloon to do when the car (a) accelerates from rest and (b) brakes to a stop? (The balloon does not touch the roof of the car.)arrow_forward
- A rocket-powered hockey puck moves on a horizontal frictionless table. The figure shows the graphs of vx and vy, the x- and y-components of the puck’s velocity. The puck starts at the origin. What is the magnitude of the puck’s acceleration at t = 5 s?arrow_forward1. Write Good if the statement is True else write Bad if the statement is false. a) Dynamics and Kinematics both study moving objects without considering the forces that acts on the body. b) In a projectile motion, motion should be treated independently where it is found that velocity along x is changing and velocity along y is constant. c) Static friction force is always greater than kinetic friction force.arrow_forward42. A block initially at rest slides down a ramp of length L that makes an angle of θ with the horizontal. (a) Derive an equation that predicts the time required for the block to reach the bottom of the ramp in terms of L, θ, g, and μ, the coefficient of friction. (b) This derived equation has no real solutions for angles θ ≤ tan–1 (μ). Show algebraically this is the case and explain the physical significance of this – i.e. what does this mean about an actual block on an actual ramp with actual friction?arrow_forward
- Equipment Access to the Internet Calculator App Introduction According to legend, Galileo Galilei dropped two balls of different mass from the top of the leaning tower of Pisa in 1589. Whether or not this public experiment ever took place, Galileo was able to demonstrate that, contrary to Aristotle’s teaching, all bodies fall at the same rate regardless of mass, assuming that one is not so tenuous that it is slowed by air resistance. In this experiment, an equation is presented relating the acceleration of gravity at Earth’s surface, g, to the height that an object falls from, h, and the time it takes the object to reach the ground, t. Gravity acceleration at Earth’s surface has been measured many times. In British Imperial Units, Small Metric Units, and Large Metric Units, the standard values of g are: g = 32 feet per second-squared (ft/s2) g = 980 centimeters per second-squared (cm/s2) g = 9.8 meters per second-squared (m/s2). Theory…arrow_forwardA hockey puck slides with an initial speed of 56.7 m/s on a large frozen lake. The coefficient of kinetic friction between the puck and the ice is 0.05. What is the acceleration on the hockey puck caused by friction? Assume the puck's velocity is in the positive-x direction. And what is the speed of the puck after 6 s?arrow_forwardQ4 / Leaving an object to fall from a height of (50 m) from the surface of the earth is calculated 1- The speed of an object when it reaches the surface of the earth 2- The time required for the object to reach the surface of the eartharrow_forward
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning