Explanation Given data: The value of the spring constant ( k ) = 5.0 × 10 4 N m . The mass of the car ( m ) = 1400 kg . The velocity of the car ( v ) = 25 m s . The radius of the circular dip on the road ( r ) = 600 m . Formula used: Formula to calculate the elastic potential energy as follows, U s = 1 2 k ( Δ x B ) 2 (1) Here, k is the spring constant, Δ x B is the spring compression at the maximum dip position of the car in circular dip vertically. Formula to calculate the kinetic energy as follows, E = 1 2 m v 2 (2) Here, m is the car mass, v is the velocity of the car. The net force producing the centripetal acceleration of uniform circular motion as given by, F = m a = m v 2 r (3) Here, r is the radius of the dip. Form the Hook’s law the force of the spring is proportional to the compression displacement of the spring at the end. Formula to calculate the compressed force of the spring using by using Hook’s law, F sp = k Δ x f (4) Here, Δ x f is the spring compression on the flat road. On the bumpy road: Refer to Figure 1, at the maximum dip point the potential angry and the kinetic energy of the car is equal. Equate the equations (1) and (2), 1 2 k ( Δ x B ) 2 = 1 2 m v 2 ( Δ x B ) 2 = m v 2 k Δ x B = m v 2 k (5) Substitute 1400 kg for m , 25 m s for v and 5.0 × 10 4 N m for k in equation (5), Δ x B = ( 1400 kg ) ( 25 m s ) 2 5.0 × 10 4 N m Rearrange the equation as, Δ x B = 875000 kg ⋅ m 2 s 2 5.0 × 10 4 N m = 17.5 kg ⋅ m 3 N ⋅ s 2 Substitute the unit kg ⋅ m s 2 for N in above equation, Δ x B = 17

College Physics: A Strategic Approach (4th Edition)

4th Edition

ISBN: 9780134609034

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 6, Problem 30P

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The comparison of the spring compression of the car when it is drive on a flat road and bumpy road.

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Chapter 6, Problem 29P

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Chapter 6 Solutions

College Physics: A Strategic Approach (4th Edition)

Ch. 6 - A cyclist goes around a level, circular track at...Ch. 6 - In uniform circular motion, which of the following...Ch. 6 - Prob. 3CQ Ch. 6 - Prob. 4CQ Ch. 6 - Large birds like pheasants often walk short...Ch. 6 - When you drive fast on the highway with muddy...Ch. 6 - A ball on a string moves in a vertical circle as...Ch. 6 - Give an everyday example of circular motion for...Ch. 6 - Give an everyday example of circular motion for...Ch. 6 - Prob. 10CQ

Ch. 6 - A car coasts at a constant speed over a circular...Ch. 6 - In Figure Q6.11, at the instant shown, is the...Ch. 6 - Riding in the back of a pickup truck can be very...Ch. 6 - Playground swings move through an arc of a circle....Ch. 6 - Variation in your apparent weight is desirable...Ch. 6 - Prob. 16CQ Ch. 6 - Why is it impossible for an astronaut inside an...Ch. 6 - If every object in the universe feels an...Ch. 6 - A mountain climbers weight is slightly less on the...Ch. 6 - Prob. 20CQ Ch. 6 - A ball on a string moves around a complete circle,...Ch. 6 - As seen from above, a car rounds the curved path...Ch. 6 - As we saw in the chapter, wings on race cars push...Ch. 6 - Prob. 24MCQ Ch. 6 - Prob. 25MCQ Ch. 6 - The cylindrical space station in Figure Q6.25, 200...Ch. 6 - The radius of Jupiter is 11 times that of earth,...Ch. 6 - A newly discovered planet has twice the mass and...Ch. 6 - Suppose one night the radius of the earth doubled...Ch. 6 - Currently, the moon goes around the earth once...Ch. 6 - Two planets orbit a star. You can ignore the...Ch. 6 - A 5.0-m-diameter merry-go-round is turning with a...Ch. 6 - Prob. 2P Ch. 6 - An old-fashioned LP record rotates at 3313rpm. a....Ch. 6 - A typical hard disk in a computer spins at 5400...Ch. 6 - Prob. 5P Ch. 6 - The horse on a carousel is 4.0 m from the central...Ch. 6 - The radius of the earths very nearly circular...Ch. 6 - Modern wind turbines are larger than they appear,...Ch. 6 - Prob. 9P Ch. 6 - Prob. 10P Ch. 6 - Prob. 11P Ch. 6 - A typical running track is an oval with...Ch. 6 - Figure P6.13 is a birds-eye view of particles on a...Ch. 6 - In short-track speed skating, the track has...Ch. 6 - Prob. 15P Ch. 6 - A cyclist is rounding a 20-m-radius curve at 12...Ch. 6 - A 1500 kg car drives around a flat 200-m-diameter...Ch. 6 - A fast pitch softball player does a windmill...Ch. 6 - Prob. 19P Ch. 6 - A wind turbine has 12,000 kg blades that are 38 m...Ch. 6 - Youre driving your pickup truck around a curve...Ch. 6 - Prob. 22P Ch. 6 - Gibbons, small Asian apes, move by brachiation,...Ch. 6 - The passengers in a roller coaster car feel 50%...Ch. 6 - Prob. 25P Ch. 6 - A roller coaster car is going over the top of a...Ch. 6 - As a roller coaster car crosses the top of a...Ch. 6 - Prob. 28P Ch. 6 - Prob. 29P Ch. 6 - Prob. 30P Ch. 6 - Prob. 31P Ch. 6 - A satellite orbiting the moon very near the...Ch. 6 - Spacecraft have been sent to Mars in recent years....Ch. 6 - The centers of a 10 kg lead ball and a 100 g lead...Ch. 6 - The gravitational force of a star on an orbiting...Ch. 6 - The free-fall acceleration at the surface of...Ch. 6 - What is the ratio of the suns gravitational force...Ch. 6 - Prob. 38P Ch. 6 - In recent years, astronomers have found planets...Ch. 6 - Prob. 40P Ch. 6 - a. What is the gravitational force of the sun on...Ch. 6 - What is the value of g on the surface of Saturn?...Ch. 6 - What is the free-fall acceleration at the surface...Ch. 6 - Prob. 44P Ch. 6 - Prob. 45P Ch. 6 - Prob. 46P Ch. 6 - Prob. 47P Ch. 6 - Planet X orbits the star Omega with a year that is...Ch. 6 - The International Space Station is in a...Ch. 6 - An earth satellite moves in a circular orbit at a...Ch. 6 - In recent years, scientists have discovered...Ch. 6 - In recent years, scientists have discovered...Ch. 6 - In recent years, scientists have discovered...Ch. 6 - How fast must a plane fly along the earths equator...Ch. 6 - Prob. 55GP Ch. 6 - A 75 kg man weighs himself at the north pole and...Ch. 6 - Prob. 57GP Ch. 6 - Prob. 58GP Ch. 6 - Prob. 60GP Ch. 6 - Prob. 61GP Ch. 6 - Prob. 62GP Ch. 6 - Prob. 63GP Ch. 6 - Prob. 64GP Ch. 6 - A 5.0 g coin is placed 15 cm from the center of a...Ch. 6 - In an old-fashioned amusement park ride,...Ch. 6 - The 0.20 kg puck on the frictionless, horizontal...Ch. 6 - While at the county fair, you decide to ride the...Ch. 6 - A car drives over the top of a hill that has a...Ch. 6 - The ultracentrifuge is an important tool for...Ch. 6 - A sensitive gravimeter at a mountain observatory...Ch. 6 - Prob. 72GP Ch. 6 - Planet Z is 10,000 km in diameter. The free-fall...Ch. 6 - How long will it take a rock dropped from 2.0 m...Ch. 6 - A 20 kg sphere is at the origin and a 10 kg sphere...Ch. 6 - a. At what height above the earth is the free-fall...Ch. 6 - Mars has a small moon, Phobos, that orbits with a...Ch. 6 - You are the science officer on a visit to a...Ch. 6 - Europa, a satellite of Jupiter, is believed to...Ch. 6 - The direction of the net force on the craft is A....Ch. 6 - Suppose a spacecraft orbits the moon in a very...Ch. 6 - How much time does it take for the spacecraft to...Ch. 6 - The material that comprises the side of the moon...

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