Question 1

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 magnitude of the acceleration of the vehicle?

Accepted Answer

The acceleration of an object moving in a circle at constant speed is given by the formula a = v^2 / r, where v is the speed and r is the radius. Substituting the given values, a = (22 m/s)^2 / 85 m = 5.7 m/s^2.

Question 2

A spaceship is in orbit around the earth at an altitude of 12 000 miles. Which one of the following statements best explains why the astronauts experience "weightlessness?"

Accepted Answer

The astronauts experience weightlessness because the spaceship is in free fall and its floor cannot press upwards on the astronauts. Essentially, the acceleration due to gravity that the astronauts experience is cancelled out by the acceleration of the spaceship's orbit around the Earth, resulting in the sensation of weightlessness.

Question 3

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing.

Note these arrows:

-At the instant shown in the drawing, which arrow shows the direction of the reaction force exerted on the planet by the rocket?

Accepted Answer

According to Newton's third law, for every action, there is an equal and opposite reaction. As the rocket exerts a force on the planet to keep it in circular motion, the planet exerts an equal and opposite reaction force on the rocket. This reaction force is always directed towards the planet and is perpendicular to the velocity of the rocket. Arrow 2 shows the direction of this reaction force.

Question 4

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 radius of the curve that the plane follows in making the turn?

Accepted Answer

The answer of An airplane flying at 115 m/s due...

Question 5

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m.
-Which statement is true concerning this vehicle?

Accepted Answer

The answer of A 1500-kg vehicle travels at a constant...

Question 6

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.

Accepted Answer

The net force acting on the vehicle is the centripetal force required to keep it moving in a circle, calculated using the formula F = mv²/r. Substituting the given values: F = (1500 kg)(22 m/s)² / 85 m = 8.5 × 10³ N.

Question 7

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?

Accepted Answer

The centripetal acceleration required for artificial gravity is given by a = ω²r, where ω is the angular velocity and r is the radius. Solving for ω gives ω = sqrt(a/r). The period T is related to ω by T = 2π/ω. Substituting the values, T = 2π/sqrt(9.8/350) ≈ 38 s.

Question 8

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?

Accepted Answer

The answer of An airplane flying at 115 m/s due...

Question 9

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?

Accepted Answer

The answer of A 25-kg box is sliding down an...

Question 10

The record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 10³ m/s for a 0.15-m long carbon rod. What was the period of rotation of the rod?

Accepted Answer

The answer of The record for the highest speed achieved...

Question 11

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing.

Note these arrows:

-Suppose that the radius of the circular path is r when the speed of the rocket is v and the acceleration of the rocket has magnitude a. If the radius and speed are increased to 2r and 2v respectively, what is the magnitude of the rocket's subsequent acceleration?

Accepted Answer

The answer of A rocket orbits a planet in a...

Question 12

A plane is traveling at 200 m/s following the arc of a vertical circle of radius R. At the top of its path, the passengers experience "weightlessness." To one significant figure, what is the value of R?

Accepted Answer

The answer of A plane is traveling at 200 m/s...

Question 13

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?

Accepted Answer

The average velocity of an object in circular motion over one complete revolution is zero because the displacement is zero (the object returns to its starting point).

Question 14

The radius of the earth is 6400 km. An incoming meteorite approaches the earth along the trajectory shown. The point C in the figure is 6400 km above the earth's surface. The point A is located at the earth's center. At point C, what acceleration would the meteorite experience due to the earth's gravity?

Accepted Answer

The acceleration due to gravity is inversely proportional to the square of the distance between the centers of the two objects. At point C, the distance between the meteorite and the center of the earth is 6400 + 6400 = 12,800 km. Therefore, the acceleration due to gravity at point C is (6400/12800)^2 times the acceleration due to gravity on the earth's surface, which is approximately 2.5 m/s^2. The direction of the acceleration is toward the center of the earth, which is point A. Therefore, the correct answer is B.

Question 15

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing.

Note these arrows:

-At the instant shown in the drawing, which arrow indicates the direction of the acceleration of the rocket?

Accepted Answer

The answer of A rocket orbits a planet in a...

Question 16

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle. The rope will break when the tension exceeds 450 N. What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?

Accepted Answer

At the bottom of the circle, the tension is maximum and is the sum of the gravitational force and the centripetal force. Using the formula T = mg + mv^2/r, where T is the tension, m is the mass, g is the acceleration due to gravity (9.8 m/s²), v is the velocity, and r is the radius, we solve for v: 450 = 0.75*9.8 + 0.75*v^2/1. Solving gives v ≈ 24 m/s.

Question 17

A small car of mass M travels along a straight, horizontal track. As suggested in the figure, the track then bends into a vertical circle of radius R. 
-What is the minimum acceleration that the car must have at the top of the track if it is to remain in contact with the track?

Accepted Answer

For the car to remain in contact with the track, the normal force on the car must be non-zero at the top of the track. This means that the gravitational force must be balanced by a centrifugal force. At the top of the track, the car is moving in a circular path of radius R with a velocity of v=√(2gR), where g is the acceleration due to gravity. Therefore, the minimum acceleration that the car must have at the top of the track is given by a=v^2/R=2g, which is downward. So, the correct answer is C) 9.8 m/s^2, downward.

Question 18

Jupiter has a mass that is roughly 320 times that of the Earth and a radius equal to 11 times that of the Earth. What is the acceleration due to gravity on the surface of Jupiter?

Accepted Answer

The acceleration due to gravity on a planet's surface is given by the formula g = G * M / R^2. For Jupiter, the mass is 320 times that of Earth and the radius is 11 times that of Earth. Therefore, the acceleration due to gravity on Jupiter is approximately 26 m/s².

Question 19

A small car of mass M travels along a straight, horizontal track. As suggested in the figure, the track then bends into a vertical circle of radius R. 
-Which one of the following expressions determines the minimum speed that the car must have at the top of the track if it is to remain in contact with the track?

Accepted Answer

At the top of the track, the centripetal force required to keep the car in contact with the track is provided by the gravitational force. Thus, mv²/R = mg, leading to v² = gR.

Quiz 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 magnitude of the acceleration of the vehicle?

A spaceship is in orbit around the earth at an altitude of 12 000 miles. Which one of the following statements best explains why the astronauts experience "weightlessness?"

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -At the instant shown in the drawing, which arrow shows the direction of the reaction force exerted on the planet by the rocket?

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 radius of the curve that the plane follows in making the turn?

A 1500-kg vehicle travels at a constant speed of 22 m/s around a circular track that has a radius of 85 m. -Which statement is true concerning this vehicle?

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.

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?

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?

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?

The record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 103 m/s for a 0.15-m long carbon rod. What was the period of rotation of the rod?

A plane is traveling at 200 m/s following the arc of a vertical circle of radius R. At the top of its path, the passengers experience "weightlessness." To one significant figure, what is the value of R?

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?

A rocket orbits a planet in a circular orbit at a constant speed as shown in the drawing. Note these arrows: -At the instant shown in the drawing, which arrow indicates the direction of the acceleration of the rocket?

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle. The rope will break when the tension exceeds 450 N. What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?

A small car of mass M travels along a straight, horizontal track. As suggested in the figure, the track then bends into a vertical circle of radius R. -What is the minimum acceleration that the car must have at the top of the track if it is to remain in contact with the track?

Jupiter has a mass that is roughly 320 times that of the Earth and a radius equal to 11 times that of the Earth. What is the acceleration due to gravity on the surface of Jupiter?

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 record for the highest speed achieved in a laboratory for a uniformly rotating object was 2.01 × 10³ m/s for a 0.15-m long carbon rod. What was the period of rotation of the rod?