Exam 5: Circular Motion

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The curved section of a speedway is a circular arc having a radius of 190 m.This curve is properly banked for racecars moving at 34 m/s.At what angle with the horizontal is the curved part of the speedway banked?

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A small 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m.The ball makes 2.0 revolutions every 1.0 s. (a)What are the magnitude and direction of the acceleration of the ball? (b)Find the tension force that the string exerts on the ball.

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In another solar system,a planet has a moon that is 4.0 × 105 m in diameter.Measurements reveal that this moon takes 3.0 x 105 s to make each orbit of diameter 1.8 × 108 m.What is the mass of the planet? (G = 6.67 × 10-11 N ∙ m2/kg2)

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You are the science officer on a visit to a distant solar system.Prior to landing on a planet you measure its diameter to be 1.8 × 107 m.You have previously determined that the planet orbits 2.9 × 1011 m from its star with a period of 402 earth days.Once on the surface you find that the free-fall acceleration is 19.5 m/s2.What are the masses of (a)the planet and (b)the star? (G = 6.67 × 10-11 N ∙ m2/kg2)

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A 20-g bead is attached to a light 120-cm-long string as shown in the figure.This bead moves in a horizontal circle with a constant speed of 1.5 m/s.What is the tension force that the string exerts on the bead if the angle α is measured to be 25°? A 20-g bead is attached to a light 120-cm-long string as shown in the figure.This bead moves in a horizontal circle with a constant speed of 1.5 m/s.What is the tension force that the string exerts on the bead if the angle α is measured to be 25°?

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A 250-kg motorcycle goes around an unbanked turn of radius 13.7 m at a steady 96.5 km/h.What is the magnitude of the sum of the forces exerted on the motorcycle?

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A spaceship is traveling to the Moon.At what point is there no more gravitational force exerted on it by Earth?

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From what height above the surface of the earth should an object be dropped to initially have an acceleration of 0.54g? (G = 6.67 × 10-11 N ∙ m2/kg2,Mearth = 5.97 × 1024 kg,Rearth = 6.38 × 106 m)

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Pulling out of a dive,the pilot of an airplane guides his plane into a vertical circle.At the bottom of the dive,the speed of the airplane is 320 m/s.What is the smallest radius allowable for the vertical circle if the pilot's apparent weight (the force that the pilot exerts on the seat)is not to exceed 7.0 times his true weight?

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A satellite having orbital speed V orbits a planet of mass M.If the planet had half as much mass,the orbital speed of the satellite at the same distance from the center would be

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If you stood on a planet having a mass four times that of Earth's mass,and a radius two times that of Earth's radius,the gravitational force that the planet exerts on you would be

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What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?

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Asteroid Ida was photographed by the Galileo spacecraft in 1993,and the photograph revealed that the asteroid has a small moon,which has been named Dactyl.From the dimensions of Ida and its general features,one can estimate the mass of Ida to be 4.5 × 1016 kg,and the distance between Dactyl and Ida is approximately 90 km.Assuming a circular orbit,what would be the orbital speed of Dactyl? (G = 6.67 × 10-11 N ∙ m2/kg2)

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You need to design a wheel for testing purposes such that its rim will have an acceleration of 1.5 g when the rim is moving at 37 m/s while spinning.What should be the diameter of this wheel?

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A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars.If gm is the free-fall acceleration at the surface of Mars,what is the free-fall acceleration at the location of the satellite?

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Two planets have the same free-fall acceleration on the surface,but planet B has twice the mass of planet A.If planet A has radius r,what is the radius of planet B?

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If a satellite moves with constant speed in a perfectly circular orbit around the earth,what is the direction of the acceleration of the satellite?

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Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of diameter 60 m.What are the magnitude and direction of her acceleration?

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You are driving at 30.0 m/s30.0 \mathrm {~m} / \mathrm { s } on a freeway curve of radius 25.0 m25.0 \mathrm {~m} What is the magnitude of your acceleration?

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Suppose NASA wants a satellite to revolve around Earth 5 times a day.What should be the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10-11 N ∙ m2/kg2,Mearth = 5.97 × 1024 kg)

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