Exam 5: Circular Motion; Gravitation

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.

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the radius of the earth is $6.38 \times 10 ^ { 6 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$ 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?

If Earth had twice its present mass but it orbited at the same distance from the sun as it does now, its orbital period would be

The reason an astronaut in an earth satellite feels weightless is that

A highway curve of radius 80 m is banked at $45 ^ { \circ }$ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?

An astronaut drops a marble on the surface of the airless Planet Z-49 and observes that it takes 1.02 s for the marble to fall 2.00 m starting from rest. She also knows that the radius of Z-49 is 3.39 $\times 10 ^ { 6 } \mathrm {~m}$ From this information, what will she determine for the mass of Z-49? $\left( G = 6.67 \times 10 ^ { - 11 } N \right.$ $\left. m ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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 in the string if the angle θ is Measured to be 25°?

Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is $5.68 \times 10 ^ { 26 } \mathrm {~kg}$ and use an orbital radius of $1.00 \times 10 ^ { 5 } \mathrm {~km} \cdot \left( \mathrm { G } = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A satellite of mass M takes time T to orbit a planet. If the satellite had twice as much mass, the time for it to orbit the planet at the same altitude would be

If you swing a bucket of water fast enough in a vertical circle, at the highest point the water does not spill out. This happens because an outward force balances the pull of gravity on the water.

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?

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If gm is the acceleration due to gravity at the surface of Mars, what is the acceleration due to gravity at the Location of the satellite?

The mass of Pluto is $1.31 \times 10 ^ { 22 } \mathrm {~kg}$ and its radius is $1.15 \times 10 ^ { 6 } \mathrm {~m}$ What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

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?

Two small objects, with masses m and M, are originally a distance r apart, and the magnitude of the gravitational force on each one is F. The masses are changed to 2m and 2M, and the distance is Changed to 4r. What is the magnitude of the new gravitational force?

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 $2.00 \mathrm {~cm} / \mathrm { s } ^ { 2 }$ What is the mass of each of them? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is v . What is the safe speed on the larger-radius curve?

A highway curve of radius 100 m, banked at an angle of $45 ^ { \circ }$ may be negotiated without friction at a speed of

Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does. What would be the length of the year on the earth under those conditions?

An object weighs 432 N on the surface of the earth. The earth has radius R . If the object is raised to a height of 3 R above the earth's surface, what is its weight?