Exam 5: Dynamics of Uniform Circular Motion

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -What is the average velocity of the vehicle during one revolution?

Holly puts a box into the trunk of her car. Later, she drives around an unbanked curve that has a radius of 48 m. The speed of the car on the curve is 16 m/s, but the box remains stationary relative to the floor of the trunk. Determine the minimum coefficient of static friction for the box on the floor of the trunk.

The second hand on a watch has a length of 4.50 mm and makes one revolution in 60.00 s. What is the speed of the end of the second hand as it moves in uniform circular motion?

Approximately one billion years ago, the Moon orbited the Earth much closer than it does today. The radius of the orbit was only 24 400 km. The orbital period was only 23 400 s. Today, the average radius is 385 000 km; and the present period is 2.36 × 10⁶ s. Assuming that the orbit of the Moon is circular, calculate the ratio of the speed of the Moon in its ancient orbit to the speed that it has today.

A 1800-kg Jeep travels along a straight 500-m portion of highway (from A to B) at a constant speed of 10 m/s. At B, the Jeep encounters an unbanked curve of radius 50 m. The Jeep follows the road from B to C traveling at a constant speed of 10 m/s while the direction of the Jeep changes from east to south. -What is the magnitude of the acceleration of the Jeep as it travels from A to B?

Consider a satellite in a circular orbit around the Earth. If it were at an altitude equal to twice the radius of the Earth, 2R_E, how would its speed v relate to the Earth's radius R_E, and the magnitude g of the acceleration due to gravity on the Earth's surface?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Determine the magnitude of the net force that acts on the vehicle.

Which force is responsible for holding a car in a frictionless banked curve?

One of the world's largest Ferris wheels, the Cosmo Clock 21 with a radius of 50.0 m is located in Yokohama City, Japan. Each of the sixty gondolas on the wheel takes 1.00 minute to complete one revolution when it is running at full speed. Note: Ignore gravitational effects. -What is the centripetal acceleration of the gondola when the Ferris wheel is running at full speed?

A boy is whirling a stone around his head by means of a string. The string makes one complete revolution every second; and the magnitude of the tension in the string is F. The boy then speeds up the stone, keeping the radius of the circle unchanged, so that the string makes two complete revolutions every second. What happens to the tension in the sting?

A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. Complete the following statement: The centripetal acceleration of the ball can be increased by a factor of 4 by

The radius of the earth is 6.38 × 10⁶ m and its mass is 5.98 × 10²⁴ kg. What is the acceleration due to gravity at a height of 1.28 × 10⁷ m above the earth's surface?

A 2400-kg satellite is in a circular orbit around a planet. The satellite travels with a constant speed of 6670 m/s. The radius of the circular orbit is 8.92 x 10⁶m. -What is the acceleration of the satellite?

An artificial satellite in a circular orbit around the Sun has a period of 8 years. Determine the ratio of the satellite's orbital radius to that of the earth's orbital radius. Assume that the earth's orbit around the Sun is circular.

A 25-kg box is sliding down an ice-covered hill. When it reaches point A, the box is moving at 11 m/s. Point A is at the bottom of a circular arc that has a radius R = 7.5 m. What is the magnitude of the normal force on the box at Point A?

A space station is designed in the shape of a large, hollow donut that is uniformly rotating. The outer radius of the station is 350 m. With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e. an acceleration of 9.8 m/s²?

The radius of Saturn's orbit around the Sun is about 10 times that of Earth. Complete the following statement: The period of Saturn is about

An airplane flying at 115 m/s due east makes a gradual turn following a circular path to fly south. The turn takes 15 seconds to complete. -What is the magnitude of the centripetal acceleration during the turn?

Complete the following statement: The maximum speed at which a car can safely negotiate a frictionless banked curve depends on all of the following except