Chapter 6

How much time does the station take to complete one rotation?

20 s

The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s2?

0.41 R

A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be 18°, what is the speed of the mass?

1.1 m/s

In another solar system, a planet has an airless moon Zygo that is 4.0 × 105 m in diameter. Experiments reveal that a freely falling object at the surface of Zygo accelerates at 0.20 m/s2. What is the mass of Zygo? (G = 6.67 × 10-11 N • m2/kg2)

1.2 × 1020 kg

Europa, a satellite of Jupiter, has an orbital diameter of 1.34 × 109 m and a period of 3.55 days. What is the mass of Jupiter? (G = 6.67 × 10-11 N • m2/kg2)

1.89 × 1027 kg

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

1160 N

A spherically symmetric planet has four times the earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet?

12 N

In order to simulate weightlessness for astronauts in training, they are flown in a vertical circle. If the passengers are to experience weightlessness, how fast should an airplane be moving at the top of a vertical circle with a radius of 2.5 km?

160 m/s

A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked curve whose radius is 100 m. The coefficient of static friction between the tires and the road is 0.35. At what speed will the car begin to skid sideways?

19 m/s

Suppose one night the radius of the earth doubled but its mass stayed the same. What would be an approximate new value for the free-fall acceleration at the surface of the earth?

2.5m/s2

When a spacecraft is launched from the earth toward the sun, at what distance from the earth will the gravitational forces due to the sun and the earth cancel?Earth's mass is 5.97 × 1024 kg, the sun's mass is 1.99 × 1030 kg, and the Earth-sun distance is 1.5 × 1011 m.

2.6 × 108 m

The captain of a spaceship orbiting planet X discovers that to remain in orbit at 410 km from the planet's center, she needs to maintain a speed of 68 m/s. What is the mass of planet X? (G = 6.67× 10−11 N⋅m2/kg2)

2.8× 1019 kg

Suppose you and a friend, each of mass 65 kg , go to the park and get on a 4.5-m-diameter merry-go-round. You stand on the outside edge of the merry-go-round, while your friend pushes so that it rotates once every 5.0 seconds. What is the magnitude of the (apparent) outward force that you feel?

230 N

A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in a horizontal circular path on a frictionless tabletop. If the maximum tension that the string can withstand without breaking is 350 N. What is the maximum speed the mass can have without breaking the string?

26 m/s

A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

29.1°

What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

290 N

Mithra is an unknown planet that has two moons, A and B, in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the mass of Mithra? (G = 6.67 × 10-11 N • m2/kg2)

3 × 1023 kg

What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 1024 kg, the mass of the Moon is 7.35 × 1022 kg, the center-to-center distance between Earth and the Moon is 3.84 × 108 m, and G = 6.67 × 10-11 N • m2/kg2.

3.84 × 107 m

A highway curve of radius 100 m, banked at an angle of 45°, may be negotiated without friction at a speed of

31 m/s.

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?

32°

Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight of the 70-kg pilot at that point?

3300 N

The tension in the string is measured to be 10 N. What would the tension be if the ball went around in only half a second?

40 N

A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the road surface is the same in both cases?

40 m/s

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

51°

A satellite that is in a circular orbit 230 km above the surface of the planet Zeeman-474 has an orbital period of 89 min. The radius of Zeeman-474 is 6.38 × 106 m. What is the mass of this planet? (G = 6.67 × 10-11 N • m2/kg2)

6.0 × 1024 kg

At a given point above Earth's surface, the acceleration due to gravity is equal to 7.8 m/s2 What is the altitude of this point above Earth's surface? (G = 6.67× 10−11 N⋅m2/kg2, Mearth = 5.97× 1024 kg, Rearth = 6.38× 106 m)

770 km

A car moving at a steady 10 m/s on a level highway encounters a depression that has a circular cross-section with a radius of 30 m. The car maintains its speed as it drives through the depression. What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the bottom of the depression?

790 N

In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the passengers can have so they do not fall if the coefficient of static friction between the passengers and the wall is 0.25?

8.9 m/s

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is the radius of curvature of the circular part of the path in which the plane is flying?

9200 m

If the moon could be brought into a new circular orbit with a smaller radius, its orbital period would be

less than 27.3 days.