College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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EXAMPLE 5.8 Hit the Ski Slopes GOAL Combine conservation of mechanical energy with the work-energy theorem involving friction on a A horizontal surface. h = 20.0 m y 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 The skier slides down the slope and onto a level surface, stopping after traveling a distance d from the encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.210. (a) Find the skier's bottom of the hill. 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 ve at the bottom. On the flat, rough surface, use the work-energy theorem with Wp = Wtric = -f,d, where f, is the nc 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 VB = V2gh = V2(9.80 m/s²)(20.0 m) = 19.8 m/s conservation of energy, insert the values vA = 0 and yB = 0, solve for ve and substitute values for g and ye as the skier moves from the top, point O, to the bottom, point ®. (B) Find the distance traveled on the horizontal, rough surface. Apply the work-energy theorem as the skier moves from ® to ©. Wnet = - fid = AKE = mve? - mvg? Substitute ve = 0 and -HAmgd = --mve? fk = Hyn = Hmg. Solve for d. (19.8 m/s)² 2(0.210)(9.8 m/s²) d = = 95.2 m LEARN MORE REMARKS Substituting the symbolic expression Ve = 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 lowers the skier's center of mass, making it easier to balance. In the crouching position there is less air resistance. O The acceleration of gravity g is increased by crouching. Crouching decreases the mass of the skier. Crouching decreases the skier's inertia.
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Transcribed Image Text:EXAMPLE 5.8 Hit the Ski Slopes GOAL Combine conservation of mechanical energy with the work-energy theorem involving friction on a A horizontal surface. h = 20.0 m y 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 The skier slides down the slope and onto a level surface, stopping after traveling a distance d from the encounters a horizontal surface where the coefficient of kinetic friction between skis and snow is 0.210. (a) Find the skier's bottom of the hill. 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 ve at the bottom. On the flat, rough surface, use the work-energy theorem with Wp = Wtric = -f,d, where f, is the nc 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 VB = V2gh = V2(9.80 m/s²)(20.0 m) = 19.8 m/s conservation of energy, insert the values vA = 0 and yB = 0, solve for ve and substitute values for g and ye as the skier moves from the top, point O, to the bottom, point ®. (B) Find the distance traveled on the horizontal, rough surface. Apply the work-energy theorem as the skier moves from ® to ©. Wnet = - fid = AKE = mve? - mvg? Substitute ve = 0 and -HAmgd = --mve? fk = Hyn = Hmg. Solve for d. (19.8 m/s)² 2(0.210)(9.8 m/s²) d = = 95.2 m LEARN MORE REMARKS Substituting the symbolic expression Ve = 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 lowers the skier's center of mass, making it easier to balance. In the crouching position there is less air resistance. O The acceleration of gravity g is increased by crouching. Crouching decreases the mass of the skier. Crouching decreases the skier's inertia.
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