EXAMPLE 5.8 Hit the Ski Slopes GOAL Combine conservation of mechanical energy with the work-energy theorem involving friction on a horizontal surface. Consider the following figure. h = 20.0 m х The skier slides down the slope and onto a level surface Customize and control Google Chrome. Update is distance d from the bottom of the hill. available. PROBLEM A skier starts from rest at the top of a frictionless incline of height 20.0 m, as in the figure. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.210. (a) Find the skier's speed at the bottom. (b) How far does the skier travel on the horizontal surface before coming to rest? Neglect air resistance. STRATEGY Going down the frictionless incline is physically no different than going down a frictionless slide and is handled the same way, using conservation of mechanical energy to find the speed v at the в bottom. On the flat, rough surface, use the work-energy theorem with W, =D nc -fd, where fis the W fric magnitude of the force of friction and d is the distance traveled on the horizontal surface before coming to rest. SOLUTION (A) Find the skier's speed at the bottom. Write down the equation for 2gh = V 2(9.80 m/s²)(20.0 m) = 19.8 m/s %3D conservation of energy, insert the values v O and yB = 0, solve for v B and substitute values for g and y, as the skier moves from the top, point O9, to the bottom, point ®. (B) Find the distance traveled on the horizontal, rough surface. mv? 글깨요 Apply the work-energy theorem as the W. net 2 - fd = AKE = -mv skier moves from B to ©. Substitute ve = 0 and -Hymgd = -mvg? 2 fk = Hkn = Hxmg. - fка = AKE = 2mvc net skier moves from B to © Substitute v, = 0 and 2 -Hymgd k = H = Hymg. Customize and control Google Chrome. Update is available. Solve for d. (19.8 m/s)2 2(0.210)(9.8 m/s²) d = = 95.2 m 249 LEARN MORE REMARKS Substituting the symbolic expression v, 2gh into the equation for the distance d shows that d is linearly proportional to h: Doubling the height doubles the distance traveled. QUESTION Give two reasons why skiers typically assume a crouching position when going down a slope. (Select all that apply.) O Crouching decreases the mass of the skier. Crouching lowers the skier's center of mass, making it easier to balance. Crouching decreases the skier's inertia. The acceleration of gravity g is increased by crouching. In the crouching position there is less air resistance. PRACTICE IT Use the worked example above to help you solve this problem. A skier starts from rest at the top of a frictionless incline of height 20.0 m, as shown in the figure. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.226. Neglect air resistance. (a) Find the skier's speed at the bottom. 19.79 m/s (b) How far does the skier travel on the horizontal surface before coming to rest? 88.50 EXERCISE HINTS: GETTING STARTED | I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. Find the horizontal distance the skier travels before coming to rest if the incline also has a coefficient of kinetic friction equal to 0.226. Assume that 0 = 20.0°. | 4 61.02 What is the initial energy of the skier? How much work is done as the skier slides down the incline? How much work is done as the skier slides to a stop on the horizontal surface? In other words, write expressions for these three amounts of energy, then relate them to each other. m Need Heln? Read It
EXAMPLE 5.8 Hit the Ski Slopes GOAL Combine conservation of mechanical energy with the work-energy theorem involving friction on a horizontal surface. Consider the following figure. h = 20.0 m х The skier slides down the slope and onto a level surface Customize and control Google Chrome. Update is distance d from the bottom of the hill. available. PROBLEM A skier starts from rest at the top of a frictionless incline of height 20.0 m, as in the figure. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.210. (a) Find the skier's speed at the bottom. (b) How far does the skier travel on the horizontal surface before coming to rest? Neglect air resistance. STRATEGY Going down the frictionless incline is physically no different than going down a frictionless slide and is handled the same way, using conservation of mechanical energy to find the speed v at the в bottom. On the flat, rough surface, use the work-energy theorem with W, =D nc -fd, where fis the W fric magnitude of the force of friction and d is the distance traveled on the horizontal surface before coming to rest. SOLUTION (A) Find the skier's speed at the bottom. Write down the equation for 2gh = V 2(9.80 m/s²)(20.0 m) = 19.8 m/s %3D conservation of energy, insert the values v O and yB = 0, solve for v B and substitute values for g and y, as the skier moves from the top, point O9, to the bottom, point ®. (B) Find the distance traveled on the horizontal, rough surface. mv? 글깨요 Apply the work-energy theorem as the W. net 2 - fd = AKE = -mv skier moves from B to ©. Substitute ve = 0 and -Hymgd = -mvg? 2 fk = Hkn = Hxmg. - fка = AKE = 2mvc net skier moves from B to © Substitute v, = 0 and 2 -Hymgd k = H = Hymg. Customize and control Google Chrome. Update is available. Solve for d. (19.8 m/s)2 2(0.210)(9.8 m/s²) d = = 95.2 m 249 LEARN MORE REMARKS Substituting the symbolic expression v, 2gh into the equation for the distance d shows that d is linearly proportional to h: Doubling the height doubles the distance traveled. QUESTION Give two reasons why skiers typically assume a crouching position when going down a slope. (Select all that apply.) O Crouching decreases the mass of the skier. Crouching lowers the skier's center of mass, making it easier to balance. Crouching decreases the skier's inertia. The acceleration of gravity g is increased by crouching. In the crouching position there is less air resistance. PRACTICE IT Use the worked example above to help you solve this problem. A skier starts from rest at the top of a frictionless incline of height 20.0 m, as shown in the figure. At the bottom of the incline, the skier encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.226. Neglect air resistance. (a) Find the skier's speed at the bottom. 19.79 m/s (b) How far does the skier travel on the horizontal surface before coming to rest? 88.50 EXERCISE HINTS: GETTING STARTED | I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. Find the horizontal distance the skier travels before coming to rest if the incline also has a coefficient of kinetic friction equal to 0.226. Assume that 0 = 20.0°. | 4 61.02 What is the initial energy of the skier? How much work is done as the skier slides down the incline? How much work is done as the skier slides to a stop on the horizontal surface? In other words, write expressions for these three amounts of energy, then relate them to each other. m Need Heln? Read It
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
100%
The answer is not 61.02 m or 60.94 m
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON