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8.

A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of her motion?

10.

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 in the string.

11.

A curved portion of highway has a radius of curvature of 65 m. As a highway engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s. (a) What banking angle should you specify for this curve? (b) At the proper banking angle, what normal force and what friction force does the highway exert on a 750-kg car going around the curve at the proper speed?

13.

Two identical tiny balls of highly compressed matter are 1.50 m apart. When released in an orbiting space station, they accelerate toward each other at 2.00 cm/s². What is the mass of each of them? (G= 6.67 10^-11 N m²/kg²)

22.

A 2.10-kg hammer is transported to the Moon. The radius of the Moon is 1.74 10⁶ m, its mass is 7.35 10²² kg, and G= 6.67 10^-11 N m²/kg². How much does the hammer weigh on Earth and on the Moon?

23.

A satellite orbits the Earth once every 6.0 hours in a circle. What are the magnitude and direction of the acceleration of the satellite? (G= 6.67 10^-11 N m²/kg², M_earth = 5.97 10²⁴ kg)

26.

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 10²⁴ kg, the radius of the earth is 6.38 10⁶ m, and G= 6.67 10^-11 N m²/kg². Assume a circular orbit. (a) What is the period of the International Space Station's orbit? (b) What is the speed of the International Space Station in its orbit?

27.

A satellite of mass 500 kg orbits the earth with a period of 6,000 s. The earth has a mass of 5.97 10²⁴kg, a radius of 6.38 10⁶ m, and G= 6.67 10^-11 N m²/kg². (a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the earth's surface.

28.

A large telescope of mass 8410 kg is in a circular orbit around the earth, making one revolution every 927 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (G= 6.67 10^-11 N m²/kg², M_earth = 6.0 10²⁴ kg)

29.

As you know, the earth has an orbital period of 1.0 year at an orbital radius of 1.0 AU (astronomical unit, the average distance between the earth and the sun). If a new "minor planet" were to be found in a circular orbit with radius 13 AU, what would be its orbital period?