Unit 4 Remediation: Circular Motion and Gravitation

Answer explanation

The correct expression for the gravitational force between two masses is given by Newton's law of universal gravitation, which states that the force is proportional to the product of the masses and inversely proportional to the square of the distance between them: F = \frac{G m_1 m_2}{r^2}.

Tags

NGSS.HS-PS2-4

Which of the following best describes uniform circular motion?

• Motion in a straight line with constant speed and zero net force

• Motion in a circle with constant speed and a net centripetal force directed towards the center

• Motion in a circle with increasing speed and a net force tangential to the path

• Motion in a circle with decreasing speed and a net force opposite to the direction of motion

Answer explanation

Uniform circular motion involves moving in a circle at constant speed, requiring a net centripetal force directed towards the center to maintain that motion. Thus, the correct choice is motion in a circle with constant speed and a net centripetal force.

Answer explanation

The gravitational field strength formula is given by g = \frac{G M}{r^2}. This shows that g is inversely proportional to the square of the distance r from the mass M, confirming that the correct choice is g = \frac{G M}{r^2}.

Tags

NGSS.HS-PS2-4

Consider a planet moving in an elliptical orbit around the sun. Which of Kepler's Laws provides a quantitative description of the variation in the planet's orbital speed at different points along its path?

• First Law: The Law of Ellipses

• Second Law: The Law of Equal Areas

• Third Law: The Law of Harmonies

• Fourth Law: The Law of Universal Gravitation

Answer explanation

Kepler's Second Law, the Law of Equal Areas, states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This law quantitatively describes how a planet's speed varies in its elliptical orbit.

Tags

NGSS.HS-ESS1-4

A car is moving in a circular track of radius 50 m with a constant speed of 20 m/s. If the car's speed is doubled, what will be the new centripetal acceleration of the car?

• 16 m/s²

• 32 m/s²

• 40 m/s²

• 48 m/s²

Answer explanation

Centripetal acceleration (a) is given by the formula a = v²/r. Initially, v = 20 m/s, so a = (20)²/50 = 8 m/s². If speed is doubled to 40 m/s, a = (40)²/50 = 32 m/s². Thus, the new centripetal acceleration is 32 m/s².

Tags

NGSS.HS-PS2-1

Which of the following statements is true about gravitational field strength?

• It is a vector quantity and points towards the center of the mass creating the field.

• It is a scalar quantity and has no direction.

• It is a vector quantity and points away from the center of the mass creating the field.

• It is a scalar quantity and points towards the center of the mass creating the field.

Answer explanation

Gravitational field strength is a vector quantity, meaning it has both magnitude and direction. It always points towards the center of the mass creating the field, which is why the correct statement is that it points towards the center.

Tags

NGSS.HS-PS2-4

A satellite is in a stable orbit around Earth. If the radius of the orbit is doubled, by what factor does the gravitational force acting on the satellite change, and what is the new velocity of the satellite compared to its original velocity?

• The gravitational force is halved, and the velocity is reduced by a factor of √2.

• The gravitational force is quartered, and the velocity is reduced by a factor of 2.

• The gravitational force remains the same, and the velocity is unchanged.

• The gravitational force is quartered, and the velocity is reduced by a factor of √2.

Answer explanation

The gravitational force is given by F = G(m1*m2)/r^2. Doubling the radius (r) results in F being quartered (1/2^2). The orbital velocity v = √(GM/r) decreases by √2 when r is doubled.

Tags

NGSS.HS-ESS1-4

NGSS.HS-PS2-4

Using Kepler's Third Law, if the period of a planet's orbit around the Sun is 8 years, what would be the mean distance of its orbit in astronomical units (AU) from the Sun? Assume Earth has a mean distance of 1 AU.

• 8 AU

• 64 AU

• 4 AU

• 22.6 AU

Answer explanation

Using Kepler's Third Law, T^2 = a^3 / M, where T is the period in years, a is the semi-major axis in AU, and M is the mass of the star in solar masses. For a star with 2 solar masses, a^3 = 8^2 / 2 = 32, so a = 2.8 AU.

Tags

NGSS.HS-ESS1-4

A 5 kg object is moving in a vertical circle of radius 2 m with a speed of 3 m/s at the top of the circle. Calculate the centripetal force acting on the object.

• 15 N

• 22.5 N

• 30 N

• 45 N

Answer explanation

At the top of the circle, the gravitational force (mg = 5kg * 9.81m/s² = 49.05N) acts downward. The centripetal force needed (mv²/r = 5kg * (3m/s)² / 2m = 22.5N) is also downward. Net force = gravitational force - centripetal force = 49.05N - 22.5N = 15N.

Tags

NGSS.HS-PS2-1

Analyze why an object undergoing uniform circular motion is considered to be experiencing acceleration, despite maintaining a constant speed.

• Because its tangential speed is increasing.

• Because its velocity vector is continuously changing direction.

• Because its radial speed is decreasing.

• Because it is moving along a linear path.

Answer explanation

An object in uniform circular motion has a constant speed, but its velocity vector changes direction continuously. This change in direction indicates that the object is accelerating, as acceleration is defined as a change in velocity.

Tags

NGSS.HS-PS2-1