03 Circular Motion Review

An object moves at constant speed in a circular path. Which of the following statements are true?

Select two answers.

• The velocity is changing.

• The velocity is constant.

• The magnitude of acceleration is constant.

• The magnitude of acceleration is changing.

Answer explanation

In uniform circular motion, the speed is constant, but the velocity is constantly changing because the direction is changing. Because the direction is changing, there is an acceleration. The magnitude of acceleration is constant; however, the acceleration is directed toward the center and perpendicular to the velocity. As a result, since the velocity is always changing, so is the direction of acceleration.

A 60 cm rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is 3 kg.

At the lowest point in its path, the tension in the rope is 50 N. What is the speed of the bucket?

• 1 m/s

• 2 m/s

• 3 m/s

• 4 m/s

Tags

NGSS.HS-PS2-1

A 60 cm rope is tied to the handle of a bucket which is then whirled in a vertical circle. The mass of the bucket is 3 kg.

What is the critical speed below which the rope would become slack when the bucket reaches the highest point in the circle?

• 0.6 m/s

• 1.8 m/s

• 2.4 m/s

• 4.8 m/s

Tags

NGSS.HS-PS2-4

An object moves at a constant speed in a circular path of radius r at a rate of 1 revolution per second. What is its acceleration?

• 0

• 2π²r

• 2π²r²

• 4π²r

Tags

NGSS.HS-PS2-1

If the distance between two point particles is doubled, then the gravitational force between them

• decreases by a factor of 4

• decreases by a factor of 2

• increases by a factor of 2

• increases by a factor of 4

Tags

NGSS.HS-PS2-4

At the surface of Earth, an object of mass m has weight w. If this object is transported to an altitude that is twice the radius of Earth, then at the new location,

• its mass is m and its weight is w/2

• its mass is m/2 and its weight is w/4

• its mass is m and its weight is w/4

• its mass is m and its weight is w/9

Answer explanation

Mass is an intrinsic property of an object and does not change with location. This eliminates (B). If an object's height above the surface of the Earth is equal to 2R_E, then its distance from the center of the Earth is 3R_E. Thus, the object's distance from the Earth's center increases by a factor of 3, so its weight decreases by a factor of 3² = 9.

Tags

NGSS.HS-PS2-4

A moon of mass m orbits a planet of mass 100m. Let the strength of the gravitational force exerted by the planet on the moon be denoted by F₁, and let the strength of the gravitational force exerted by the moon on the planet be F₂. Which of the following is true?

• F₁ = 100F₂

• F₁ = 10F₂

• F₁ = F₂

• F₂ = 10F₁

Answer explanation

The gravitational force that the Moon exerts on the planet is equal in magnitude to the gravitational force that the planet exerts on the Moon (Newton's Third Law).

Tags

NGSS.HS-PS2-4

The dwarf planet Pluto has 1/500 the mass and 1/15 the radius of Earth. What is the value of g (in m/s²) on the surface of Pluto?

Tags

NGSS.HS-PS2-4

A moon of Jupiter has an early circular orbit of radius R

and an orbit period of T. Which of the following expressions gives the mass of Jupiter?

Answer explanation

The gravitational pull by Jupiter provides the centripetal force on its moon:

Tags

NGSS.HS-ESS1-4

NGSS.HS-PS2-4

Two large bodies, Body A of mass m and Body B of mass 4m, are separated by a distance R. At what distance from Body A, along the line joining the bodies, would the gravitational force on an object be equal to zero? (Ignore the presence of any other bodies.)

Answer explanation

Let the object's distance from Body A be x; then its distance from Body B is R-x In order for the object to feel no net gravitational force, the gravitational pull by A must balance the gravitational pull by B.Therefore, if you let M denote the mass of the object, then

Tags

NGSS.HS-PS2-4