Exam 5: Circular Motion; Gravitation

One way that future space stations may create artificial gravity is by rotating the station. Consider a cylindrical space station 380 m in diameter that is rotating about its longitudinal axis. Astronauts Walk on the inside surface of the space station. How long will it take for each rotation of the Cylinder if it is to provide "normal" gravity for the astronauts?

At a distance of 14,000 km from the center of Planet Z-99, the acceleration due to gravity is 32 $\mathrm { m } / \mathrm { s } ^ { 2 }$ What is the acceleration due to gravity at a point 28,000 km from the center of this planet?

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth. Compared to its weight on Earth, the weight of this debris is

Two cars go around a banked curve at the proper speed for the banking angle. One car has tires with excellent traction, while the other car has bald slippery tires. Which of these cars is more likely To slide on the pavement as it goes around the curve?

Europa, a satellite of Jupiter, has an orbital diameter of $1.34 \times 10 ^ { 9 } \mathrm {~m}$ and a period of 3.55 days. What is the mass of Jupiter? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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 is not to exceed 7.0 times his true weight?

The planet Jupiter is 7.78 × 1011 m from the sun. How long does it take for Jupiter to orbit once about the sun given that the distance from the earth to the sun is 1.50 × 1011 m?

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?

Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B?

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 $4.5 \times 10 ^ { 16 } \mathrm {~kg}$ , and the distance between Dactyl and Ida is approximately 90 \mathrm{~km} . Assuming a circular orbit, what would be the orbital speed of Dactyl? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A large telescope of mass 8410 \mathrm{~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? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg }^ 2 , M _ { \text {earth } } = 6.0 \times 10 ^ { 24 } \mathrm {~kg} \right)$

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?

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?

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 $1.8 \times 10 ^ { 7 } \mathrm {~m}$ You have previously determined that the planet orbits $2.9$ $\times 10 ^ { 11 }$ m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 19.5 \mathrm{~m} / \mathrm{s}^{2} . What are the masses of (a) the planet and (b) the star? $( G =$ $\left. 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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 net force on the motorcycle?

Halley's Comet is in a highly elliptical orbit around the sun. Therefore the orbital speed of Halley's Comet, while traveling around the sun,

If the earth were twice as far from the sun as it presently is, how long (in terms of the present year) would it take it to make one orbit around the sun?

Mass Radius Orbital radius Orbital period Moon A 4.0\times1 unknown 2.0\times1 4.0\times1 Moon B 1.5\times1 2.0\times1 3.0\times1 unknown Mithra is an unknown planet that has two airless moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. If you dropped a laser at the surface of Moon B, at what rate would it accelerate toward the ground? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , M _ { \text {earth } } = 5.97 \times \right.$ $\left. 10 ^ { 24 } \mathrm { kq } \right)$