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Review. Consider a tall building located on the Earth’s equator. As the Earth rotates, a person on the top floor of the building moves faster than someone on the ground with respect to an inertial reference frame because the person on the ground is closer to the Earth’s axis. Consequently, if an object is dropped from the top floor to the ground a distance h below, it lands east of the point vertically below where it was dropped. (a) How far to the east will the object land? Express sour answer in terms of h, g, and the angular speed ω of the Earth. Ignore air resistance and assume the free-fall acceleration is constant over this range of heights. (b) Evaluate the eastward displacement for h = 50.0 m. (c) In your judgment, were we justified in ignoring this aspect of the Coriolis effect in our previous study of free fall? (d) Suppose the angular speed of the Earth were to decrease with constant
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Chapter 10 Solutions
Physics for Scientists and Engineers with Modern Physics
- Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .arrow_forwardWhich of the following is impossible for a car moving in a circular path? Assume that the car is never at rest. (a) The car has tangential acceleration but no centripetal acceleration. (b) The car has centripetal acceleration but no tangential acceleration. (c) The car has both centripetal acceleration and tangential acceleration.arrow_forwardConsider a tall building located on the Earth's equator. As the Earth rotates, a person on the top floor of the building moves faster than someone on the ground with respect to an inertial reference frame because the person on the ground is closer to the Earth's axis. Consequently, if an object is dropped from the top floor to the ground a distance h below, it lands east of the point vertically below where it was dropped. (a) How far to the east will the object land? Express your answer in terms of h, g, and the angular speed w of the Earth. Ignore air resistance and assume the free-fall acceleration is constant over this range of heights. Ax = (b) Evaluate the eastward displacement (in cm) for h = 44.0 m. cm (c) In your judgment, were we justified in ignoring this aspect of the Coriolis effect in our previous study of free fall? O Yes O No (d) Suppose the angular speed of the Earth were to decrease with constant angular acceleration due to tidal friction. Would the eastward…arrow_forward
- An Earth satellite moves in a circular orbit 892 km above Earth's surface with a period of 102.6 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite? (a) Number 1.02014e-3 Units (b) Number i 7.567 Units m/s^2arrow_forwardA skater with mass 66 kg is skating on a horizontal surface at a constant speed 4.2 m/s. There is a ramp ahead, and the skater has just enough speed to make it to the top of the ramp (meaning the speed at the top of the ramp is 0 m/s). What is the height of the ramp in the unit of meters? Use g = 10 m/s2 for the acceleration due to gravity.arrow_forwardA car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 236 m, and the car completes the turn in 35.0 s. 35.0° В (a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors î and î m/s? î + m/s? j (b) Determine the car's average speed. m/s (c) Determine its average acceleratiorr during the 35.0-s interval. m/s² î m/s² î +arrow_forward
- An astronaut is rotated in a horizontal centrifuge at a radius of 5.0 m. (a) What is the astronaut’s speed if the centripetal acceleration has a magnitude of 7.0g? (b) How many revolutions per minute are required to produce this acceleration? (c) What is the period of the motion?arrow_forwardThe average distance of the earth from the sun is about 1.5 x 108 km (Figure 1). Assume that the earth's orbit around the sun is circular and that the sun is at the origin of your coordinate system. (a) Estimate the speed of the earth as it moves in its orbit around the sun. Express your answer in miles per hour with the appropriate number of significant figures. (b) Estimate the angle between the position vector of the earth now and what it will be in 4 months. (c) Calculate the distance between these two positions.arrow_forwardDuring a portion of a vertical loop, an airplane flies in an arc of radius p = 581 m with a constant speed v = 372 km/h. When the airplane is at A, the angle made by v with the horizontal is B = 31°, and rada tracking gives r = 721 m and 8 = 36°. Calculate v,, ve, a,, and O for this instant. Answers: Im/s ve = Im/s Im/s? a, = rad/s?arrow_forward
- The radius of the earth’s orbit around the sun (assumed circular) is 1.50 x 108 km and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth in m/s? (b) What is the radial acceleration of the earth toward the sun in m/s2?arrow_forwardAn object moves in a horizontal circle at constant speed v (in units of m>s). It takes the object T seconds to complete one revolution. Derive an expression that gives the radial acceleration of the ball in terms of v and T, but not r. (a) If the speed doubles, by what factor must the period T change if arad is to remain unchanged? (b) If the radius doubles, by what factor must the period change to keep arad the same?arrow_forwardAn Earth satellite moves in a circular orbit 878 km above Earth's surface with a period of 102.3 min. What are (a) the speed and (b) the magnitude of the centripetal acceleration of the satellite?arrow_forward
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