Question 1

What is the linear momentum, p, of an object?

Accepted Answer

Linear momentum (p) of an object is defined as the product of the object's mass (m) and its velocity (v), which is accurately represented by the equation p = mv.

Question 2

Suppose that an object has a certain speed, kinetic energy, and momentum. If the object's speed increases until it has 4 times the kinetic energy that it had before, then its momentum is

Accepted Answer

The kinetic energy (KE) of an object is given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity. If the kinetic energy becomes 4 times greater, it implies that $v^2$ has become 4 times greater (since mass $m$ is constant), meaning $v$ has become 2 times greater. Momentum ($p$) is given by $p = mv$. Therefore, if $v$ doubles, $p$ also doubles.

Question 3

Kepler's third law, as derived by Newton from the law of gravitation, applies

Accepted Answer

Kepler's third law, as generalized by Newton, applies to any two objects that orbit each other solely under the influence of their mutual gravitational attraction, not just to planets orbiting the Sun. This generalization is a consequence of Newton's law of universal gravitation, which extends the applicability of Kepler's laws beyond the specific cases for which they were originally formulated.

Question 4

An astronomer has a massive purple object in her laboratory. If she were to take it to the Moon, which of its characteristics would be guaranteed to change?

Accepted Answer

Weight would change due to the Moon's weaker gravitational pull compared to Earth's, affecting how much the object weighs.

Question 5

Which of these descriptions characterizes the Newtonian understanding of the mechanics of the solar system?

Accepted Answer

A) Newton's laws of motion and his law of universal gravitation imply that the natural motion of an object in the absence of a force is a straight line at constant velocity. The gravitational force of the Sun alters this straight-line motion, causing the planets to orbit the Sun.

Question 6

How are kinetic energy and potential energy related for a freely falling object?

Accepted Answer

For a freely falling object (ignoring air resistance), the sum of its kinetic energy (energy due to motion) and potential energy (energy due to position) remains constant. This is a demonstration of the conservation of mechanical energy principle.

Question 7

What is the angular momentum, L, of an object?

Accepted Answer

Angular momentum is defined as the product of an object's moment of inertia and its angular velocity, which is accurately represented by option C.

Question 8

For the angular momentum of an object to be conserved (i.e., to not change), the

Accepted Answer

Angular momentum is conserved in a system when there is no external torque acting on it. Internal forces, like those from a skater's muscles, do not affect the total angular momentum of a system, but external torques do. Changes in speed, size, or internal forces do not directly imply a change in angular momentum unless they result in an external torque.

Question 9

If a person travels from Earth to the Moon, which of these quantities will be unchanged?

Accepted Answer

The person's mass remains constant regardless of their location in space because mass is a measure of the amount of matter in an object and does not change with the object's position or the gravitational force acting upon it.

Question 10

In which order (from earliest to latest) did these people make their major contributions to astronomy?

Accepted Answer

Copernicus (1473–1543) proposed the heliocentric model. Brahe (1546–1601) made comprehensive astronomical observations. Kepler (1571–1630), who was an assistant to Brahe, formulated the laws of planetary motion. Newton (1642–1727) developed the law of universal gravitation.

Question 11

Two solid spheres of equal size and mass are joined by a spring-loaded, extendible rod. The whole unit is spinning like a baton (end-over-end) 5 times per second. Suddenly the rod stretches, pushing the spheres farther apart. What change takes place as a result of the stretching?

Accepted Answer

The angular momentum of the system (spheres and rod) is conserved. When the distance between the spheres increases due to the stretching of the rod, the moment of inertia of the system increases. To conserve angular momentum, the rate of spin (angular velocity) must decrease.

Question 12

The angular momentum of an object depends on which of these sets of factors?

Accepted Answer

The angular momentum of an object depends on its mass, the distribution of that mass (moment of inertia), and its angular velocity (how fast it is spinning). The local gravitational field does not directly affect an object's angular momentum.

Question 13

Suppose two asteroids are located at the same distance from the Sun. One asteroid has twice the mass of the other. According to Newton's law of gravitation (and ignoring all forces except that from the Sun),

Accepted Answer

According to Newton's law of gravitation, the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers: F = G * (m1 * m2) / r^2. If one asteroid has twice the mass of the other but both are at the same distance from the Sun, the more massive asteroid will feel twice the gravitational force because the force depends directly on the mass of the asteroid.

Question 14

A gravitational force is exerted by a large mass on a small mass a certain distance away. If the separation is increased to 3 times its original value and the large and small masses are then switched, what will happen to the gravitational force?

Accepted Answer

The gravitational force between two masses is inversely proportional to the square of the distance between them. If the distance is increased to 3 times its original value, the force decreases by a factor of 3^2, which is 9. Switching the masses does not affect the magnitude of the force.

Question 15

Was Newton's DERIVED version of Kepler's third law the same as the version Kepler discovered by trial and error?

Accepted Answer

Newton's version of Kepler's third law included the effect of the mass of the planets in addition to the mass of the sun, which was a significant advancement over Kepler's original formulation. Kepler's laws were empirical, based on observations, and did not account for the masses of the planets.

Question 16

If two massive bodies, initially held at rest in space, are released, then they will begin to

Accepted Answer

According to Newton's law of universal gravitation, any two bodies with mass will attract each other, causing them to move toward one another when released in space.

Question 17

If one uses a force of 100 N to push a packing crate through a distance of 5 m, then the amount of work he has done on the crate is

Accepted Answer

Work is calculated as the product of force and distance when the force is applied in the direction of motion. Here, work = 100 N * 5 m = 500 Joules.

Question 18

If an astronaut landed on a planet of the same radius as Earth but 4 times the mass, then the astronaut's weight on the planet would be

Accepted Answer

Weight is directly proportional to the mass of the planet. If the mass of the planet is 4 times that of Earth, the astronaut's weight would also increase by a factor of 4, assuming the radius of the planet is the same as Earth's.

Question 19

Which concept in Newton's mechanics provides an answer to the question: Why don't the planets fall into the Sun?

Accepted Answer

The concept of conservation of angular momentum explains why planets do not fall into the Sun. It states that an object will maintain its angular momentum unless acted upon by an external torque. In the case of planets orbiting the Sun, their angular momentum keeps them in orbit, preventing them from spiraling into the Sun.

Question 20

Compared with a person's mass on Earth, that person's mass out in space among the stars would be

Accepted Answer

A person's mass remains constant regardless of location, including in space, because mass is a measure of the amount of matter in an object, not dependent on gravity or location.

Quiz 2: Gravitation and the Motion of the Planets